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Agrawal, Manish, and C. S. Jog. "A quadratic time finite element method for nonlinear elastodynamics within the context of hybrid finite elements." Applied Mathematics and Computation 305 (July 2017): 203–20. http://dx.doi.org/10.1016/j.amc.2017.01.059.
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Tang, Qiong, Luohua Liu, and Yujun Zheng. "Continuous Finite Element Methods of Molecular Dynamics Simulations." Modelling and Simulation in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/904140.
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Molecular dynamics simulations are necessary to perform very long integration times. In this paper, we discuss continuous finite element methods for molecular dynamics simulation problems. Our numerical results aboutABdiatomic molecular system andA2Btriatomic molecules show that linear finite element and quadratic finite element methods can better preserve the motion characteristics of molecular dynamics, that is, properties of energy conservation and long-term stability. So finite element method is also a reliable method to simulate long-time classical trajectory of molecular systems.
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Mahesh, S., Schiffel Marco, Ramesh S. Sharma, MK Praveenkumar, Vishal Wadagavi, and Lakshminarasimhan Subbarao. "A machine learning approach to predict the stress results of quadratic tetrahedral elements." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 2 (December 7, 2021): 1128–35. http://dx.doi.org/10.1177/09544062211010828.
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Industries are always looking for an effective and efficient way to reduce the computation time of simulation because of the huge expenditure involved. From basics of Finite Element Method (FEM), it is known that, linear order finite elements consume less computation time and are less accurate compared to higher order finite elements say quadratic elements. An approach to get the benefit of less computation cost of linear elements and the good accuracy of quadratic elements can be of a good thought. The methodology to get the accurate results of quadratic elements with the advantage of less simulation run time of linear elements is presented here. Machine Learning (ML) algorithms are found to be effective in making predictions based on some known data set. The present paper discusses a methodology to implement ML model to predict the results equivalent to that of quadratic elements based on the solutions obtained from the linear elements. Here, a ML model is developed using python code, the stress results from Finite Element (FE) model of linear tetrahedral elements is given as the input to it to predict the stress results of quadratic tetrahedral elements. Abaqus is used as the FEM tool to develop the FE models. A python script is used to extract the stresses and the corresponding node numbers. The results showed that the developed ML model is successful in prediction of the accurate stress results for the set of test data. The scatter plots showed that the Z-score method was effective in removing the singularities. The proposed methodology is effective to reduce the computation time for simulation.
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Harari, Isaac, and Danny Avraham. "High-Order Finite Element Methods for Acoustic Problems." Journal of Computational Acoustics 05, no. 01 (March 1997): 33–51. http://dx.doi.org/10.1142/s0218396x97000046.
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The goal of this work is to design and analyze quadratic finite elements for problems of time-harmonic acoustics, and to compare the computational efficiency of quadratic elements to that of lower-order elements. Non-reflecting boundary conditions yield an equivalent problem in a bounded region which is suitable for domain-based computation of solutions to exterior problems. Galerkin/least-squares technology is utilized to develop robust methods in which stability properties are enhanced while maintaining higher-order accuracy. The design of Galerkin/least-squares methods depends on the order of interpolation employed, and in this case quadratic elements are designed to yield dispersion-free solutions to model problems. The accuracy of Galerkin/least-squares and traditional Galerkin elements is compared, as well as the accuracy of quadratic versus standard linear interpolation, incorporating the effects of representing the radiation condition in exterior problems. The efficiency of the various methods is measured in terms of the cost of computation, rather than resolution requirements. In this manner, clear guidelines for selecting the order of interpolation are derived. Numerical testing validates the superior performance of the proposed methods. This work is a first step to gaining a thorough analytical understanding of the performance of p refinement as a basis for the development of h-p finite element methods for large-scale computation of solutions to acoustic problems.
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Akpobi, John A., and E. D. Akpobi. "Development of a Model for Analysing Radial Flow of Slightly Compressible Fluids." Advanced Materials Research 62-64 (February 2009): 629–36. http://dx.doi.org/10.4028/www.scientific.net/amr.62-64.629.
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In this work, we develop a finite element-finite difference method to solve the differential equation governing the radial flow of slightly compressible fluids. The finite element method is used to carry out spatial approximations so as to study the variation of fluid properties at the various nodes to which effect we divided the entire radial domain of the fluid into a mesh of four radial 1-D quadratic elements which exposes nine nodes to intense study. Time approximation is done with the aid of the Crank-Nicolson finite difference scheme.
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Purba, Baby, Roesyanto Roesyanto, Gina Cyntia Raphita, and Rudianto Surbakti. "Analisis Konsolidasi dengan Metode Preloading dikombinasikan dengan PVD berdasarkan Perhitungan Analitis dan Plaxis 2d." Jurnal Syntax Admiration 3, no. 12 (December 27, 2022): 1569–85. http://dx.doi.org/10.46799/jsa.v3i12.518.
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Soft soil has poor soil characteristics. These soils generally have high compressibility, low permeability and low carrying capacity. Soil improvement by preloading and PVD is one of the common soil improvement methods to speed up the process of soil consolidation. The initial loading is carried out with the aim of consolidating the soft soil layer with the same or more loading amount than the load that will be carried by the soil both during and after construction. While vertical drainage can speed up the consolidation process. This analysis aims to determine the magnitude of consolidation settlement using analytical methods and finite element methods with PLAXIS 2D modeling, the effect of modeling using quadratic triangle elements (6 nodal points) and quartic triangle elements (15 nodal points) on the consolidation magnitude and calculation processing time. The method used in this thesis is the analytical method using Terzaghi's theory and the finite element method using PLAXIS 2D. From the results of the analysis it was found that the use of a quadratic triangle element with 6 nodal points and 15 nodal points did not have a significant effect on the reduction results, but had a large effect on the length of the calculation process. After analyzing using 2D modeling using a quadratic triangle element with 6 nodal points and a quartic triangle element with 15 nodal points, a decrease of -6.673 meters for 6 nodal points and -6.669 meters for 15 nodal points is obtained. There was no significant difference between the two methods, which was only 4 mm different. The time needed to calculate with 6 nodes is about 1 hour and 15 nodes is about 4 hours.
