Статті в журналах: "PRISMATIC ELEMENT"

1

Klochkov, Yu V., A. P. Nikolaev, O. V. Vakhnina, and M. Yu Klochkov. "Finit element model of pipeline discretization by prismatic elements." IOP Conference Series: Materials Science and Engineering 698 (December 18, 2019): 066012. http://dx.doi.org/10.1088/1757-899x/698/6/066012.

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2

Gong, Jian, John L. Volakis, and Helen T. G. Wang. "Efficient finite element simulation of slot antennas using prismatic elements." Radio Science 31, no. 6 (November 1996): 1837–44. http://dx.doi.org/10.1029/96rs02423.

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3

LEUNG, A. Y. T., and B. ZHU. "HEXAHEDRAL FOURIER p-ELEMENTS FOR VIBRATION OF PRISMATIC SOLIDS." International Journal of Structural Stability and Dynamics 04, no. 01 (March 2004): 125–38. http://dx.doi.org/10.1142/s0219455404001100.

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Fourier p-elements of trapezoidal and cubical hexahedron shapes for the free vibration analysis of 3D elastic solids are presented. Trigonometric functions are used as enriching functions to avoid ill-conditioning problems associated with high order polynomials. The element matrices are analytically integrated in closed form. With the additional Fourier degrees-of-freedom, the accuracy of the computed natural frequencies is greatly improved. As an example, the natural frequencies of a cantilever cube are analyzed by a rectangular hexahedron Fourier p-element, two trapezoidal hexahedron Fourier p-elements and the conventional linear finite elements. The results show that the convergence rate of the present elements is very fast with respect to the number of trigonometric terms. The present elements also produce higher accurate modes than the linear finite elements for the same number of degrees-of-freedom. Furthermore, the first six natural frequencies of a cantilever hexagonal prism and a number of concrete dams with different lengths are given as numerical examples.

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4

Ghesmi, Mahdi, and Bettar Ould el Moctar. "Application of contact elements to represent prismatic mechanical couplings." MATEC Web of Conferences 272 (2019): 01028. http://dx.doi.org/10.1051/matecconf/201927201028.

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Accurate prediction of loads on mechanical couplings is crucial in assessment of loads on coupled structures and in optimization of mechanical coupling design. In this paper, a contact element model is introduced to represent prismatic joints. A twofold pushing convoy in shallow water was taken for time domain numerical simulations in regular waves. The prismatic joints interconnecting the convoy bodies allowed relative heave and pitch motions of the bodies relative to each other. The articulation forces and body motions were compared to model basin measurements to assess the reliability of contact element model. The contact element model could simulate the prismatic joints efficiently and it provided a suitable method to idealize free and suppressed modes at articulation locations.

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5

Dharma, Adrian Pramudita, and Bambang Suryoatmono. "Non-Linear Buckling Analysis of Axially Loaded Column with Non-Prismatic I-Section." Journal of the Civil Engineering Forum 5, no. 3 (September 18, 2019): 263. http://dx.doi.org/10.22146/jcef.47607.

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In order to use material efficiently, non-prismatic column sections are frequently employed. Tapered-web column cross-sections are commonly used, and design guides of such sections are available. In this study, various web-and-flange-tapered column sections were analysed numerically using finite element method to obtain each buckling load assuming the material as elastic-perfectly plastic material. For each non-prismatic column, the analysis was also performed assuming the column is prismatic using average cross-section with the same length and boundary conditions. Buckling load of the prismatic columns were obtained using equation provided by AISC 360-16. This study proposes a multiplier that can be applied to the buckling load of a prismatic column with an average cross-section to acquire the buckling load of the corresponding non-prismatic column. The multiplier proposed in this study depends on three variables, namely the depth tapered ratio, width tapered ratio, and slenderness ratio of the prismatic section. The equation that uses those three variables to obtain the multiplier is obtained using regression of the finite element results with a coefficient of determination of 0.96.

