Journal articles on the topic 'Finite element methods (FEMs)'
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Cen, Song, Cheng Jin Wu, Zhi Li, Yan Shang, and Chenfeng Li. "Some advances in high-performance finite element methods." Engineering Computations 36, no. 8 (October 7, 2019): 2811–34. http://dx.doi.org/10.1108/ec-10-2018-0479.
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Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time. Design/methodology/approach Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions. Findings The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate. Originality/value These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.
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Nair, M. Thamban, and Devika Shylaja. "Conforming and nonconforming finite element methods for biharmonic inverse source problem." Inverse Problems 38, no. 2 (December 20, 2021): 025001. http://dx.doi.org/10.1088/1361-6420/ac3ec5.
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Abstract This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov regularization is considered to obtain a stable approximate solution. Error estimate is established for the regularized solution for different regularization schemes. Numerical results that confirm the theoretical results are also presented.
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Rong, Xin, Ruiping Niu, and Guirong Liu. "Stability Analysis of Smoothed Finite Element Methods with Explicit Method for Transient Heat Transfer Problems." International Journal of Computational Methods 17, no. 02 (October 24, 2019): 1845005. http://dx.doi.org/10.1142/s0219876218450056.
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In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods (S-FEMs) with explicit time integration. For a numerical method with spatial discretization, the computational cost per time step in the explicit method is less than that in the implicit method, but the time step is much smaller in the explicit analysis than that in the implicit analysis when the same mesh is used. This is because the stability is of essential importance. This work thus studies the stability of S-FEMs, when applied to transient heat transfer problems. Relationships are established between the critical time steps used in S-FEMs with the maximum eigenvalues of the thermal stiffness (conduction) matrix and mass matrix. It is found that the critical time step relates to the “softness” of the model. For example, node-based smoothed finite element method (NS-FEM) is softer than edge-based smoothed finite element method (ES-FEM), which leads to that the critical time step of NS-FEM is larger than that of ES-FEM. Because computing the eigenvalues and condition numbers of the stiffness matrices is very expensive but valuable for stability analysis, we proposed a concise and effective algorithm to estimate the maximum eigenvalue and condition number. Intensive numerical examples show that our scheme for computing the critical time step can work accurately and stably for the explicit method in FEM and S-FEMs.
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D’Elia, Marta, Max Gunzburger, and Christian Vollmann. "A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems." Mathematical Models and Methods in Applied Sciences 31, no. 08 (June 19, 2021): 1505–67. http://dx.doi.org/10.1142/s0218202521500317.
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The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms involving double integrals which lead to discrete systems having higher assembly and solving costs due to possibly much lower sparsity compared to that of FEMs for PDEs. In addition, one may encounter nonsmooth integrands. In many nonlocal models, nonlocal interactions are limited to bounded neighborhoods that are ubiquitously chosen to be Euclidean balls, resulting in the challenge of dealing with intersections of such balls with the finite elements. We focus on developing recipes for the efficient assembly of FEM stiffness matrices and on the choice of quadrature rules for the double integrals that contribute to the assembly efficiency and also posses sufficient accuracy. A major feature of our recipes is the use of approximate balls, e.g. several polygonal approximations of Euclidean balls, that, among other advantages, mitigate the challenge of dealing with ball-element intersections. We provide numerical illustrations of the relative accuracy and efficiency of the several approaches we develop.
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Mackerle, Jaroslav. "Finite element analyses and simulations in biomedicine: a bibliography (1985‐1999)." Engineering Computations 17, no. 7 (November 1, 2000): 813–56. http://dx.doi.org/10.1108/02644400010352270.
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Gives a bibliographical review of the finite element methods (FEMs) applied in biomedicine from the theoretical as well as practical points of view. The bibliography at the end of the paper contains 748 references to papers, conference proceedings and theses/dissertations dealing with the finite element analyses and simulations in biomedicine that were published between 1985 and 1999.
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Wu, Jilian, Xinlong Feng, and Fei Liu. "Pressure-Correction Projection FEM for Time-Dependent Natural Convection Problem." Communications in Computational Physics 21, no. 4 (March 8, 2017): 1090–117. http://dx.doi.org/10.4208/cicp.oa-2016-0064.
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AbstractPressure-correction projection finite element methods (FEMs) are proposed to solve nonstationary natural convection problems in this paper. The first-order and second-order backward difference formulas are applied for time derivative, the stability analysis and error estimates of the semi-discrete schemes are presented using energy method. Compared with characteristic variational multiscale FEM, pressure-correction projection FEMs are more efficient and unconditionally energy stable. Ample numerical results are presented to demonstrate the effectiveness of the pressure-correction projection FEMs for solving these problems.
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He, Yanfei, Xingwu Zhang, Jia Geng, Xuefeng Chen, and Zengguang Li. "Two Kinds of Finite Element Variables Based on B-Spline Wavelet on Interval for Curved Beam." International Journal of Applied Mechanics 11, no. 02 (March 2019): 1950017. http://dx.doi.org/10.1142/s1758825119500170.
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Curved beam structure has been widely used in engineering, due to its good load-bearing and geometric characteristics. More common methods for analyzing and designing this structure are the finite element methods (FEMs), but these methods have many disadvantages. Fortunately, the multivariable wavelet FEMs can solve these drawbacks. However, the multivariable generalized potential energy functional of curved beam, used to construct this element, has not been given in previous literature. In this paper, the generalized potential energy functional for curved beam with two kinds of variables is derived initially. On this basis, the B-spline wavelet on the interval (BSWI) is used as the interpolation function to construct the wavelet curved beam element with two kinds of variables. In the end, several typical numerical examples of thin to thick curved beams are given, which show that the present element is more effective in static and free vibration analysis of curved beam structures.
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Jiang, Chen, Xu Han, G. R. Liu, Zhi-Qian Zhang, Gang Yang, and Guang-Jun Gao. "Smoothed finite element methods (S-FEMs) with polynomial pressure projection (P3) for incompressible solids." Engineering Analysis with Boundary Elements 84 (November 2017): 253–69. http://dx.doi.org/10.1016/j.enganabound.2017.07.022.
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CHIEN, C. S., H. T. HUANG, B. W. JENG, and Z. C. LI. "SUPERCONVERGENCE OF FEMS AND NUMERICAL CONTINUATION FOR PARAMETER-DEPENDENT PROBLEMS WITH FOLDS." International Journal of Bifurcation and Chaos 18, no. 05 (May 2008): 1321–36. http://dx.doi.org/10.1142/s0218127408021014.
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We study finite element approximations for positive solutions of semilinear elliptic eigenvalue problems with folds, and exploit the superconvergence of finite element methods (FEM). In order to apply the superconvergence of FEM for Poisson's equation in [Chen & Huang, 1995; Huang et al., 2004, 2006; Lin & Yan, 1996] to parameter-dependent problems with folds, this paper provides the framework of analysis, accompanied with the proof of the strong monotonicity of the nonlinear form. It is worthy to point out that the superconvergence of the nonlinear problem in this paper is different from that in [Chen & Huang, 1995]. A continuation algorithm is described to trace solution curves of semilinear elliptic eigenvalue problems, where the Adini elements are exploited to discretize the PDEs. Numerical results on some sample test problems with folds and bifurcations are reported.