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Bentahar, Mohammed. "Fatigue Analysis of an Inclined Crack Propagation Problem by the X-FEM Method." International Journal of Applied and Structural Mechanics, no. 34 (June 30, 2023): 23–31. http://dx.doi.org/10.55529/ijasm.34.23.31.
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The extended finite element method (X-FEM) has been used to solve fracture mechanics, problems in materials with various behavior laws (for example, isotropic, orthotropic or piezoelectric materials... For each type of material, it is necessary to obtain “enrichment functions” which model the behavior of the fields of displacement and stresses in the vicinity of the front of crack. In this paper, fatigue crack propagation analysis was modeled, by the extended finite element method X-FEM to evaluate the total energy and strain energy at the angled crack length, and to have the development of the increment time concerning the different values of α which is equal to 15°, 30° and 45, this development has been studied numerically by solving the problem of finite elements by the computer code ABAQUS. Quadratic 4-node elements (CPS4R) were used.
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SINGH, CHANDAN, and EKTA WALIA. "FAST HYBRID SHADING: AN APPLICATION OF FINITE ELEMENT METHODS IN 3D RENDERING." International Journal of Image and Graphics 05, no. 04 (October 2005): 789–810. http://dx.doi.org/10.1142/s0219467805002002.
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This paper is an attempt to improve the quality of Gouraud shading with minimum increase in the computation requirements. It presents algorithms for intermediate quality shading i.e. the quality of shading is better than Gouraud shading and nearly comparable to the quality of bi-quadratic Phong shading, at the same time, algorithms are very fast as compared to bi-quadratic Phong shading. Three algorithms are discussed. The first algorithm uses hybrid shading in which bi-quadratic interpolation of intensity is performed on the edges of a triangle and linear interpolation of intensity is performed on the scan line. Hybrid shading, in which bi-quadratic interpolation of normals is performed on the edges and linear interpolation of intensity is performed on the scan line, has been proposed in the second algorithm. In the third algorithm, bi-cubic interpolation of intensity is performed on the edges and linear interpolation of intensity is performed on the scan line. The paper also presents an incremental method for fast calculation of area coordinates and shape functions enhancing the speed of the algorithms.
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Tang, Y., and Y. Hua. "Superconvergence of Fully Discrete Finite Elements for Parabolic Control Problems with Integral Constraints." East Asian Journal on Applied Mathematics 3, no. 2 (May 2013): 138–53. http://dx.doi.org/10.4208/eajam.240313.280513a.
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AbstractA quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical examples are performed to confirm theoretical results.
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Pineda, E., M. H. Aliabadi, and Janis Zapata. "The Boundary Element Method Applied to Visco-Plastic Analysis." Key Engineering Materials 449 (September 2010): 37–45. http://dx.doi.org/10.4028/www.scientific.net/kem.449.37.
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This paper presents a new formulation of the Dual Boundary Element Method to visco-plastic problems in a two-dimensional analysis. Visco-plastic stresses and strains around the crack tip are obtained until the visco-plastic strain rate reaches the steady state condition. A perfect visco-plastic analysis is also carried out in linear strain hardening (H’=0) materials. Part of the domain, the part that is susceptible to yield is discretized into quadratic, quadrilateral continuous cells. The loads are used to demonstrate time effects in the analysis carried out. Numerical results are compared with solution obtained from the Finite Element Method (FEM).
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GHADIMI, PARVIZ, MOHAMMAD HADI JABBARI, and ARSHAM REISINEZHAD. "FINITE ELEMENT MODELING OF ONE-DIMENSIONAL BOUSSINESQ EQUATIONS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 02 (June 2011): 207–35. http://dx.doi.org/10.1142/s1793962311000414.
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Finite element modeling of one-dimensional Beji and Nadaoka Boussinesq equation is presented. The continuous equations are spatially discretized using standard Galerkin method. Since the extended Boussinesq equations contain high-order derivatives, two different numerical techniques are proposed in this paper in order to simplify the discretization task of the third-order terms. In the first technique, an auxiliary equation is introduced to eliminate the third-order derivatives of the momentum equation while non-overlapping elements with linear interpolating functions are employed to account for the dependent variables. However, in the second method, overlapping elements with quadratic interpolating functions are applied for discretizing the governing equations. Time integration is performed using the Adams–Bashforth–Moulton predictor–corrector method. By considering the truncation error and theoretical analysis for both of the numerical techniques, accuracy and stability of the adopted finite element schemes have been studied. Finally, a computer code is developed based on the proposed schemes. To show the validity as well as the practicality of the developed code, five different test cases are presented, and the results are compared with some analytical solutions and experimental data. Favorable agreements have been achieved in all cases.
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Sundararaman, KA, KP Padmanaban, M. Sabareeswaran, and S. Guharaja. "An integrated finite element method, response surface methodology, and evolutionary techniques for modeling and optimization of machining fixture layout for 3D hollow workpiece geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 23 (August 31, 2016): 4344–59. http://dx.doi.org/10.1177/0954406216668208.
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Machining fixtures play inevitable role in manufacturing to ensure the machining accuracy and workpiece quality. The layout of fixture elements, clamping forces, and machining forces significantly affect the workpiece elastic deformation during machining. The clamping and machining forces are necessary to immobilize and machine the workpiece, respectively. Finding the appropriate layout of fixture elements is the other possible way to reduce the workpiece deformation, which in turn improves the machining accuracy. The finite element method interfaced with evolutionary techniques is normally used for fixture layout optimization. In the finite element method, the workpiece is discretized into a number of small elements and fixture elements are placed only on the nodes. Hence, evolutionary techniques are capable of searching the optimal fixture layout from those discrete nodal points than from the entire area on the locating and clamping face. To overcome these limitations, in this research paper, response surface methodology is employed to establish a quadratic model between the position of fixture elements and maximum workpiece deformation. This enables the optimization techniques to search for the optimal solution in the continuous domain of the solution space. Then, the real-coded genetic algorithm based discrete optimization, continuous optimization based on binary-coded genetic algorithm and particle swarm optimization are employed to optimize the developed quadratic model and their performances are compared. The result clearly shows that the integration of finite element method, response surface methodology with particle swarm optimization is better than the integration with genetic algorithm to optimize the machining fixture layout and also reduces the computational complexity and time to a greater extent.