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6

Maksymiuk, Yurii, Andrii Kozak, Ivan Martyniuk, and Oleksandr Maksymiuk. "Features of derivation of formulas for calculation of nodal reactions and coefficients of matrix of rigidity of a finite element with averaged mechanical and geometrical parameters." Building constructions. Theory and Practice, no. 8 (November 29, 2021): 97–108. http://dx.doi.org/10.32347/2522-4182.8.2021.97-108.

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Currently, the most widely used finite element method for the calculation of spatial structures, significant progress in the development of which is associated with the work of domestic and foreign scientists. In Ukrainian publications the problems of theoretical substantiation of the finite element method and its connection with other methods are considered, concrete types of finite elements and their application to various problems of mechanics of a continuous environment are studied. Much attention is paid to the choice of the appropriate shape of the finite element, the type and degree of approximating functions, as well as the development of methods for deriving stiffness matrices. The study of prismatic bodies with constants along one of the coordinates of mechanical and geometric parameters is most appropriate to carry out on the basis of the semi-analytical method of finite elements. Its essence is a combination of finite element sampling and decomposition of displacements in the characteristic direction by a system of trigonometric coordinate functions. The analysis of the literature shows that the issues related to the application of the semi-analytical finite element method to the calculation of thin-walled prismatic bodies in elastic-plastic, and massive even in elastic formulations, have not been properly reflected. In addition, there are no publications in this area devoted to the development of universal prismatic finite elements that allow you to explore massive, thin-walled and combined structures. The direction of this study is to create on the basis of the semi-analytical method of finite elements of an effective apparatus for numerical analysis of the stress-strain state of massive and thin-walled arbitrarily loaded properties of the material and solve a number of new practically important problems. Therefore, in this work, based on the moment diagram of finite elements, formulas for calculating nodal reactions and stiffness matrix coefficients of a finite element with averaged mechanical and geometric parameters for the study of massive, thin-walled and combined structures are derived.

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7

Coulomb, J. L., F. X. Zgainski, and Y. Marechal. "A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements." IEEE Transactions on Magnetics 33, no. 2 (March 1997): 1362–65. http://dx.doi.org/10.1109/20.582509.

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8

Bai, Rui, Si-Wei Liu, Siu-Lai Chan, and Feng Yu. "Flexural Buckling Strength of Tapered-I-Section Steel Columns Based on ANSI/AISC-360-16." International Journal of Structural Stability and Dynamics 19, no. 11 (October 23, 2019): 1950134. http://dx.doi.org/10.1142/s0219455419501347.

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Steel tapered-I-columns are popular in modern buildings due to its material efficiency and the convenience in construction. For evaluating the flexural buckling strength of these columns, the current design methods with empirical and idealized assumptions are sometimes unreliable, especially for slender columns with significant tapering ratios. To accurately calculate the flexural buckling resistance, this paper proposes a numerical framework for tapered-I-sections. The direct analysis method (DM) with the non-prismatic high-order beam-column elements considering the factors, including the second-order effects, the geometric imperfections, and the residual stresses is developed. A new shape-function representing the most critical initial out-of-straightness curve of a tapered member is adopted. An advanced non-prismatic beam-column element incorporating this imperfection shape-function named the curved tapered-three-hinges (TTH) element is derived. With the availability of the internal degree-of-freedoms, the one-element-per-member (OEPM) modeling method is permitted. Sequentially, a series of parametric studies using the proposed numerical method are conducted for generating the buckling curves for the non-prismatic columns with various tapered-stiffness ratios. The sophisticated finite-element method is adopted to verify the proposed numerical framework. Based on the proposed numerical approach, the design method in ANSI/AISC-360-16 is modified for tapered-I-section columns.

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9

Ivanchenko, Grigory, Yurii Maksimyuk, Andriy Kozak, and Ivan Martyniuk. "CONSTRUCTION OF SOLVING EQUATIONS OF SEMI-ANALYTICAL METHOD OF FINISHED ELEMENTS FOR PRISMATIC BODIES OF COMPLEX SHAPE." Management of Development of Complex Systems, no. 46 (June 24, 2021): 55–62. http://dx.doi.org/10.32347/2412-9933.2021.46.55-62.