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Hu, Jun, and Mira Schedensack. "Two low-order nonconforming finite element methods for the Stokes flow in three dimensions." IMA Journal of Numerical Analysis 39, no. 3 (April 19, 2018): 1447–70. http://dx.doi.org/10.1093/imanum/dry021.
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Abstract In this paper, we propose two low-order nonconforming finite element methods (FEMs) for the three-dimensional Stokes flow that generalize the nonconforming FEM of Kouhia & Stenberg (1995, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Eng, 124, 195–212). The finite element spaces proposed in this paper consist of two globally continuous components (one piecewise affine and one enriched component) and one component that is continuous at the midpoints of interior faces. We prove that the discrete Korn inequality and a discrete inf–sup condition hold uniformly in the mesh size and also for a nonempty Neumann boundary. Based on these two results, we show the well-posedness of the discrete problem. Two counterexamples prove that there is no direct generalization of the Kouhia–Stenberg FEM to three space dimensions: the finite element space with one nonconforming and two conforming piecewise affine components does not satisfy a discrete inf–sup condition with piecewise constant pressure approximations, while finite element functions with two nonconforming and one conforming component do not satisfy a discrete Korn inequality.
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Followell, David, Salvatore Liguore, Rigo Perez, W. Yates, and William Bocchi. "Computer-Aided Reliability Finite Element Methods." Journal of the IEST 34, no. 5 (September 1, 1991): 46–52. http://dx.doi.org/10.17764/jiet.2.34.5.9720337614871186.
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Finite element analyses (FEA) have emerged as a process for assessing stresses and strains in electronic equipment in order to compute the expected structural life. However, potential pitfalls may compromise accuracy. Guidelines have been established to improve the accuracy of these results. A method has been outlined that allows simplified linear FEAs to be used instead of the more complex elastic-plastic nonlinear FEA. Guidelines for mesh generation have been established to eliminate arithmetic errors caused when materials with large stiffness differences are adjacent to each other. The accuracy of FEAs when dealing with very small dimensions has been verified. Procedures for combining various loadings in order to predict life have been established for materials that exhibit stress relaxation and for those that do not. With these guidelines, FEAs can be an effective tool to predict the structural life of electronic equipment.
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Farah, Khaled, Mounir Ltifi, and Hedi Hassis. "A Study of Probabilistic FEMs for a Slope Reliability Analysis Using the Stress Fields." Open Civil Engineering Journal 9, no. 1 (May 14, 2015): 196–206. http://dx.doi.org/10.2174/1874149501509010196.
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In this paper, the applicability and the effectiveness of the probabilistic finite element methods (FEMs) such as the perturbation method, and the Spectral Stochastic Finite Element Method (SSFEM) applied to the reliability analysis of the slope stability have been studied. The results were checked by the Monte Carlo simulation and a direct coupling ap-proach combining the deterministic finite elements code and First Order Reliability Method (FORM) algorithm. These methods are presented considering the spatial variation of soil strength parameters and Young modulus. The random field is used to describe the spatial variation. Also, the reliability analysis is conducted using a performance function formulat-ed in terms of the stochastic stress mobilized along the sliding surface. The present study shows that the perturbation method and SSFEM can be considered as practical methods to conduct a second moment analysis of the slope stability taking into account the spatial variability of soil properties since good results are obtained with acceptable estimated rela-tive errors. Finally, the perturbation method is performed to delimit the location of the critical probabilistic sliding surfac-es and to evaluate the effect of the correlation length of soil strength parameters on the safety factor. In addition, the two methods are used to estimate the probability density and the cumulative distribution function of the factor of safety.
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Rabus, H. "A Natural Adaptive Nonconforming FEM Of Quasi-Optimal Complexity." Computational Methods in Applied Mathematics 10, no. 3 (2010): 315–25. http://dx.doi.org/10.2478/cmam-2010-0018.
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AbstractIn recent years, the question on the convergence and optimality in the context of adaptive finite element methods has been the subject of intensive studies. However, for nonstandard FEMs such as mixed or nonconforming ones, the lack of Galerkin's orthogonality requires new mathematical arguments. The presented adap- tive algorithm for the Crouzeix-Raviart finite element method and the Poisson model problem is of quasi-optimal complexity. Furthermore it is natural in the sense that collective marking rather than a separate marking is applied or the estimated error and the volume term.
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ABDULLE, ASSYR, and GILLES VILMART. "COUPLING HETEROGENEOUS MULTISCALE FEM WITH RUNGE–KUTTA METHODS FOR PARABOLIC HOMOGENIZATION PROBLEMS: A FULLY DISCRETE SPACETIME ANALYSIS." Mathematical Models and Methods in Applied Sciences 22, no. 06 (April 26, 2012): 1250002. http://dx.doi.org/10.1142/s0218202512500029.
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Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge–Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following the framework of the Heterogeneous Multiscale Method (HMM). We present a fully discrete analysis in both space and time. Our analysis relies on new (optimal) error bounds in the norms L2(H1), [Formula: see text], and [Formula: see text] for the fully discrete analysis in space. These bounds can then be used to derive fully discrete spacetime error estimates for a variety of Runge–Kutta methods, including implicit methods (e.g. Radau methods) and explicit stabilized method (e.g. Chebyshev methods). Numerical experiments confirm our theoretical convergence rates and illustrate the performance of the methods.
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Cao, Juan, Xiaoyi Zhang, Jiannan Huang, and Yongjie Jessica Zhang. "Polygonal finite element-based content-aware image warping." Computational Visual Media 9, no. 2 (January 3, 2023): 367–83. http://dx.doi.org/10.1007/s41095-022-0283-7.
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AbstractMesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.
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Ren, Dan, Zhan Gao, Xiao Yu Xu, and Zhuo Xiang Ren. "Parasitic Capacitance Extraction Using Finite Element Method on Polygonal Mesh through Piecewise Interpolation." Applied Mechanics and Materials 734 (February 2015): 827–33. http://dx.doi.org/10.4028/www.scientific.net/amm.734.827.
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Parasitic capacitance extraction is a critical issue in the area of integrated circuit (IC), its performance heavily depends on the electromagnetic field solver involved. To improve the computation accuracy and efficiency, the interpolation finite element methods (FEM) have been investigated to deal with polygonal elements. Such methods are based on the thinking of generalized barycentric coordinates, such as mostly used mean value coordinates, Sibson coordinates, andetc. They have demonstrated good convergence and accuracy. However, they are time consuming during processing shape functions for Galerkin-schema FEM. A kind of piecewise interpolation method within convex polygonal element is presented. The polygon is divided into triangular sub-regions utilizing its barycenter, where the shape functions related to the whole polygon are conveniently and quickly acquired. The method has excellent performance in computation speed and shows good convergence and high accuracy. A comparison between different FEMs is performed with a typical electrostatic capacitance extraction example.