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Zhu, Bao, Hongwei Yang, and Jiefu Chen. "A novel finite element time domain method for nonlinear Maxwell's equations based on the parametric quadratic programming method." Microwave and Optical Technology Letters 57, no. 7 (April 27, 2015): 1640–45. http://dx.doi.org/10.1002/mop.29170.
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Shang Hsu, Yang, and Igor Alexandre Deitos. "Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 18 (April 8, 2020): 3629–49. http://dx.doi.org/10.1177/0954406220916487.
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This work contributes to the generalized finite element approach in free vibration, dynamic elastic, and elastoplastic analysis of plane frame subjected to random excitation generated by the wind action. The wind velocity is modeled mathematically by using power spectral density method in combination with Shinozuka’s model, along with the commonly employed wind spectra. From these spectra, the dynamic wind loading is determined from the sum of the mean and floating wind velocities. The governing equation is formulated by Euler–Bernoulli beam theory, and it is discretized by using the enriched beam element. The enrichment is done by employing enriched finite element shape function to construct the enriched mathematical space. This strategy is constituted by the enrichment space, which is constructed by trigonometric functions, and the conventional space, which is constructed by conventional two-node Lagrange–Hermite shape function. The time increment procedure is carried out by Hilber-Hughes-Taylor algorithm and the material nonlinearity is modeled by von Mises isotropic hardening model, solved by the Newton–Raphson algorithm. A flowchart is presented to summarize the proposed numerical modeling procedure. Finally, several applications are presented, and the results obtained by the generalized finite element method are compared with those obtained by conventional beam element. Natural frequencies are determined in a one-story plane frame and are compared with reference results. The relative error in displacement is determined in h-refine strategy for quadratic beam element (FEM3), while the generalized finite element method adopts the enrichment increment strategy. The results demonstrate the competitiveness and numerical stability of generalized finite element method in this type of application. Even in comparison to the quadratic beam element, the generalized finite element method presents good performance and accuracy in numerical modeling.
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Cui, Li Kun, Wei Wang, and Zhuo Li. "Computing Method and Circuit Realization of Neural Network on Finite Element Analysis." Applied Mechanics and Materials 195-196 (August 2012): 758–63. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.758.
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The finite element analysis in theory of elasticity is corresponded to the quadratic programming with equality constraint, which can be further transformed into the unconstrained optimization. In the paper, the question is solved by modified Hopfield neural network based on the energy function of the neural network equals to the objective function of the finite element method and the minimum point, which is the stable equilibrium point of the network system, is the solution. In addition the authors present the computer simulation and analogue circuit experiment to verify this method. The results are revealed that: 1) The results of improved Hopfield neural network are reliable and accuracy; 2) The improved Hopfield neural network model has an advantage on circuit realization and the computing time, which is unrelated with complexity of the structure, is constant. It is practical significance for the research and calculation.
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Nguyen, Nghia-Danh, and Shyh-Chour Huang. "Trawl Grid Structure Design and Analysis Using the Finite Element Method." Applied Sciences 13, no. 13 (June 26, 2023): 7536. http://dx.doi.org/10.3390/app13137536.
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The structure of fishnet knots has been simplified in previous studies to facilitate the construction of numerical equations of the fishnet structure. This leads to errors in the dynamic analysis of the trawl mesh structure with water flow. In this study, the finite element method was used to analyze the interaction of the trawl mesh structure with the solid object in a dynamic explicit environment. At the same time, design variables were optimized through impact assessment and the displacement of grid cells. The results show that the polyamide (PA) material, a 0.4 mm cross-section, and a 25 mm mesh size are the optimal choices. When the displacement speed of the solid body increased, the displacement and collision values of the mesh structure tended to increase gradually along the quadratic curve. Confirmation tests performed on the tensile tester machine showed a good load-carrying capacity of up to 1280 MPa for trawl mesh structures using the PA material. The characteristic curve for the stress of the trawl mesh structure is shown through the higher-order curve.
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Bernat, J., S. Stępień, A. Stranz, G. Szymański, and J. K. Sykulski. "Infinite time horizon optimal current control of a stepper motor exploiting a finite element model." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 4 (December 1, 2014): 835–41. http://dx.doi.org/10.2478/bpasts-2014-0092.
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Abstract An optimal control theory based method is presented aiming at minimizing the energy delivered from source and the power loss in a stepper motor circuit. A linear quadratic current regulator with an infinite time horizon is employed and its appropriateness for this type of a problem explained. With the purpose of improving the accuracy of the control system, the self and mutual inductances of windings are calculated using a finite element model. The numerically computed results are verified experimentally.
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Pineda, E., and M. H. Aliabadi. "Dual Boundary Element Analysis for Time-Dependent Fracture Problems in Creeping Materials." Key Engineering Materials 383 (June 2008): 109–21. http://dx.doi.org/10.4028/www.scientific.net/kem.383.109.
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This paper presents the development of a new boundary element formulation for analysis of fracture problems in creeping materials. For the creep crack analysis the Dual Boundary Element Method (DBEM), which contains two independent integral equations, was formulated. The implementation of creep strain in the formulation is achieved through domain integrals in both boundary integral equations. The domain, where the creep phenomena takes place, is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with secondary creep behaviour. This is con ned to standard power law creep equations. Constant applied loads are used to demonstrate time e¤ects. Numerical results are compared with solutions obtained from the Finite Element Method (FEM) and others reported in the literature.
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Fazio, P., K. Gowri, and K. H. Ha. "Rectangular hybrid elements for the analysis of sandwich plate structures." Canadian Journal of Civil Engineering 14, no. 4 (August 1, 1987): 455–60. http://dx.doi.org/10.1139/l87-069.