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The article presents an effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can take place beyond the elasticity of the material. The equations of the semi-analytical finite element method (SAFEM) when used to decompose the displacements of Fourier series. The main relations between the spatial problem of the theory of elasticity in a curvilinear coordinate system and the theory of plastic flow for an isotropically reinforcing material under the Mises fluidity condition are presented. In accordance with the method of the moment scheme of finite elements (MSFE), the expressions of deformations of the prismatic finite element due to the nodal values of amplitude displacements are obtained. Formulas for calculating the stiffness matrix coefficients of a finite element (FE) with variable and averaged in the cross-sectional plane mechanical and geometric parameters are derived.

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10

Suprun, T. T. "LOCAL APPROACH FOR EVALUATING HEAT TRANSFER OF PRISMATIC ELEMENTS ON A FLAT SURFACE." Eurasian Physical Technical Journal 18, no. 3 (37) (September 24, 2021): 43–47. http://dx.doi.org/10.31489/2021no3/43-47.

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Heat-exchange prismatic elements located on a flat surface are typical for many technical applications. The purpose of the work is to develop local approach for evaluating heat transfer of working surfaces based on local control of thermophysical parameters in characteristic zones of the working environment, using the methods of heat and mass analogy and hot-wire anemometry. The local approach allows more accurately diagnosing the types of flow in the boundary layer of a streamlined element and thereby, the temperature state of individual prismatic elements and the entire arrangement as a whole is determined more accurately. For calculating the local heat transfer of each face of the prism separately and the average surface heat transfer depending on the geometric and operating parameters equations of similarity are proposed.

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11

Shahba, Ahmad, Reza Attarnejad, and Mehran Eslaminia. "Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions." Shock and Vibration 19, no. 2 (2012): 187–204. http://dx.doi.org/10.1155/2012/786191.

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The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

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12

Pini, G. "Prismatic versus tetrahedral elements in three-dimensional finite element analyses of subsurface systems." Numerical Methods for Partial Differential Equations 7, no. 1 (1991): 25–41. http://dx.doi.org/10.1002/num.1690070104.

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13

Mataix, Vicente, Fernando G. Flores, Riccardo Rossi, and Eugenio Oñate. "Triangular prismatic solid-shell element with generalised deformation description." European Journal of Computational Mechanics 27, no. 1 (June 23, 2017): 1–32. http://dx.doi.org/10.1080/17797179.2017.1340013.

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14

Torby, B. J., and I. Kimura. "Dynamic Modeling of a Flexible Manipulator With Prismatic Links." Journal of Dynamic Systems, Measurement, and Control 121, no. 4 (December 1, 1999): 691–96. http://dx.doi.org/10.1115/1.2802536.

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In this paper the equations of motion for a flexible multi-link manipulator are derived. Each link of the manipulator, including those with prismatic motion, is represented by two finite elements in three-dimensional space. The prismatic links are treated as beams with moving boundary conditions, and the position of finite-element node points are not changed relative to the link. The equations are generated using Maple V, and the paper discusses a general approach for eliminating small terms. A sample calculation is performed for a RRP (Stanford arm) manipulator, and the shift of natural frequencies with time are plotted. Results are compared to those obtained by the assumed-mode method.

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15

Hill, G. F. J., and P. M. Weaver. "Analysis of anisotropic prismatic sectiosn." Aeronautical Journal 108, no. 1082 (April 2004): 197–205. http://dx.doi.org/10.1017/s0001924000000105.

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The dynamic behaviour of rotor blades is often modelled using onedimensional beam analysis with equivalent mass and stiffness properties to those of the full blade. Calculation of accurate elastic stiffness terms for these arbitrarily shaped sections with differing material properties is vital to this process. A method which produces these properties using standard finite element analysis codes is presented. The method is then compared with theoretical results for a simple rectangular section beam and case studies are performed on a composite laminate and box-section.