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Benaroya, H., and M. Rehak. "Finite Element Methods in Probabilistic Structural Analysis: A Selective Review." Applied Mechanics Reviews 41, no. 5 (May 1, 1988): 201–13. http://dx.doi.org/10.1115/1.3151892.
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This review examines the field of structural analysis where finite element methods (FEMs) are used in a probabilistic setting. The finite element method is widely used, and its application in the field of structural analysis is universally accepted as an efficient numerical solution method. The analysis of structures, whether subjected to random or deterministic external loads, has been developed mainly under the assumption that the structure’s parameters are deterministic quantities. For a significant number of circumstances, this assumption is not valid, and the probabilistic aspects of the structure need to be taken into account. We present a review of this emerging field: stochastic finite element methods. The terminology denotes the application of finite element methods with a probabilistic context. This broad definition includes two classes of methods: (i) first- and second-order second moment methods, and (ii) reliability methods. This paper addresses only the first category, leaving the second to specialists in that area. The contribution of this review is to illustrate the similarities and differences of the various methods falling in the first category. Also excluded from this review are simulation methods such as Monte Carlo and response surface, and methods that use FEM to solve deterministic equations (Fokker–Planck) governing probability densities. The essential conclusion is that the second moment methods are mathematically identical to the second order (except for the Neumann expansion). The essential distinction that can be made regarding stochastic FEM is the nature of the structure: It can be deterministic or random. By random structure is meant one with parameters that have associated uncertainties, and thus which must be modeled in a random form. Although the randomness in the structure can be of three types, random variable, random process in space, and random process in time, discussion will be limited to the first two categories. While keeping the emphasis on finite element methods, other techniques involving finite differences, which are useful in the study of multi-degree-of-freedom systems, are briefly mentioned. The present review covers only developments that are derived from the engineering literature, thus implying near-term applicability.
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XUE, B. Y., S. C. WU, W. H. ZHANG, and G. R. LIU. "A SMOOTHED FEM (S-FEM) FOR HEAT TRANSFER PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340001. http://dx.doi.org/10.1142/s021987621340001x.
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By smoothing, via various ways, the compatible strain fields of the standard finite element method (FEM) using the gradient smoothing technique, a family of smoothed FEMs (S-FEMs) has been developed recently. The S-FEM possesses the advantages of both mesh-free methods and the standard FEM and works well with triangular and tetrahedral background cells and elements. Intensive theoretical investigations have shown that the S-FEM models can achieve numerical solutions for many important properties, such as the upper bound solution in strain energy, free from volumetric locking, insensitive to the distortion of the background cells, super-accuracy and super-convergence in displacement or stress solutions or both. Engineering problems, including complex heat transfer problems, have also been analyzed with better accuracy and efficiency. This paper presents the general formulation of the S-FEM for thermal problems in one, two and three dimensions. To examine our formulation, some computational results are compared with those obtained using other established means.
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De Basabe, Jonás D., and Mrinal K. Sen. "Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations." GEOPHYSICS 72, no. 6 (November 2007): T81—T95. http://dx.doi.org/10.1190/1.2785046.
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Purely numerical methods based on finite-element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms. We present formulas for the grid dispersion and stability criteria for some popular finite-element methods (FEM) for wave propagation, namely, classical and spectral FEM. We develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these FEMs for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high-order polynomials, as is the case for spectral FEM. Analysis reveals that for spectral FEM of order four or greater, dispersion is less than 0.2% at four to five nodes per wavelength, and dispersion is not angle dependent. New results can be compared with grid-dispersion results of some classical finite-difference methods (FDM) used for acoustic or elastic wave propagation. Analysis reveals that FDM and classical FEM require a larger sampling ratio than a spectral FEM to obtain results with the same degree of accuracy. The staggered-grid FDM is an efficient scheme, but the dispersion is angle dependent with larger values along the grid axes. On the other hand, spectral FEM of order four or greater is isotropic with small dispersion, making it attractive for simulations with long propagation times.
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Chen, Shizhe, Chao Zhou, and Zhan Wang. "Experimental Study and Comparative Numerical Analysis of the Mechanical Behavior of Extended End-Plate Connections with End-Plate Stiffeners." Open Mechanical Engineering Journal 9, no. 1 (September 16, 2015): 653–65. http://dx.doi.org/10.2174/1874155x01509010653.
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To investigate the influence of end-plate stiffeners on the initial rotational stiffness of extended end-plate internal joints, an experimental program was carried out to investigate the rotational behavior of the joints. Two finite element methods (FEMs) were proposed using ABAQUS software. The stress distribution, plastic development, and deformation characteristics of extended end-plate joints were determined from a comparison of the results of experiments and numerical analyses, and a calculation method for the initial tensile stiffness of the end-plate stiffener was proposed. This investigation presented herein demonstrates that (1) the angle and thickness of the stiffener strongly influence the initial tensile stiffness of the joint; and (2) component-based FEMs can accurately reflect the entire loading process of joints in a simple and efficient manner.
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Kwak, Dae-Kyung, Seog-Hyun Oh, Sung-Jae Lee, Seung-Hun Lee, Yong-Min Lee, and Je-Hyun Yoo. "Effect of the additional anteroposterior blocking screw on nail/medullary canal mismatch after cephalomedullary nailing in unstable pertrochanteric fracture." Bone & Joint Research 11, no. 3 (March 1, 2022): 152–61. http://dx.doi.org/10.1302/2046-3758.113.bjr-2021-0363.r1.
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Aims There are concerns regarding nail/medullary canal mismatch and initial stability after cephalomedullary nailing in unstable pertrochanteric fractures. This study aimed to investigate the effect of an additional anteroposterior blocking screw on fixation stability in unstable pertrochanteric fracture models with a nail/medullary canal mismatch after short cephalomedullary nail (CMN) fixation. Methods Eight finite element models (FEMs), comprising four different femoral diameters, with and without blocking screws, were constructed, and unstable intertrochanteric fractures fixed with short CMNs were reproduced in all FEMs. Micromotions of distal shaft fragment related to proximal fragment, and stress concentrations at the nail construct were measured. Results Micromotions in FEMs without a blocking screw significantly increased as nail/medullary canal mismatch increased, but were similar between FEMs with a blocking screw regardless of mismatch. Stress concentration at the nail construct was observed at the junction of the nail body and lag screw in all FEMs, and increased as nail/medullary canal mismatch increased, regardless of blocking screws. Mean stresses over regions of interest in FEMs with a blocking screw were much lower than regions of interest in those without. Mean stresses in FEMs with a blocking screw were lower than the yield strength, yet mean stresses in FEMs without blocking screws having 8 mm and 10 mm mismatch exceeded the yield strength. All mean stresses at distal locking screws were less than the yield strength. Conclusion Using an additional anteroposterior blocking screw may be a simple and effective method to enhance fixation stability in unstable pertrochanteric fractures with a large nail/medullary canal mismatch due to osteoporosis. Cite this article: Bone Joint Res 2022;11(3):152–161.