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The structural behaviour of sandwich plate structures are characterized by transverse shear deformations in the core. The assumed stress hybrid finite element technique is particularly suitable for developing sandwich plate bending elements. In the present study, rectangular three-layer sandwich plate elements have been formulated using simple assumed stress functions. Numerical test problems have been solved to examine the convergence property and suitability of these elements. The results are compared with that of a complete quadratic stress mode element and with analytical solutions. Six degrees of freedom per node shell elements are formulated by combining the plate bending elements with membrane elements. A folded plate sandwich panel roof has been analyzed using these elements and the results are compared with the experimental values. The use of simple stress function gives satisfactory results and reduces the size of the matrices to be used, the length of the program, and the computation time for the formulation of element stiffness matrices. Key words: sandwich panel, structural analysis, finite element method, stress hybrid approach, folded plates.
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Bernat, Jakub, Slawomir Jan Stepien, Artur Stranz, and Paulina Superczynska. "Infinite-time linear–quadratic optimal control of the BLDC motor exploiting a nonlinear finite element model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 3 (May 2, 2017): 633–48. http://dx.doi.org/10.1108/compel-09-2016-0419.
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Purpose This paper aims to present a nonlinear finite element model (FEM) of the Brushless DC (BLDC) motor and the application of the optimal linear–quadratic control-based method to determine the excitation voltage and current waveform considering the minimization of the energy injected to the input circuit and energy lost. The control problem is designed and analyzed using the feedback gain strategy for the infinite time horizon problem. Design/methodology/approach The method exploits the distributed parameters, nonlinear FEM of the device. First, dynamic equations of the BLDC motor are transformed into a suitable form that makes an ARE (algebraic Riccati equation)-based control technique applicable. Moreover, in the controller design, a Bryson scaling method is used to obtain desirable properties of the closed-loop system. The numerical techniques for solving ARE with the gradient damping factor are proposed and described. Results for applied control strategy are obtained by simulations and compared with measurement. Findings The proposed control technique can ensure optimal dynamic response, small steady-state error and energy saving. The effectiveness of the proposed control strategy is verified via numerical simulation and experiment. Originality/value The authors introduced an innovative approach to the well-known control methodology and settled their research in the newest literature coverage for this issue.
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AL-saedi, Akeel A., and Jalil Rashidinia. "Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation." Electronic Research Archive 31, no. 7 (2023): 4248–65. http://dx.doi.org/10.3934/era.2023216.
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<abstract> <p>This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $ {L_\infty } $ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method.</p> </abstract>
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Karaagac, Berat, Yusuf Ucar, and Alaattin Esen. "Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method." Filomat 32, no. 16 (2018): 5573–83. http://dx.doi.org/10.2298/fil1816573k.
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In this paper, we are going to obtain numerical solutions of the improved Boussinesq equation with the aid of Galerkin quadratic B-spline finite element method. To test the accuracy and efficiency of the current method, four test problems have been used. These are solitary wave movement, interaction of two solitary waves, wave break-up and blow-up of solutions. Their results have been compared with those available in the literature for different values of space and time steps. Also, the error norms L2 and L1 have been computed and presented in comparison.
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Karpik, Anna, Francesco Cosco, and Domenico Mundo. "Higher-Order Hexahedral Finite Elements for Structural Dynamics: A Comparative Review." Machines 11, no. 3 (February 24, 2023): 326. http://dx.doi.org/10.3390/machines11030326.
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The finite element method (FEM) is widely used in many engineering applications. The popularity of FEM led to the development of several variants of formulations, and hexahedral meshes surged as one of the most computationally effective. After briefly reviewing the reasons and advantages behind the formulation of increasing order elements, including the serendipity variants and the associated reduced integration schemes, a systematic comparison of the most common hexahedral formulations is presented. A numerical benchmark was used to assess convergency rates and computational efficiencies when solving the eigenvalue problem for linear dynamic analysis. The obtained results confirmed the superior performances of the higher-order brick element formulations. In terms of computational efficiency, defined as the ratio between achievable accuracy and computational execution time, quadratic or cubic formulations exhibited the best results for the stages of FE model assembly and solution computation, respectively.
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Liu, Qiyu, Qunxiong Zhu, Zhiqiang Geng, and Longjin Lv. "Time Optimal Control of a Thermoelastic System." Mathematical Problems in Engineering 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/6047670.
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This paper considers the numerical approximation for the time optimal control problem of a thermoelastic system with some control and state constraints. By the Galerkin finite element method (FEM), the original problem is projected into a semidiscrete optimal control problem governed by a system of ordinary differential equations. Then the optimal time and control parameterization method is applied to reduce the original system to an optimal parameter selection problem, in which both the optimal time and control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a hybrid algorithm consisting of chaotic particle swarm optimization (CPSO) and sequential quadratic programming (SQP) algorithm. The numerical simulations demonstrate the effectiveness of the proposed numerical approximation method.
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Esen, Alaattin, and Orkun Tasbozan. "Numerical Solution of Time Fractional Schrödinger Equation by Using Quadratic B-Spline Finite Elements." Annales Mathematicae Silesianae 31, no. 1 (September 26, 2017): 83–98. http://dx.doi.org/10.1515/amsil-2016-0015.
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Abstract In this article, quadratic B-spline Galerkin method has been employed to solve the time fractional order Schrödinger equation. Numerical solutions and error norms L2 and L∞ are presented in tables.
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Mukae, Shunichi, Takeshi Okuzono, and Kimihiro Sakagami. "On the Robustness and Efficiency of the Plane-Wave-Enriched FEM with Variable q-Approach on the 2D Room Acoustics Problem." Acoustics 4, no. 1 (January 20, 2022): 53–73. http://dx.doi.org/10.3390/acoustics4010004.