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16

Jia, X., Y. Tian, D. Zhang, and J. Liu. "Stiffness Modeling and Analysis of Passive Four-Bar Parallelogram in Fully Compliant Parallel Positioning Stage." International Journal of Intelligent Mechatronics and Robotics 1, no. 1 (January 2011): 61–78. http://dx.doi.org/10.4018/ijimr.2011010104.

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In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair are studied based on the developed model. The relative geometric parameters are changed to show the rules of the stiffness variation and to obtain the demands for simplification in the stiffness modeling of the prismatic pair. Furthermore, the finite element analysis has been conducted to validate the analytical model.

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17

Bazhenov, Viktor, Oleksii Shkril’, Yurii Maksymiuk, Ivan Martyniuk, and Oleksandr Maksymiuk. "Semi-analytical method of finished elements in elastic and elastic-plastic position for curviline prismatic objects." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 24–32. http://dx.doi.org/10.32347/2410-2547.2020.105.24-32.

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In [4, 5, 6] the algorithm of the method of block iterations of solving linear and nonlinear equations by the semivanalytic finite element method for curvilinear inhomogeneous prismatic bodies is realized. This paper presents the results of the effectiveness of the semi-analytical finite element method for the consideration of curvilinear prismatic objects in elastic and elastic-plastic formulation. The choice of the optimal in terms of machine time and speed of convergence of the iterative process algorithm for solving systems of linear and nonlinear equations by the semivanalytic finite element method [1, 2, 3] is an important factor influencing the efficiency of the method as a whole. Numerous studies have shown that using the block iteration method to solve systems of equations of the semivanalytic finite element method for prismatic bodies with variable parameters has a number of important advantages over solving systems of the traditional variant of the finite element method. The organization of the computational process and its software implementation takes into account the basic requirements for software for calculating strength on modern software packages. The modular structure of the developed system of programs provides its non-closedness concerning new classes of tasks. The use of the block iteration method to solve systems of nonlinear equations of SAFEM is approximately an order of magnitude superior to the traditional finite element method.

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18

Ipatov, A. A., F. dell'Isola, I. Giorgio, I. Rahali, S. R. Eugster, and A. A. Zaikin. "DYNAMICS OF POROVISCOELASTIC PRISMATIC SOLID FOR VARIOUS VALUES OF MATERIAL PERMEABILITY." Problems of strenght and plasticity 81, no. 4 (2019): 416–28. http://dx.doi.org/10.32326/1814-9146-2019-81-4-416-428.

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In present paper wave propagation poroviscoelastic solids is studied. Study of wave propagation in saturated porous media is an important issue of engineering sciences. The poroelasticity theory was developed and nowadays is an important to engineering applications. Also research is dedicated to modeling of a slow compressional wave in poroviscoelastic media by means of boundary-element method. Poroviscoelastic formulation is based on Biot's model of fully saturated poroelastic media with a correspondence principal usage. Standard linear solid model is employed in order to describe viscoelastic behavior of the skeleton in porous medium. The boundary-value problem of the three-dimensional dynamic poroviscoelasticity is written in terms of Laplace transforms. Direct approach of the boundary integral equation method is employed. The boundary-element approach is based on the mixed boundary-element discretization of surface with generalized quadrangular elements. Subsequent application of collocation method leads to the system of linear equations, and then to the solution in Laplace domain. Numerical inversion of Laplace transform is used to obtain time-domain solution. The problem of the load acting on a poroelastic prismatic solid is solved by means of developed software based on boundary element approach. An influence of permeability of porous material on dynamic responses is studied. Slow wave phenomena appearance is demonstrated. Viscosity parameter influence on dynamic responses of displacements and pore pressure is studied.

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19

Al-Sadder, Samir Z., and Mohammad H. Dado. "An Accurate Numerical Scheme for Large Deflection Analysis of Non-Prismatic Inextensible Slender Beams Subjected to General Loading and Boundary Conditions." Advances in Structural Engineering 8, no. 6 (December 2005): 585–94. http://dx.doi.org/10.1260/136943305776318392.