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Gao, Zheng Ming, Jun Bo Jia, Sheng Ping He, and Bin Wang. "Study of Normal Force-Displacement Relationship in Spherical Joints." Advanced Materials Research 588-589 (November 2012): 340–43. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.340.
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In order to analyze the structural characteristics or calculate the support force of large-scale complex systems with spherical joints, an approximated method was raised simplifying the force of inner bodies to contact pressure with a hypothesis that the contact zones is ideally spherical. The contact pressure distribution is obtained and normal force-displacement relationship is simulated with finite element methods (FEMs). Finally, the goodness of fit is calculated with statistical hypothetical test theory treating the FEM results as the sample data.
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Wang, Haitao, Xiangyang Zeng, and Ye Lei. "A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers." Shock and Vibration 2019 (April 1, 2019): 1–9. http://dx.doi.org/10.1155/2019/7137036.
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Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.
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Niu, R. P., G. R. Liu, and J. H. Yue. "Development of a Software Package of Smoothed Finite Element Method (S-FEM) for Solid Mechanics Problems." International Journal of Computational Methods 17, no. 02 (October 24, 2019): 1845004. http://dx.doi.org/10.1142/s0219876218450044.
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This paper reports a work to develop a general solver of smoothed finite element methods (S-FEMs) for stress analysis of 2D and 3D solid mechanics problems. In the solver, several efficient algorithms are proposed to construct the real smoothing domains and calculate all the connectivity for later computation. The present implementation of S-FEM distinguishes from the existing published implementation of S-FEM in terms of computing the smoothed strains. The existing implementation uses the volume/area-weighted average method to compute the smoothed strains for the smoothing domain. The present algorithm uses surface/line integrals to compute the smoothed strains strictly following the general [Formula: see text] formulation of S-FEM. Therefore, the present solver is the most general, applicable to any polygon elements, and even to higher order interpolation including using radial basis functions. Numerical experiments for a number of 2D and 3D solid mechanics examples are carried out to demonstrate the effectiveness and reliability of our solver.
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Vavalle, Nicholas A., A. Bradley Thompson, Ashley R. Hayes, Daniel P. Moreno, Joel D. Stitzel, and F. Scott Gayzik. "Investigation of the Mass Distribution of a Detailed Seated Male Finite Element Model." Journal of Applied Biomechanics 30, no. 3 (June 2014): 471–76. http://dx.doi.org/10.1123/jab.2013-0007.
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Accurate mass distribution in computational human body models is essential for proper kinematic and kinetic simulations. The purpose of this study was to investigate the mass distribution of a 50th percentile male (M50) full body finite element model (FEM) in the seated position. The FEM was partitioned into 10 segments, using segment planes constructed from bony landmarks per the methods described in previous research studies. Body segment masses and centers of gravity (CGs) of the FEM were compared with values found from these studies, which unlike the present work assumed homogeneous body density. Segment masses compared well to literature while CGs showed an average deviation of 6.0% to 7.0% when normalized by regional characteristic lengths. The discrete mass distribution of the FEM appears to affect the mass and CGs of some segments, particularly those with low-density soft tissues. The locations of the segment CGs are provided in local coordinate systems, thus facilitating comparison with other full body FEMs and human surrogates. The model provides insights into the effects of inhomogeneous mass on the location of body segment CGs.
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Greco, Francesco, Domenico Umbrello, Serena Di Renzo, Luigino Filice, I. Alfaro, and E. Cueto. "Application of the Nodal Integrated Finite Element Method to Cutting: a Preliminary Comparison with the “Traditional” FEM Approach." Advanced Materials Research 223 (April 2011): 172–81. http://dx.doi.org/10.4028/www.scientific.net/amr.223.172.
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FEM implicit formulation shows specific limitations in processes such as cutting, where large deformation results in a heavy mesh distortion. Powerful rezoning-remeshing algorithms strongly reduce the effects of such a limitation but the computational times are significantly increased and additional errors are introduced. Nodal Integration is a recently introduced technique that allows finite element method to provide more reliable results when mesh becomes distorted in traditional FEMs. Furthermore, volumetric locking phenomenon seems to be avoided by using this integration technique instead of other methods, such as the coupled formulations. In this paper, a comparison between a “classical” FEM simulation and the Nodal Integration one is carried out taking into account a simple orthogonal cutting process.
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Lv, Yujie, Jie Tian, Wenxiang Cong, and Ge Wang. "Experimental Study on Bioluminescence Tomography with Multimodality Fusion." International Journal of Biomedical Imaging 2007 (2007): 1–4. http://dx.doi.org/10.1155/2007/86741.
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To verify the influence of a priori information on the nonuniqueness problem of bioluminescence tomography (BLT), the multimodality imaging fusion based BLT experiment is performed by multiview noncontact detection mode, which incorporates the anatomical information obtained by the microCT scanner and the background optical properties based on diffuse reflectance measurements. In the reconstruction procedure, the utilization of adaptive finite element methods (FEMs) and a priori permissible source region refines the reconstructed results and improves numerical robustness and efficiency. The comparison between the absence and employment of a priori information shows that multimodality imaging fusion is essential to quantitative BLT reconstruction.
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Finley, Sean M., J. Harley Astin, Evan Joyce, Andrew T. Dailey, Douglas L. Brockmeyer, and Benjamin J. Ellis. "FEBio finite element model of a pediatric cervical spine." Journal of Neurosurgery: Pediatrics 29, no. 2 (February 1, 2022): 218–24. http://dx.doi.org/10.3171/2021.7.peds21276.
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OBJECTIVE The underlying biomechanical differences between the pediatric and adult cervical spine are incompletely understood. Computational spine modeling can address that knowledge gap. Using a computational method known as finite element modeling, the authors describe the creation and evaluation of a complete pediatric cervical spine model. METHODS Using a thin-slice CT scan of the cervical spine from a 5-year-old boy, a 3D model was created for finite element analysis. The material properties and boundary and loading conditions were created and model analysis performed using open-source software. Because the precise material properties of the pediatric cervical spine are not known, a published parametric approach of scaling adult properties by 50%, 25%, and 10% was used. Each scaled finite element model (FEM) underwent two types of simulations for pediatric cadaver testing (axial tension and cardinal ranges of motion [ROMs]) to assess axial stiffness, ROM, and facet joint force (FJF). The authors evaluated the axial stiffness and flexion-extension ROM predicted by the model using previously published experimental measurements obtained from pediatric cadaveric tissues. RESULTS In the axial tension simulation, the model with 50% adult ligamentous and annulus material properties predicted an axial stiffness of 49 N/mm, which corresponded with previously published data from similarly aged cadavers (46.1 ± 9.6 N/mm). In the flexion-extension simulation, the same 50% model predicted an ROM that was within the range of the similarly aged cohort of cadavers. The subaxial FJFs predicted by the model in extension, lateral bending, and axial rotation were in the range of 1–4 N and, as expected, tended to increase as the ligament and disc material properties decreased. CONCLUSIONS A pediatric cervical spine FEM was created that accurately predicts axial tension and flexion-extension ROM when ligamentous and annulus material properties are reduced to 50% of published adult properties. This model shows promise for use in surgical simulation procedures and as a normal comparison for disease-specific FEMs.