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Partition of unity finite element method with plane wave enrichment (PW-FEM) uses a shape function with a set of plane waves propagating in various directions. For room acoustic simulations in a frequency domain, PW-FEM can be an efficient wave-based prediction method, but its practical applications and especially its robustness must be studied further. This study elucidates PW-FEM robustness via 2D real-scale office room problems including rib-type acoustic diffusers. We also demonstrate PW-FEM performance using a sparse direct solver and a high-order Gauss–Legendre rule with a recently developed rule for ascertaining the number of integration points against the classical linear and quadratic FEMs. Numerical experiments investigating mesh size and room geometrical complexity effects on the robustness of PW-FEM demonstrated that PW-FEM becomes more robust at wide bands when using a mesh in which the maximum element size maintains a comparable value to the wavelength of the upper-limit frequency. Moreover, PW-FEM becomes unstable with lower spatial resolution mesh, especially for rooms with complex shape. Comparisons of accuracies and computational costs of linear and quadratic FEM revealed that PW-FEM requires twice the computational time of the quadratic FEM with a mesh having spatial resolution of six elements per wavelength, but it is highly accurate at wide bands with lower memory and with markedly fewer degrees of freedom. As an additional benefit of PW-FEM, the impulse response waveform of quadratic FEM in a time domain was found to deteriorate over time, but the PW-FEM waveform can maintain accurate waveforms over a long time.
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Peng, Jia Chung, Yong Xiang Zhao, L. Y. Yu, and A. G. Yang. "Finite Element Analysis on Fatigue Stress History of a Railway Bogie Bolster." Advanced Materials Research 44-46 (June 2008): 195–200. http://dx.doi.org/10.4028/www.scientific.net/amr.44-46.195.
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An efficient finite element (FE) method, multivariate quadratic regression approach, is proposed for calculating the fatigue stress spectrum of engineering structures. The calculation starts from a dynamic load history. A regression function is established as a relation from the concurrent components of structural balance force systems into the structural stress. Parameters of the relation are measured by the stress data using an elastic-plastic FE method under selected groups of balance force systems. The selected systems should cover the possible load range with a similar service condition. After passing the fit effect check, the regression equation can transfer the structural load history into the stress history at the preferred position. Application on the determination of fatigue stress spectrum for the bolster of K6 type bogie has indicated availability of the present approach. Some deficiencies have been overcome from the much time cost by transient approach and the entire elastic material relation by quasi-static approach.
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Yigit Akargun, Hayri, and Cuneyt Sert. "Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 7 (August 26, 2014): 1487–503. http://dx.doi.org/10.1108/hff-01-2013-0006.
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Purpose – The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows. Design/methodology/approach – Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems. Findings – Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of. Originality/value – LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.
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KERUR, S. B., and ANUP GHOSH. "ACTIVE VIBRATION CONTROL OF COMPOSITE PLATE USING AFC ACTUATOR AND PVDF SENSOR." International Journal of Structural Stability and Dynamics 11, no. 02 (April 2011): 237–55. http://dx.doi.org/10.1142/s0219455411004075.
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A finite element formulation for active vibration control of laminated composite plate integrated with active fiber composite (AFC) layer acting as distributed actuator and PVDF layer as sensor is presented in this paper. An eight noded quadratic isoparametric element with five mechanical degrees of freedom and one electrical degree of freedom per node of the element is considered. Newmark time integration method is used to calculate the dynamic response and negative velocity feedback control algorithm is used to control the dynamic response of the laminated composite plate. The effect of piezoelectric fiber orientation in actuator layer on the control of vibration is studied.
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Tota-Maharaj, Kiran, Ghassan Nounu, and Navin Ramroop. "Modelling of Quadratic-Surface Sludge Digesters by Smoothed Particle Hydrodynamics (SPH) – Finite Element (FE) Methods." Archives of Hydro-Engineering and Environmental Mechanics 67, no. 1-4 (December 1, 2020): 35–53. http://dx.doi.org/10.1515/heem-2020-0003.
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Abstract The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoided. The stresses developed in the shell of the sludge digester, vary along the meridian and equatorial diameters. A non-dimensional parameter, ξ, defines the height-to-diameter aspect ratio which is used to delineate the parametric boundary conditions of the shell’s surface. Three groups of analyses were conducted to determine the orthogonal stresses in the shell of the QSD. The first-principles numerical models ran reasonably quickly, and many simulations were made during the study. The results showed that they were in within the range 5.34% to 7.2% to 2D FEA results. The 3D FEA simulation results were within the range of 8.3% to 9.2% to those from the MATLAB time-history models. This is a good indicator that the first principles numerical models are an excellent time-saving method to predict the behaviour of the QSD under seismic excitation. Upon examining the criteria for the design, analysing the results for the 2D FEA simulations showed that the fill height is not a significant variable with sloshing however the 3D FEA showed that the hydrostatic pressure is a significant variable. With the maximum tensile stress of the 3D-printed Acrylonitrile Butadiene Styrene (ABS)-a common thermoplastic polymer typically used for injection molding applications, being 24.4 MPa, the overall maximum stress of 5.45 MPa, the material can be a viable option for the use of QSD construction in small island developing states (SIDS).
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LISTERUD, EIVIND, and WALTER EVERSMAN. "FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART I: NONUNIFORM DUCT PROPAGATION." Journal of Computational Acoustics 12, no. 03 (September 2004): 397–429. http://dx.doi.org/10.1142/s0218396x0400233x.
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Cubic serendipity elements have been implemented into a nonuniform duct model of acoustic propagation in a moving medium. This model uses a convective potential formulation derived from the inviscid linearized mass and momentum equations. The model requires post-processing to calculate acoustic pressure. These elements outperform the quadratic serendipity elements in terms of computational efficiency based on visual observations and error norm analysis of acoustic pressure. CPU time reduction of up to 40% has been observed without sacrificing accuracy. Any penalty in numerical accuracy incurred by using serendipity elements rather than Lagrangian elements is far outweighed by the gains in dimensionality. The computational gains for calculation of acoustic potential are considerably less. Analytical expressions for the modal and convective effects on the propagating wavelength have been formulated and compared to numerical results. Preliminary assessment of alternative finite element approaches to model the convective potential formulation has been conducted. Stabilization and wave approximation methods have been implemented to solve simple one-dimensional problems.