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This paper studies the large deflection behavior of prismatic and non-prismatic inextensible beams subjected to various types of loading and boundary conditions. The formulation is based on representing the angle of rotation by a power series and substituting it into the derived governing nonlinear differential equation. The coefficients of the power series are obtained by minimizing the integral of the residual error over the deflected beam axis. Several numerical examples are presented covering prismatic and non-prismatic beams subjected to uniform and non-uniform distributed loads. A large displacement finite element analysis using the package MSC/NASTRAN was used to check the accuracy and efficiency of the present numerical method. Excellent agreement was observed between the two numerical schemes.

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20

Suprun, T. "Optimization of working surfaces heat transfer based on local control of thermophysical parameters." Energy and automation, no. 5(51) (October 28, 2020): 69–80. http://dx.doi.org/10.31548/energiya2020.05.069.

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The progressive trend of increasing the efficiency and operational reliability of equipment requires continuous improvement of methods for monitoring and managing work processes. One of the most promising methods for studying transport processes occurring in difficult conditions is physical modeling. The object of this research is heat-exchange prismatic surfaces, which are typical for many technical applications. The purpose of the work is to develop methods for optimizing heat transfer of working surfaces based on local control of thermophysical parameters in characteristic zones of the working environment. The studies were carried out in the ADS-1 aerodynamic stand using the methods of heat and mass analogy and hot-wire anemometry. The arrangement included four rows of prismatic elements. The essence of the local approach is to determine the average surface heat transfer coefficient from the local velocity, measured above each prismatic element, which makes it possible to estimate the spatial temperature heterogeneity of a specific arrangement and take measures to change the temperature in the desired direction by maneuvering the location of the elements. The proposed approach is fundamentally different from another widespread approach, which we called the channel one, in which information about the velocity and temperature fields is ignored, and the influence of the configuration and size of elements and their location on the hydrodynamic structure of the flow is insufficiently taken into account. The local approach allows, firstly, to more accurately diagnose the types of flow in the boundary layer of a streamlined element, determining laminar, turbulent, pseudolaminar, quasiturbulent, transition and separated flow regimes. Second, on the basis of a set of statistical data, make the transition to an arbitrarily specified arrangement of elements and thereby increase the accuracy of determining the temperature state of individual prismatic elements and the entire arrangement as a whole. Equations of similarity are proposed for calculating the local heat transfer of each face of the prism separately and the average surface heat transfer depending on the geometric and operating parameters. On the basis of the recommendations received, the thermal state of the elements of a specific arrangement was evaluated and measures were developed to improve it through targeted rearrangements of the elements.

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21

Nazarenko, Sergey, and Nina Blokhina. "Finite elements with continuous stress fields in calculation of folded prismatic thin-walled rods and shells." MATEC Web of Conferences 196 (2018): 01018. http://dx.doi.org/10.1051/matecconf/201819601018.

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The article deals with methods of creating a rectangular wall-beam finite element with eight degrees of freedom per node and continuous stress fields along the boundaries. This effect is achieved by specifying displacement fields in the plane of the element in forms similar to those in finite elements of Bogner, Fox, and Schmitt plate. The article provides algebraic expressions for displacement forms; methods of forming reaction and stress matrices are also considered. Test calculations carried out with the help of “Computational mechanics” FEM complex have proved high efficiency of the finite element analysis performed. A rectangular shell finite element with twelve degrees of freedom per node was developed as a combination of membrane finite element and Bogner, Fox and Schmitt plate element.

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22

Yang, Qi Zhi, Dai Min Yuan, Jia Qi Zhuang, and Dian Feng Cao. "Analysis of the Flexible Prismatic Pair Processing Errors of a Flexible Parallel Vibration Platform with High Frequency." Key Engineering Materials 575-576 (September 2013): 331–36. http://dx.doi.org/10.4028/www.scientific.net/kem.575-576.331.