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Hohmann, Ansgar, Uwe Wolfram, Martin Geiger, Andrew Boryor, Christian Sander, Rolf Faltin, Kurt Faltin, and Franz Guenter Sander. "Periodontal Ligament Hydrostatic Pressure with Areas of Root Resorption after Application of a Continuous Torque Moment." Angle Orthodontist 77, no. 4 (July 1, 2007): 653–59. http://dx.doi.org/10.2319/060806-234.
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Abstract Objective: To evaluate the risk of root resorption, individual finite element models (FEMs) of extracted human maxillary first premolars were created, and the distribution of the hydrostatic pressure in the periodontal ligament (PDL) of these models was simulated. Materials and Methods: A continuous lingual torque of 3 Nmm and 6 Nmm respectively was applied in vivo to the aforementioned teeth. After extraction, FEMs of these double-rooted teeth were created based on high-resolution microcomputed tomographics (micro CT, voxel size: 35 microns). This high volumetric resolution made the recognition of very small resorption lacunae possible. Scanning electron micrographs of the root surfaces were created as well. This enabled the investigation of advantages and disadvantages of the different imaging techniques from the viewpoint of the examination of root resorption. Using the FEMs, the same loading conditions as applied in vivo were simulated. Results: The results of clinical examination and simulations were compared using the identical roots of the teeth. The regions that showed increased hydrostatic pressure (>0.0047 MPa) correlated well with the locations of root resorption for each tooth. Increased torque resulted in increased high-pressure areas and increased magnitudes of hydrostatic pressure, correlating with the experiments. Conclusion: If hydrostatic pressure exceeds typical human capillary blood pressure in the PDL, the risk of root resorption increases.
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Wang, Yanzhong, Peng Liu, and Delong Dou. "Investigation of Load Capacity of High-Contact-Ratio Internal Spur Gear Drive with Arc Path of Contact." Applied Sciences 12, no. 7 (March 25, 2022): 3345. http://dx.doi.org/10.3390/app12073345.
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Tooth root bending stress and surface contact stress are two major determinants of the load carrying capacity of gear drives. Generally, a high contact ratio has the potential to enhance the gear strength. In this paper, the basic procedures and methods for constructing a high-contact-ratio (HCR) internal spur gear pair with the arc path of the contact are presented. The effects of design and modification parameters such as deflection angle, modification angle, and addendum coefficient on gear drive are analyzed in detail based on 2D finite-element models (FEMs). A comparison of experimental and finite-element analyses (FEA) of the bending stress, contact stress, and contact ratio between HCR and involute internal spur gear drives was conducted to demonstrate the advantages of the HCR gear drive in terms of load capacity. The results show that appropriately increasing the deflection angle and addendum coefficient is beneficial for reducing bending and contact stresses. It was also observed that the bending and contact stresses of a HCR pinion are lower than those of an involute one. Moreover, the contact ratio increases with input torque.
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SAKURAI, Hideyuki, Toshiko YAMADA, and Toshio NAGASHIMA. "421 Modelling thin inclusions in extended finite element methods." Proceedings of The Computational Mechanics Conference 2008.21 (2008): 484–85. http://dx.doi.org/10.1299/jsmecmd.2008.21.484.
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Weichert, Frank, Lars Walczak, Denis Fisseler, Tobias Opfermann, Mudassar Razzaq, Raphael Münster, Stefan Turek, et al. "Simulation of Intra-Aneurysmal Blood Flow by Different Numerical Methods." Computational and Mathematical Methods in Medicine 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/527654.
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The occlusional performance of sole endoluminal stenting of intracranial aneurysms is controversially discussed in the literature. Simulation of blood flow has been studied to shed light on possible causal attributions. The outcome, however, largely depends on the numerical method and various free parameters. The present study is therefore conducted to find ways to define parameters and efficiently explore the huge parameter space with finite element methods (FEMs) and lattice Boltzmann methods (LBMs). The goal is to identify both the impact of different parameters on the results of computational fluid dynamics (CFD) and their advantages and disadvantages. CFD is applied to assess flow and aneurysmal vorticity in 2D and 3D models. To assess and compare initial simulation results, simplified 2D and 3D models based on key features of real geometries and medical expert knowledge were used. A result obtained from this analysis indicates that a combined use of the different numerical methods, LBM for fast exploration and FEM for a more in-depth look, may result in a better understanding of blood flow and may also lead to more accurate information about factors that influence conditions for stenting of intracranial aneurysms.
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Sumit, Rahul Shukla, and A. K. Sinha. "Finite element method coupled with TLBO for shape control optimization of piezoelectric bimorph in COMSOL Multiphysics." SIMULATION 97, no. 9 (July 6, 2021): 635–44. http://dx.doi.org/10.1177/00375497211025640.
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Finite element methods (FEMs) are more advantageous for analyzing complex geometry and structures than analytical methods. Local search optimization techniques are suitable for the unimodal problem because final result depends on the starting point. On the other hand, to optimize the parameters of multi-minima/maxima problems, global optimization-based FEM is used. Unfortunately, global optimization solvers are not present in, COMSOL Multiphysics, a versatile tool for solving varieties of problems using FEM. Teaching–learning-based optimization (TLBO) is a global optimization technique and does not require any algorithm-specific parameter. In this paper, FEM is coupled with TLBO algorithms in COMSOL Multiphysics for solving the global optimization problem. The TLBO algorithm is implemented in COMSOL Multiphysics using the JAVA application programming interface and tested with the standard benchmark functions. The solutions of the standard benchmark problem in COMSOL Multiphysics are in close agreement with the results presented in literature. Furthermore, the optimization procedure thus established is used for the optimization of actuator voltage for piezoelectric bimorphs to achieve the desired shapes. The FEM-based TLBO method is compared with two optimization methods present in COMSOL Multiphysics for a shape control problem; (i) method of moving asymptotes (MMA) and (ii) Bound Optimization BY Quadratic Approximation (BOBYQA). The root mean square error shows that the FEM-based TLBO algorithm converges to a global minimum and gives the same result (19.3 nm) at multiple runs, whereas MMA and BOBYQA trapped in local minimum and gave different results for different starting points.
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Lin, Jianhui, Junqing Xue, Fuyun Huang, and Baochun Chen. "Research on the Internal Thermal Boundary Conditions of Concrete Closed Girder Cross-Sections under Historically Extreme Temperature Conditions." Applied Sciences 10, no. 4 (February 14, 2020): 1274. http://dx.doi.org/10.3390/app10041274.