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Koubaiti, Ouadie, Said EL Fakkoussi, Jaouad El-Mekkaoui, Hassan Moustachir, Ahmed Elkhalfi, and Catalin I. Pruncu. "The treatment of constraints due to standard boundary conditions in the context of the mixed Web-spline finite element method." Engineering Computations 38, no. 7 (February 8, 2021): 2937–68. http://dx.doi.org/10.1108/ec-02-2020-0078.
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Purpose This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution. Design/methodology/approach In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory. Findings The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity. Originality/value The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.
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WOLFF, SEBASTIAN, and CHRISTIAN BUCHER. "ON CONTINUOUS ASSUMED GRADIENT ELEMENTS OF SECOND ORDER." International Journal of Computational Methods 10, no. 01 (February 2013): 1340009. http://dx.doi.org/10.1142/s0219876213400094.
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This paper presents and compares continuous assumed gradient (CAG) methods when applied to structural elasticity. CAG elements are finite elements where the strain, i.e., the deformation gradient, is replaced by a C0-continuous interpolation. Similar approaches are found in nodal integration and SFEM. Recently, interpolation schemes for a continuous assumed deformation gradient were proposed for first order tetrahedral and hexahedral finite elements. These schemes try to balance accuracy and numerical efficiency. At the same time, the stability of the interpolation with respect to hourglassing and spurious low energy modes is ensured. This paper recalls the fundamentals of CAG elements, i.e., the formulation and linearization. Furthermore, it extends the approach to second order finite elements. Examples prove convergence and accuracy of the quadratic elements. Two interpolation schemes, one being supported by finite element nodes and interior points and the other being a higher-order tensor-product polynomial, are identified to be most accurate.
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Chen, Enwei, Mengbo Li, Neil Ferguson, and Yimin Lu. "An adaptive higher order finite element model and modal energy for the vibration of a traveling string." Journal of Vibration and Control 25, no. 5 (October 30, 2018): 996–1007. http://dx.doi.org/10.1177/1077546318808881.
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A nonlinear equation describing the transverse vibration of an axially traveling string with constant and time-varying length is obtained by developing a new finite element model described by quadratic shape functions. A novel nonlinear coordinate transform is introduced with regard to its nonlinear terms. Subsequently, a new hybrid Newmark-beta/time varying degree of freedom method, which can adjust the element number automatically according to the change of string length, is proposed to improve accuracy. The proposed method as well as normal numerical methods are compared with an analytical solution. Results show that the proposed method is in good agreement with the Newmark-beta method for the case of small variations in string length, whilst it is superior in accuracy to the latter in the case of large length variations. Complex mode theory is adopted firstly to obtain the modal components as well as subsequently the modal energy for a traveling string. A phenomenon is observed where the free vibration energy leaks from one mode to the others in a traveling string. The higher the speed of translation and the modal order, the more energy that is leaked into the modes close to the initially excited mode.
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OLATOYINBO, Seyi Festus. "Verification of a High-Order FEM-based CFD Code using the Method of Manufactured Solutions." INCAS BULLETIN 15, no. 2 (June 9, 2023): 75–89. http://dx.doi.org/10.13111/2066-8201.2023.15.2.8.
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A high-order computational fluid dynamics (CFD) code capable of solving compressible turbulent flow problems was developed. The CFD code employs the Flowfield Dependent Variation (FDV) scheme implemented in a Finite Element Method (FEM) framework. The FDV scheme is basically derived from the Lax-Wendroff Scheme (LWS) involving the replacement of LWS’s explicit time derivatives with a weighted combination of explicit and implicit time derivatives. The code utilizes linear, quadratic and cubic isoparametric quadrilateral and hexahedral Lagrange finite elements with corresponding piecewise shape functions that have formal spatial accuracy of second-order, third-order and fourth-order, respectively. In this paper, the results of observed order-of-accuracy of the implemented FDV FEM-based CFD code involving grid and polynomial order refinements on uniform Cartesian grids are reported. The Method of Manufactured Solutions (MMS) is applied to governing 2-D Euler and Navier-Stokes equations for flow cases spanning both subsonic and supersonic flow regimes. Global discretization error analyses using discrete 𝐿2 norm show that the spatial order-of-accuracy of the FDV FEM-based CFD code converges to the shape function polynomial order plus one, in excellent agreement with theory. Uniquely, this procedure establishes the wider applicability of MMS in verifying the spatial accuracy of a high-order CFD code.
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Eisler, G. R., R. D. Robinett, D. J. Segalman, and J. D. Feddema. "Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (September 1, 1993): 405–10. http://dx.doi.org/10.1115/1.2899116.
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The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.
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Grandhi, R. V., H. Cheng, and S. S. Kumar. "Design of Forging Process Parameters With Deformation and Temperature Constraints." Journal of Manufacturing Science and Engineering 118, no. 3 (August 1, 1996): 441–44. http://dx.doi.org/10.1115/1.2831051.
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This paper presents a methodology for designing optimal process parameters for forging operations. The nonlinear rigid viscoplastic finite element (FE) method is used for deformation and thermal analyses. From the FE model a state space system is developed for representing the coupled deformation and thermal behavior of the metal forming system. Constraints are imposed on the strain rate and temperature of the deforming work-piece for obtaining the desired physical/microstructural properties in the final product. The linear quadratic regulator (LQR) theory for finite time control is used in designing the initial die temperature and optimal ram velocity schedules. The approach is demonstrated on a plane strain channel section forging under nonisothermal conditions.
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Zeng, Detang, Xin Yu, Jingfang Huang, and Chunqing Tan. "Numerical Computation for a Kind of Time Optimal Control Problem for the Tubular Reactor System." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/9580470.
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This paper is devoted to the study of numerical computation for a kind of time optimal control problem for the tubular reactor system. This kind of time optimal control problem is aimed at delaying the initiation time τ of the active control as late as possible, such that the state governed by this controlled system can reach the target set at a given ending time T. To compute the time optimal control problem, we firstly approximate the original problem by finite element method and get a new approximation time optimal control problem governed by ordinary differential equations. Then, through the control parameterization method and time-scaling transformation, the approximation problem becomes an optimal parameter selection problem. Finally, we use Sequential Quadratic Program algorithm to solve the optimal parameter selection problem. A numerical simulation is given for illustration.