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In some fields, the rigid prismatic pairs have been gradually replaced by some flexible prismatic pairs. It is described a new type flexible prismatic pair in this paper. Its material is 65Mn spring steel. It is applied to the high frequency vibration field for its elasticity and structural advantages. The prismatic pair is based on a one-way four-bar linkage, which is consisted of some bent plate structures. Firstly its model is designed. Secondly the width error, the incision arc error and some other errors are analyzed in details. Based on the Paros J stiffness calculation formula and the Smith ST error analysis method, its relative stiffness error model is established. Finally by using finite element method, a simulation of deformation is made in the actual working conditions. And the error model is correct.

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23

Meftah, Kamel, and Lakhdar Sedira. "A SIX-NODE PRISMATIC SOLID FINITE ELEMENT FOR LAMINATED COMPOSITES." Composites: Mechanics, Computations, Applications: An International Journal 11, no. 3 (2020): 267–85. http://dx.doi.org/10.1615/compmechcomputapplintj.2020032289.

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24

Amor-Martin, Adrian, Luis Emilio Garcia-Castillo, and Daniel Garcia-Dooro. "Second-Order Nédélec Curl-Conforming Prismatic Element for Computational Electromagnetics." IEEE Transactions on Antennas and Propagation 64, no. 10 (October 2016): 4384–95. http://dx.doi.org/10.1109/tap.2016.2597640.

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25

Vijayakar, Sandeep M., Henry R. Busby, and Donald R. Houser. "Finite element analysis of quasi-prismatic bodies using Chebyshev polynomials." International Journal for Numerical Methods in Engineering 24, no. 8 (August 1987): 1461–77. http://dx.doi.org/10.1002/nme.1620240805.

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26

Wang, Peng, Hocine Chalal, and Farid Abed-Meraim. "Explicit dynamic analysis of sheet metal forming processes using linear prismatic and hexahedral solid-shell elements." Engineering Computations 34, no. 5 (July 3, 2017): 1413–45. http://dx.doi.org/10.1108/ec-04-2016-0150.

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Purpose The purpose of this paper is to propose two linear solid-shell finite elements, a six-node prismatic element denoted SHB6-EXP and an eight-node hexahedral element denoted SHB8PS-EXP, for the three-dimensional modeling of thin structures in the context of explicit dynamic analysis. Design/methodology/approach These two linear solid-shell elements are formulated based on a purely three-dimensional (3D) approach, with displacements as the only degrees of freedom. To prevent various locking phenomena, a reduced-integration scheme is used along with the assumed-strain method. The resulting formulations are computationally efficient, as only a single layer of elements with an arbitrary number of through-thickness integration points is required to model 3D thin structures. Findings Via the VUEL user-element subroutines, the performance of these elements is assessed through a set of selective and representative dynamic elastoplastic benchmark tests, impact-type problems and deep drawing processes involving complex non-linear loading paths, anisotropic plasticity and double-sided contact. The obtained numerical results demonstrate good performance of the SHB-EXP elements in the modeling of 3D thin structures, with only a single element layer and few integration points in the thickness direction. Originality/value The extension of the SHB-EXP solid-shell formulations to large-strain anisotropic plasticity enlarges their application range to a wide variety of dynamic elastoplastic problems and sheet metal forming simulations. All simulation results reveal that the numerical strategy adopted in this paper can efficiently prevent the various locking phenomena that commonly occur in the 3D modeling of thin structural problems.

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Tenorio-Montero, Enrique, and Gelacio Juárez-Luna. "Beam-column finite element with embedded discontinuities for modelling damage in reinforced concrete prismatic elements." Structures 29 (February 2021): 1934–53. http://dx.doi.org/10.1016/j.istruc.2020.12.055.

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28

Podsiadło, Krzysztof, Albert Oliver Serra, Anna Paszyńska, Rafael Montenegro, Ian Henriksen, Maciej Paszyński, and Keshav Pingali. "Parallel graph-grammar-based algorithm for the longest-edge refinement of triangular meshes and the pollution simulations in Lesser Poland area." Engineering with Computers 37, no. 4 (January 22, 2021): 3857–80. http://dx.doi.org/10.1007/s00366-020-01253-y.