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The accuracy of the finite element model (FEM) for concrete closed girder cross-sections is significantly influenced by thermal boundary conditions. The internal thermal boundary conditions can be simulated by inputting the convection heat transfer coefficient and the temperatures inside the cavities or by establishing air elements in the FEM. In order to analyze the influence of different simulation methods for the internal thermal boundary conditions on temperature distributions for concrete closed girder cross-sections, the temperature distributions on the cross-sections of a box girder, small box girders, and adjacent box girders were monitored, and the corresponding FEMs were implemented. By comparing the temperature data obtained from the field test and FEMs, the numerical hourly temperature curves calculated by using the measured temperatures inside the cavities provide the closest agreement with the measured results; however, the measurements of the temperatures on site are cost- and time-prohibitive. When there is a lack of measured temperatures inside the cavities, the numerical hourly temperature curves calculated by establishing air elements in the FEM provide the closest agreement. The influences of different simulation methods for the internal thermal boundary conditions on the highest hourly average effective temperatures and the trends of the vertical temperature gradients for concrete closed girder cross-sections were small. The FEM with air elements can be adopted to analyze the temperature distributions on concrete closed girder cross-sections under historically extreme temperature conditions. It can be predicted that the longitudinal thermal movement of concrete closed girders would be underestimated by considering variations in the one-year measured average effective temperature of the cross-sections or the Chinese-code-specified design effective temperature for the highway bridge structures, which are thus unconservative for engineering applications. The Chinese-code-specified design vertical temperature gradients are conservative for the bridge deck surface and unconservative for the bottom flange.
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Chen, Meng, Ming Li, and G. R. Liu. "Mathematical Basis of G Spaces." International Journal of Computational Methods 13, no. 04 (July 4, 2016): 1641007. http://dx.doi.org/10.1142/s0219876216410073.
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This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.
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Sadeghi, A., S. Μ. Seyyed Barzegar, and M. Yazdani-Asrami. "A Simple and Fast Computation Equivalent Circuit Model to Investigate the Effect of Tape Twisting on the AC Loss of HTS Cables." Engineering, Technology & Applied Science Research 12, no. 1 (February 12, 2022): 8168–74. http://dx.doi.org/10.48084/etasr.4382.
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This paper aims to evaluate the AC loss of a High Temperature Superconducting (HTS) cable with respect to the twisting angle while considering mechanical constraints in an iterative approach. A 1km 22.9kV AC HTS cable was selected in this study to assess the impact of the twisting angle alterations. The electromagnetic behavior of the selected HTS cable was modeled using an Equivalent Circuit Model (ECM). After the implementation of this model in MATLAB/SIMULINK, a series of simulations were performed without the consideration of mechanical limits. They showed that the increase in the twisting angle leads to the decrease of the AC loss. Afterwards, simulations were conducted to reduce the AC loss, while mechanical limits were taken into account. This improvement could reduce the AC loss by 27.41% with a much lower computation time than Finite Element Methods (FEMs).
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Lanzetta, Michele, Armin Gharibi, Marco Picchi Scardaoni, and Claudia Vivaldi. "FEM and Analytical Modeling of the Incipient Chip Formation for the Generation of Micro-Features." Materials 14, no. 14 (July 6, 2021): 3789. http://dx.doi.org/10.3390/ma14143789.
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This paper explores the modeling of incipient cutting by Abaqus, LS-Dyna, and Ansys Finite Element Methods (FEMs), by comparing also experimentally the results on different material classes, including common aluminum and steel alloys and an acetal polymer. The target application is the sustainable manufacturing of gecko adhesives by micromachining a durable mold for injection molding. The challenges posed by the mold shape include undercuts and sharp tips, which can be machined by a special diamond blade, which enters the material, forms a chip, and exits. An analytical model to predict the shape of the incipient chip and of the formed grove as a function of the material properties and of the cutting parameters is provided. The main scientific merit of the current work is to approach theoretically, numerically, and experimentally the very early phase of the cutting tool penetration for new sustainable machining and micro-machining processes.
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Zhang, Lei, and Jinhai Zhang. "Local wavefield refinement using Fourier interpolation and boundary extrapolation for finite-element method based on domain reduction method." GEOPHYSICS 87, no. 3 (April 18, 2022): T251—T263. http://dx.doi.org/10.1190/geo2021-0503.1.
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The domain reduction method based on the finite-element method (FEM) is promising for multiscale seismic wave simulations for local complex structures and rough topography. However, a transition region is required to refine the wavefields from coarse to fine grids, which may lead to strong artifacts. Traditional wavefield interpolation methods can only handle a small upsampling ratio due to their low accuracy. Here, we propose a high accuracy upsampling method using Fourier interpolation and boundary extrapolation. It requires that the wavefield in the transition region is evenly sampled, which may slightly reduce the flexibility of FEMs. Fortunately, this constraint only exists in two layers of nodes, in which the coarse and fine grids are collocated. To further apply our interpolation method to the wavefield upsampling on the nonuniform grid, we adopt cubic interpolation within the local region of interest, which is adequate in accuracy for regularizing the wavefield on the fine nonuniform grid. For a topographic surface, we perform wavefield extrapolation on the ground surface to avoid abnormal amplitude variations below and beyond the surface, which can greatly reduce potential artifacts caused by the Fourier interpolation. Numerical experiments find that our method is superior to traditional interpolation methods in accuracy, especially for large upsampling ratios. Its relative error is less than 2% even for a 40-time upsampling; in contrast, the relative error of linear and cubic interpolation is up to 90% and 41% in the same situation, respectively. We further verify the feasibility of our method for 3D heterogeneous models with rough topography, multilayer heterogeneity, and random perturbations of background models. The proposed method yields a significant speeding of the multiscale seismic simulation using the FEM for 3D models with complex local structures and topographies while being highly accurate.
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Liu, G. R. "A Novel Pick-Out Theory and Technique for Constructing the Smoothed Derivatives of Functions for Numerical Methods." International Journal of Computational Methods 15, no. 03 (April 25, 2018): 1850070. http://dx.doi.org/10.1142/s0219876218500706.