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Bonnet, Marc, Giulio Maier, and Castrenze Polizzotto. "Symmetric Galerkin Boundary Element Methods." Applied Mechanics Reviews 51, no. 11 (November 1, 1998): 669–704. http://dx.doi.org/10.1115/1.3098983.
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This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions; some quadratic forms have a clear energy meaning; variational properties characterize the solutions and other results, invalid in traditional boundary element methods enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, and computer implementations. Areas and aspects which at present require further research are identified, and comparative assessments are attempted with respect to traditional boundary integral-elements. This article includes 176 references.
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Bernat, Jakub, Slawomir Jan Stepien, Artur Stranz, and Paulina Superczynska. "Linear quadratic-based optimal current control of BLDC motor minimizing control error and considering accurate finite element model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 6 (November 7, 2016): 2063–73. http://dx.doi.org/10.1108/compel-03-2016-0087.
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Purpose Brushless DC (BLDC) motors are commonly used in the industry. The improvement of power switching electronic elements, especially integrated circuits, has led to the development and improvement of control strategies. The purpose of this paper is to apply the well-known LQR control method for the highly accurate model of the BLDC motor, which is a must for the control system to be optimal and stable. Design/methodology/approach The employed distributed parameter finite element motor model uses a state vector which is dependent not only on time but also on space configuration, thus enabling the end-winding effect, cogging torque or magnetic saturation to be taken into account. The adopted infinite horizon linear quadratic-based controller aims at optimally minimizing current control error considering the energy delivered to the motor. For this reason, the relationship between the quadratic forms of the performance index is investigated and the reference currents’ influence on the results was studied. The presented methodology was confirmed with the numerical analysis of the problem. Findings It was found how the configuration of the optimal control objective function influences the performance and the stability of the drive system subject to energy delivery minimization. An exact configuration was calculated for which the control error was reasonably small. The applicability of the infinite horizon optimal current control for the BLDC drive applications was proved. Originality/value The authors introduced an innovative approach to the well-known control methodology and settled their research in the newest literature coverage for this issue.
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WANG, FENGXIA. "MODEL REDUCTION WITH GEOMETRIC STIFFENING NONLINEARITIES FOR DYNAMIC SIMULATIONS OF MULTIBODY SYSTEMS." International Journal of Structural Stability and Dynamics 13, no. 08 (October 21, 2013): 1350046. http://dx.doi.org/10.1142/s0219455413500466.
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This work investigates the implementation of nonlinear model reduction to flexible multibody dynamics. Linear elastic theory will lead to instability issues with rotating beam-like structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In order to reduce the computation cost in flexible multibody dynamics, which is extremely important for complex large system simulations, modal reduction is usually implemented to a rotating flexible structure with geometric nonlinearities retained in the model. In this work, a standard model reduction process based on matrix operation is developed, and the essential geometric stiffening nonlinearities are retained in the reduced model. The time responses of a tip point on a rotating Euler–Bernoulli blade are calculated based on two nonlinear reduced models. The first reduced model is derived by the standard matrix operation from a full finite element model and the second reduced model is obtained via the Galerkin method. The matrix operation model reduction process is validated through the comparison of the simulation results obtained from these two different reduced models. An interesting phenomenon is observed in this work: In the nonlinear model, if only quadratic geometric stiffing term is retained, the two reduced models converge to the full finite element model with only one bending mode and two axial modes. While if both quadratic and cubic geometric stiffing terms are retained in the nonlinear equation, the modal-based reduced model will not converge to the finite element model unless all eigenmodes are retained, that is the reduced model has no degree of freedom reduction at all.
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Hodge, Steven M. "Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique." Journal of Glaciology 31, no. 109 (1985): 350–59. http://dx.doi.org/10.1017/s0022143000006699.
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AbstractThe two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.
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Hodge, Steven M. "Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique." Journal of Glaciology 31, no. 109 (1985): 350–59. http://dx.doi.org/10.3189/s0022143000006699.
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AbstractThe two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.
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Zhang, Liqi, and Yonghui Zhao. "Time-Varying Aeroelastic Modeling and Analysis of a Rapidly Morphing Wing." Aerospace 10, no. 2 (February 17, 2023): 197. http://dx.doi.org/10.3390/aerospace10020197.
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Advanced rotational variable-swept missile wings require the ability to rapidly deploy, retract and reach the designated position. Therefore, the establishment of an effective time-varying aeroelastic model of a rotating missile wing is the prerequisite for performing transient response analysis during the rapid morphing process. In this paper, the finite element model of the wing at the fixed configuration is combined with the floating frame method to describe the small elastic deformations and large rigid-body displacements of the wing, respectively. Combining the structural dynamic model with the supersonic piston theory, a nonlinear and time-varying aeroelastic model of a missile wing undergoing the rapid morphing process is established. A method for the real-time determination of the time-varying lifting surface during morphing is discussed. Based on the proposed aeroelastic equations of motion, the flutter characteristics of the wing at different sweep angles are obtained. The influences of the actuator spring constant, the damping ratio during the morphing and the post-lock stages, as well as the velocity quadratic term in the aeroelastic equations, on the transient responses of the system are studied. The simulation results show that the flutter characteristics of the wing are greatly influenced by the sweep angle. Moreover, the jumping phenomenon in flutter speed due to the switching of flutter modes is found with the increase of the sweep angle. The morphing simulations demonstrate that the transient aeroelastic responses mainly occur in the post-lock stage, so much more attention needs to be focused on the post-lock vibrations. In addition, under the given simulation parameters, the nonlinear quadratic velocity term has little effect on the transient responses of the system. This study provides an efficient method for predicting the transient aeroelastic responses of a rotational variable swept wing.
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Kuraishi, Takashi, Kenji Takizawa, and Tayfun E. Tezduyar. "Space–time Isogeometric flow analysis with built-in Reynolds-equation limit." Mathematical Models and Methods in Applied Sciences 29, no. 05 (May 2019): 871–904. http://dx.doi.org/10.1142/s0218202519410021.