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AbstractIn this paper, we propose parallel graph-grammar-based algorithm for the longest-edge refinements and the pollution simulations in Lesser Poland area. We introduce graph-grammar productions for Rivara’s longest-edged algorithm for the local refinement of unstructured triangular meshes. We utilize the hyper-graph to represent the computational mesh and the graph-grammar productions to express the longest-edge mesh refinement algorithm. The parallelism in the original Rivara’s longest edge refinement algorithm is obtained by processing different longest edge refinement paths in different three ads. Our graph-grammar-based algorithm allows for additional parallelization within a single longest-edge refinement path. The graph-grammar-based algorithm automatically guarantees the validity and conformity of the generated mesh; it prevents the generation of duplicated nodes and edges, elongated elements with Jacobians converging to zero, and removes all the hanging nodes automatically from the mesh. We test the algorithm on generating a surface mesh based on a topographic data of Lesser Poland area. The graph-grammar productions also generate the layers of prismatic three-dimensional elements on top of the triangular mesh, and they break each prismatic element into three tetrahedral elements. Next, we propose graph-grammar productions generating element matrices and right-hand-side vectors for each tetrahedral element. We utilize the Streamline Upwind Petrov–Galerkin (SUPG) stabilization for the pollution propagation simulations in Lesser Poland area. We use the advection–diffusion-reaction model, the Crank–Nicolson time integration scheme, and the graph-grammar-based interface to the GMRES solver.

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29

Ibrahim, Taghreed Hassan. "Buckling Loads and Effective Length Factor for Non-Prismatic Columns." Journal of Engineering 23, no. 10 (October 1, 2017): 134–45. http://dx.doi.org/10.31026/j.eng.2017.10.10.

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Based on a finite element analysis using Matlab coding, eigenvalue problem has been formulated and solved for the buckling analysis of non-prismatic columns. Different numbers of elements per column length have been used to assess the rate of convergence for the model. Then the proposed model has been used to determine the critical buckling load factor () for the idealized supported columns based on the comparison of their buckling loads with the corresponding hinge supported columns . Finally in this study the critical buckling factor () under end force (P) increases by about 3.71% with the tapered ratio increment of 10% for different end supported columns and the relationship between normalized critical load and slenderness ratio was generalized.

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30

Tayyebi, K., A. M. Haghighi, and R. Attarnejad. "A new nine-node element for analysing plates with varying thickness using basic displacement functions." Journal of Mechanical Engineering and Sciences 12, no. 4 (December 27, 2018): 4056–71. http://dx.doi.org/10.15282/jmes.12.4.2018.06.0352.

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The capability of the Finite Element Method in producing accurate and efficient results largely depends on the shape functions adopted to frame the displacement field inside the element. In this paper, a new nine-node Lagrangian element was developed to analyse thin plates with varying cross-sections using the shape functions obtained for non-prismatic straight beams with minimum number of elements. The formulated shape functions, which represent vertical displacements and rotations throughout elements, are rooted from a purely mechanical functions called Basic Displacement Functions (BDFs). These functions are obtained by implementing the force method in Euler–Bernoulli beam theory, which ensures that equilibrium equation is satisfied in all interior points of elements. To verify the competency of the proposed element, solutions for the static analysis of isotropic rectangular plates under various loading conditions, together with free vibration analysis of plates with linear thickness variation were obtained and compared with the previous literature. Results showed that the proposed nine-node Lagrangian element was computationally more cost-effective compared to other competing methods when small number of elements is employed.

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31

Chaudhury, Arkadeep Narayan, and Debasis Datta. "Analysis of prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape by analytical and finite element methods." Journal of Computational Design and Engineering 4, no. 3 (February 8, 2017): 178–91. http://dx.doi.org/10.1016/j.jcde.2017.02.001.