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In order to solve partial differential equations (PDEs) numerically, one first needs to approximate the field functions (such as the displacement functions), and then obtain the derivatives of the field functions (such as the strains), by directly differentiating the field functions. Using such direct-derivatives in formulating a numerical method is common and is used in the standard finite element method (FEM), but such models are often found to be “stiff”. In the weakened weak (W2) formulations, it is found that the use of properly re-constructed derivatives can be beneficial in ways because the model can become “softer”. This paper presents a novel “pick-out” theory and technique for re-constructing the derivatives (such as the strains) of functions defined in a local domain, using smoothing operations. The local domain can be a smoothing domain used in the smoothed finite element methods (S-FEMs), smoothed point interpolation methods (S-PIMs), and smoothed particle hydrodynamics (SPH). It is discovered that through the use of a set of linearly independent smoothing functions that are continuous in the local domain, one can simply pick out various orders of smoothed derivatives (at the center of a domain) from any given function that may discontinuous (strictly) inside the local domain. As long as the smoothing function is continuous in the smoothing domain, the picked out “smoothed derivatives” are equivalent (in a local integral sense) to the compatible direct-derivatives, which ensures the convergence of the smoothed model (such as the S-FEM) when the smoothing domains shrinking to zero. The pick-out technique can be used in strong, weak, local weak, weak-strong, or weakened weak formulations to create stable and convergent numerical models. It may offer a new window of opportunity to develop new effective numerical models using smoothed derivatives (strains) that are “softer” and can produce accurate solutions also in the derivatives (strains and stresses) of the field functions (displacements).
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YANAGIMOTO, Jun. "Analytical Methods of Rolling for Understanding for Finite Element Analysis of Plastic Working." Journal of the Japan Society for Technology of Plasticity 55, no. 644 (2014): 843–47. http://dx.doi.org/10.9773/sosei.55.843.
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Yao, Wenqing, Fuwei Sheng, Xiaoyuan Wei, Lei Zhang, and Yuan Yang. "Propagation characteristics of ultrasonic guided waves in continuously welded rail." Modern Physics Letters B 31, no. 19-21 (July 27, 2017): 1740075. http://dx.doi.org/10.1142/s0217984917400759.
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Rail defects cause numerous railway accidents. Trains are derailed and serious consequences often occur. Compared to traditional bulk wave testing, ultrasonic guided waves (UGWs) can provide larger monitoring ranges and complete coverage of the waveguide cross-section. These advantages are of significant importance for the non-destructive testing (NDT) of the continuously welded rail, and the technique is therefore widely used in high-speed railways. UGWs in continuous welded rail (CWR) and their propagation characteristics have been discussed in this paper. Finite element methods (FEMs) were used to accomplish a vibration modal analysis, which is extended by a subsequent dispersion analysis. Wave structure features were illustrated by displacement profiles. It was concluded that guided waves have the ability to detect defects in the rail via choice of proper mode and frequency. Additionally, thermal conduction that is caused by temperature variation in the rail is added into modeling and simulation. The results indicated that unbalanced thermal distribution may lead to the attenuation of UGWs in the rail.
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Meyghani, Bahman, and Mokhtar B. Awang. "Prediction of the Temperature Distribution During Friction Stir Welding (Fsw) With A Complex Curved Welding Seam: Application In The Automotive Industry." MATEC Web of Conferences 225 (2018): 01001. http://dx.doi.org/10.1051/matecconf/201822501001.
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Advanced welding of complex geometries promises significant development in the automotive industry. Friction Stir Welding (FSW) as a solid-state welding technique has spread quickly since its initial development by TWI in 1991. It has found applications in various industries, including railway, automotive, maritime and aerospace. Temperature during FSW plays a significant role, therefore thermal analysis of the process provides the opportunity to understand the process in detail, and also allows one to save energy and cost as well. However, experimental investigation of the thermal behaviour is challenging, because of inaccuracy in the measuring instruments. Thus, Finite Element Methods (FEMs) offer an appropriate approach for thermal modelling of the process. There is also a dilemma in defining the perpendicular movement of the tool on a curved surface. To clarify the problem, the tool needs to follow a regular pattern during curved movement, and it should have a perpendicular position to the surface at each point. However, previous literature modelled only a single point movement for the tool. Thus, the finite element package needs to be modified to develop a precise perpendicular movement for the tool. In this paper, a VDISP user defined subroutine is used to modify Abaqus® software for thermal analysis of a complex curved plate. The results of the paper show that the problem of the perpendicular movement of the tool is resolved and the thermal behaviour of the FSW is done with remarkable accuracy.
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HAMA, Takayuki. "Methods of Press-forming Simulation for Understanding for Finite Element Analysis of Plastic Working." Journal of the Japan Society for Technology of Plasticity 55, no. 641 (2014): 491–96. http://dx.doi.org/10.9773/sosei.55.491.
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Yuan, Daizhu, Zhanyu Wu, Siwei Luo, Qiang Zou, Zihao Zou, and Chuan Ye. "Impact of Femoral Neck Cortical Bone Defect Induced by Core Decompression on Postoperative Stability: A Finite Element Analysis." BioMed Research International 2022 (May 20, 2022): 1–13. http://dx.doi.org/10.1155/2022/3667891.
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Objective. To analyze the impact of femoral neck cortical bone defect induced by core decompression on postoperative biomechanical stability using the finite element method. Methods. Five finite element models (FEMs) were established, including the standard operating model and four models of cortical bone defects at different portions of the femoral neck (anterior, posterior, superior, and inferior). The maximum stress of the proximal femur was evaluated during normal walking and walking downstairs. Results. Under both weight-bearing conditions, the maximum stress values of the five models were as follows: femoral neck (inferior) > femoral neck (superior) > femoral neck (posterior) > femoral neck (anterior) > standard operation. Stress concentration occurred in the areas of femoral neck cortical bone defect. Under normal walking, the maximum stress of four bone defect models and its increased percentage comparing the standard operation were as follows: anterior (17.17%), posterior (39.02%), superior (57.48%), and inferior (76.42%). The maximum stress was less than the cortical bone yield strength under normal walking conditions. Under walking downstairs, the maximum stress of four bone defect models and its increased percentage comparing the standard operation under normal walking were as follows: anterior (36.75%), posterior (67.82%), superior (83.31%), and inferior (103.65%). Under walking downstairs conditions, the maximum stress of bone defect models (anterior, posterior, and superior) was less than the yield strength of cortical bone, while the maximum stress of bone defect model (inferior) excessed yield strength value. Conclusions. The femoral neck cortical bone defect induced by core decompression can carry out normal walking after surgery. To avoid an increased risk of fracture after surgery, walking downstairs should be avoided when the cortical bone defect is inferior to the femoral neck except for the other three positions (anterior, posterior, and superior).
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YOSHIDA, Yoshinori. "Methods of Shearing Process Simulation for Understanding for Finite Element Analysis of Plastic Working." Journal of the Japan Society for Technology of Plasticity 56, no. 648 (2015): 8–12. http://dx.doi.org/10.9773/sosei.56.8.
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Huang, Xiaowei, Andreas K. Nussler, Marie K. Reumann, Peter Augat, Maximilian M. Menger, Ahmed Ghallab, Jan G. Hengstler, Tina Histing, and Sabrina Ehnert. "Contribution to the 3R Principle: Description of a Specimen-Specific Finite Element Model Simulating 3-Point-Bending Tests in Mouse Tibiae." Bioengineering 9, no. 8 (July 25, 2022): 337. http://dx.doi.org/10.3390/bioengineering9080337.