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We present a space–time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.
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Cortés, Fernando, and Imanol Sarría. "Dynamic Analysis of Three-Layer Sandwich Beams with Thick Viscoelastic Damping Core for Finite Element Applications." Shock and Vibration 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/736256.
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This paper presents an analysis of the dynamic behaviour of constrained layer damping (CLD) beams with thick viscoelastic layer. A homogenised model for the flexural stiffness is formulated using Reddy-Bickford’s quadratic shear in each layer, and it is compared with Ross-Kerwin-Ungar (RKU) classical model, which considers a uniform shear deformation for the viscoelastic core. In order to analyse the efficiency of both models, a numerical application is accomplished and the provided results are compared with those of a 2D model using finite elements, which considers extensional and shear stress and longitudinal, transverse, and rotational inertias. The intermediate viscoelastic material is characterised by a fractional derivative model, with a frequency dependent complex modulus. Eigenvalues and eigenvectors are obtained from an iterative method avoiding the computational problems derived from the frequency dependence of the stiffness matrices. Also, frequency response functions are calculated. The results show that the new model provides better accuracy than the RKU one as the thickness of the core layer increases. In conclusion, a new model has been developed, being able to reproduce the mechanical behaviour of thick CLD beams, reducing storage needs and computational time compared with a 2D model, and improving the results from the RKU model.
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Najibi, Amir, and Guanghui Wang. "Two-Dimensional C-V Heat Conduction Investigation of an FG-Finite Axisymmetric Hollow Cylinder." Symmetry 15, no. 5 (April 30, 2023): 1009. http://dx.doi.org/10.3390/sym15051009.
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In the present work, we implement a graded finite element analysis to solve the axisymmetric 2D hyperbolic heat conduction equation in a finite hollow cylinder made of functionally graded materials using quadratic Lagrangian shape functions. The graded FE method is verified, and the simple rule of the mixture with power-law volume fraction is found to enhance the effective thermal properties’ gradation along the radial direction, including the thermal relaxation time. The effects of the Vernotte numbers and material distributions on temperature waves are investigated in depth, and the results are discussed for Fourier and non-Fourier heat conductions, and homogeneous and inhomogeneous material distributions. The homogeneous cylinder wall made of SUS304 shows faster temperature wave velocity in comparison to the ceramic-rich cylinder wall, which demonstrates the slowest one. Furthermore, the temperature profiles along the radial direction when n = 2 and n = 5 are almost the same in all Ve numbers, and by increasing the Ve numbers, the temperature waves move slower in all the material distributions. Finally, by tuning the material distribution which affects the thermal relaxation time, the desirable results for temperature distribution can be achieved.
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Zhang, Shu Yun, Guo Liang Bai, and Zhi Gang Gao. "Study on Reasonable Mode Number of Composite Frame and Reinforced Concrete Core Hybrid Structures in High-Rise Buildings." Advanced Materials Research 368-373 (October 2011): 285–88. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.285.
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For seismic design of composite frame and reinforced concrete core hybrid structures in high-rise buildings, the response spectrum method is influenced to a large extent by mode combination rules and number of combined modes. The dynamic characteristics of composite frame and concrete core hybrid structures were studied through modal analysis, natural vibration periods and mode shape of hybrid structures had calculated and analyzed, the results show that the natural vibration frequencies are near, the complete quadratic combination of mode combination rule was recommended for avoiding higher order mode shape lose in the response spectrum method. The reasonable number of combined modes for response spectrum method were studied by truncation error analysis, it is proposed that more than 20 modes are combined. The results of the time history analysis und The three dimensional finite element er three earthquake waves were compared with results of response spectrum, indicating that the maximum response of hybrid structures can be obtained under reasonable mode number.
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Freire-Torres, Mario, Manuel Colera, and Jaime Carpio. "Numerical Solution of Thermal Phenomena in Welding Problems." Mathematics 11, no. 13 (July 6, 2023): 3009. http://dx.doi.org/10.3390/math11133009.
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We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and non-isothermal melting models are considered to relate the enthalpy with the temperature. Quadratic triangular elements with local anisotropic mesh adaptation are employed for the space discretization of the governing equation, and a second-order backward differentiation formula is employed for the time discretization. The resulting non-linear discretized system is solved with a simple Newton algorithm with two versions: the θ-Newton algorithm, which considers the temperature as the main unknown variable, as in most works in the literature, and the h-Newton algorithm, which considers the enthalpy, which is the main novelty of the present work. Then, we show via numerical experiments that the h-Newton method is robust and converges well to the solution, both for isothermal and non-isothermal melting. However, the θ-method can only be applied to the case of non-isothermal melting and converges only for a sufficiently large melting temperature range or sufficiently small time step. Numerical experiments also confirm that the method is able to adequately capture the discontinuities or sharp variations in the solution without the need for any kind of numerical dissipation.
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Ghadimi, Parviz, and Arsham Reisinezhad. "Numerical simulation of flood waves and calculation of exerted forces on the cylindrical piers in contraction channels with different cross section profiles." Journal of Hydroinformatics 14, no. 2 (June 21, 2011): 366–85. http://dx.doi.org/10.2166/hydro.2011.062.
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A numerical model based on two-dimensional shallow water equations is presented. The depth-averaged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique is applied to discretize the spatial derivatives. Triangular elements with quadratic and linear interpolating functions are employed for two horizontal velocity components and the free-surface elevation, respectively. The standard Galerkin method is applied for discretization of the governing equations. Time discretization is performed using an implicit scheme. The resulting linear system of equations is solved by the GMRES method. The model is validated using three test cases and the results are compared with an analytical solution, the result of numerical work and experimental data, respectively. Favorable agreement was achieved in all three cases. Subsequently, the developed model is applied to simulate free-surface elevation through a channel contraction. The effects of width of the narrow section as well as the profile of the cross section of the channel on the wave forces exerted on a circular cylinder were studied. This was done in a channel with a quartic narrow section. Plots of time histories of the drag coefficient on the cylinder were produced, demonstrating the effects of the mentioned parameters.