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Bone mechanical properties are classically determined by biomechanical tests, which normally destroy the bones and disable further histological or molecular analyses. Thus, obtaining biomechanical data from bone usually requires an additional group of animals within the experimental setup. Finite element models (FEMs) may non-invasively and non-destructively simulate mechanical characteristics based on material properties. The present study aimed to establish and validate an FEM to predict the mechanical properties of mice tibiae. The FEM was established based on µCT (micro-Computed Tomography) data of 16 mouse tibiae. For validating the FEM, simulated parameters were compared to biomechanical data obtained from 3-point bending tests of the identical bones. The simulated and the measured parameters correlated well for bending stiffness (R2 = 0.9104, p < 0.0001) and yield displacement (R2 = 0.9003, p < 0.0001). The FEM has the advantage that it preserves the bones’ integrity, which can then be used for other analytical methods. By eliminating the need for an additional group of animals for biomechanical tests, the established FEM can contribute to reducing the number of research animals in studies focusing on bone biomechanics. This is especially true when in vivo µCT data can be utilized where multiple bone scans can be performed with the same animal at different time points. Thus, by partially replacing biomechanical experiments, FEM simulations may reduce the overall number of animals required for an experimental setup investigating bone biomechanics, which supports the 3R (replace, reduce, and refine) principle.
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Hasani Najafabadi, S. H., Stefano Zucca, D. S. Paolino, G. Chiandussi, and Massimo Rossetto. "Numerical Computation of Stress Intensity Factors in Ultrasonic Very-High-Cycle Fatigue Tests." Key Engineering Materials 754 (September 2017): 218–21. http://dx.doi.org/10.4028/www.scientific.net/kem.754.218.
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The correct computation of the Stress Intensity Factor (SIF) in ultrasonic Very-High-Cycle Fatigue (VHCF) loading conditions is a key issue when investigating the crack growth rate curve with pre-cracked specimens or when evaluating critical SIF values from fracture surfaces of failed specimens. Dynamic conditions related to the resonance of the vibrating specimen, contact nonlinearity between crack faces and stress singularity at the crack tip make the SIF computation difficult and cumbersome. Generally, numerical computation through Finite Element Models (FEMs) under non-linear dynamic conditions makes use of direct integration methods (implicit or explicit). However, in the high frequency regime of ultrasonic VHCF tests, the procedure may lead to an unacceptable computational time. In order to reduce the computational time, a hybrid procedure based on the Harmonic Balance Method (HBM) and on the Virtual Crack Closure Technique (VCCT) is originally presented and applied in this paper. The dynamic field parameters calculated with the HBM are used as input data for the computation of the SIF through the VCCT.
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Do, Ngoan T., Mustafa Gül, and Saeideh Fallah Nafari. "Continuous Evaluation of Track Modulus from a Moving Railcar Using ANN-Based Techniques." Vibration 3, no. 2 (June 22, 2020): 149–61. http://dx.doi.org/10.3390/vibration3020012.
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Track foundation stiffness (also referred as the track modulus) is one of the main parameters that affect the track performance, and thus, quantifying its magnitudes and variations along the track is widely accepted as a method for evaluating the track condition. In recent decades, the train-mounted vertical track deflection measurement system developed at the University of Nebraska–Lincoln (known as the MRail system) appears as a promising tool to assess track structures over long distances. Numerical methods with different levels of complexity have been proposed to simulate the MRail deflection measurements. These simulations facilitated the investigation and quantification of the relationship between the vertical deflections and the track modulus. In our previous study, finite element models (FEMs) with a stochastically varying track modulus were used for the simulation of the deflection measurements, and the relationships between the statistical properties of the track modulus and deflections were quantified over different track section lengths using curve-fitting approaches. The shortcoming is that decreasing the track section length resulted in a lower accuracy of estimations. In this study, the datasets from the same FEMs are used for the investigations, and the relationship between the measured deflection and track modulus averages and standard deviations are quantified using artificial neural networks (ANNs). Different approaches available for training the ANNs using FEM datasets are discussed. It is shown that the estimation accuracy can be significantly increased by using ANNs, especially when the estimations of track modulus and its variations are required over short track section lengths, ANNs result in more accurate estimations compared to the use of equations from curve-fitting approaches. Results also show that ANNs are effective for the estimations of track modulus even when the noisy datasets are used for training the ANNs.
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Gołębiowski, Lesław, Marek Gołębiowski, Damian Mazur, and Andrzej Smoleń. "Analysis of axial flux permanent magnet generator." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 4 (July 1, 2019): 1177–89. http://dx.doi.org/10.1108/compel-10-2018-0415.
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Purpose The purpose of this paper is to compare the methods of calculating the parameters of air-cored stator flux permanent magnet generator and to compare these results with the measurements of the designed and manufactured generator. The generator is to be designed for operation in a wind power plant. Design/methodology/approach An analytical method and 2D and 3D finite element methods (FEMs) were used to calculate the parameters of the coreless permanent magnet axial generator. The analytical method and 2D FEM were applied to individual cross-sections through the air gap of the machine. After the design and construction of the generator and measuring station, the results of calculations and measurements were compared. Findings The results of investigated calculation methods and measurements were found to be mutually compatible. Analytical methods and 2D FEM required proper interpretation of the results when comparing them with the 3D FEM. The results of the measurements and calculations showed the usefulness of the generator for operation in a wind power plant. Originality/value Full comparison of results of 2D and 3D calculations with the results of the measurements on the machine model confirmed the usefulness of fast 2D methods for the analysis of coreless generators. The results differed by the effects of leakage inductance of windings’ front connections. The application of an axial generator designed with the described methods in a wind turbine showed its proper operation.
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Yoshida, Takumi, Takeshi Okuzono, and Kimihiro Sakagami. "A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation." Buildings 12, no. 2 (January 23, 2022): 105. http://dx.doi.org/10.3390/buildings12020105.
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Wave-based acoustics simulation methods such as finite element method (FEM) are reliable computer simulation tools for predicting acoustics in architectural spaces. Nevertheless, their application to practical room acoustics design is difficult because of their high computational costs. Therefore, we propose herein a parallel wave-based acoustics simulation method using dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM) for simulating room acoustics at large-scale scenes. It can model sound absorbers with locally reacting frequency-dependent impedance boundary conditions (BCs). The method can use domain decomposition method (DDM)-based parallel computing to compute acoustics in large rooms at kilohertz frequencies. After validation studies of the proposed method via impedance tube and small cubic room problems including frequency-dependent impedance BCs of two porous type sound absorbers and a Helmholtz type sound absorber, the efficiency of the method against two implicit TD-FEMs was assessed. Faster computations and equivalent accuracy were achieved. Finally, acoustics simulation of an auditorium of 2271 m3 presenting a problem size of about 150,000,000 degrees of freedom demonstrated the practicality of the DDM-based parallel solver. Using 512 CPU cores on a parallel computer system, the proposed parallel solver can compute impulse responses with 3 s time length, including frequency components up to 3 kHz within 9000 s.