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Abstract This paper presents a methodology for designing prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape using analytical and numerical methods. To start with, simple analytical formulations for obtaining the axial deformation of the springs under axial load have been demonstrated. Next, the processes of obtaining CAD models of the springs and their subsequent finite element analysis (FEA) in commercial softwares have been outlined. In the third part, the different springs have been compared with a common cylindrical spring and their merits compared to a common spring have been demonstrated. Next, a fairly accurate analytical formulation (with maximum error of ∼7–8%) for obtaining the value and location of maximum shear stress for all the springs has been demonstrated. Next, two aspects of non-prismatic springs under dynamic loads, viz. damping introduced in a vibrating system and contribution of the spring to the equivalent mass in a one dimensional vibrating spring mass system due to shape of the spring have been discussed. The last part involves an analytical formulation for the linear elastic buckling of two springs with circular coil shapes. For the majority of the work, emphasis has been on obtaining and using closed form analytical expressions for different quantities while numerical techniques such as FEA have been used for validation of the same. Highlights Analytical formulations of axial deflection different springs under axial load. CAD modeling and FEA of prismatic and non prismatic springs of different coil shapes. Comparison of stress and deflection in mass-equivalent springs of different geometry. Approx. analytical formulation for the location and value of max. stress in springs. Effects of spring shape on damping, vibrational properties in 1D systems and buckling.

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32

Jusuf, Annisa, Fajri Syah Allam, Tatacipta Dirgantara, Leonardo Gunawan, and Ichsan Setya Putra. "Low Velocity Impact Analyses of Prismatic Columns Using Finite Element Method." Key Engineering Materials 462-463 (January 2011): 1308–13. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.1308.

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This paper presents the study of prismatic columns of different cross sections subjected to low velocity impact, which are commonly used as energy absorber components in vehicles. The impacts of the columns were numerically analyzed using FEM. Four cross sections were considered, i.e. square, hexagonal, octagonal and circular. For each cross section, columns with several combinations of perimeters and thicknesses were analyzed. The results showed that, for columns with equal perimeter and thickness, those with circular cross sections have the highest mean crushing force and those with square cross sections have the lowest crushing forces. Furthermore, keeping all other parameters constant, columns with thicker wall have significantly higher crushing force while columns with longer perimeter have only slightly higher crushing force. This parametric information will be very useful for modern automotive industry in designing front longitudinal members within an acceptable safety level.

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33

Gounaris, G., and A. Dimarogonas. "A finite element of a cracked prismatic beam for structural analysis." Computers & Structures 28, no. 3 (January 1988): 309–13. http://dx.doi.org/10.1016/0045-7949(88)90070-3.

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34

Nguyen, Cung Huy, Andrea Freda, Giovanni Solari, and Federica Tubino. "Experimental investigation of the aeroelastic behavior of a complex prismatic element." Wind and Structures 20, no. 5 (May 25, 2015): 683–99. http://dx.doi.org/10.12989/was.2015.20.5.683.

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35

Fernández-Bustos, I., J. Agirrebeitia, G. Ajuria, and C. Angulo. "A new finite element to represent prismatic joint constraints in mechanisms." Finite Elements in Analysis and Design 43, no. 1 (November 2006): 36–50. http://dx.doi.org/10.1016/j.finel.2006.06.010.

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36

Comblen, Richard, Sébastien Blaise, Vincent Legat, Jean-François Remacle, Eric Deleersnijder, and Jonathan Lambrechts. "A discontinuous finite element baroclinic marine model on unstructured prismatic meshes." Ocean Dynamics 60, no. 6 (November 26, 2010): 1395–414. http://dx.doi.org/10.1007/s10236-010-0357-4.

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37

Blaise, Sébastien, Richard Comblen, Vincent Legat, Jean-François Remacle, Eric Deleersnijder, and Jonathan Lambrechts. "A discontinuous finite element baroclinic marine model on unstructured prismatic meshes." Ocean Dynamics 60, no. 6 (November 26, 2010): 1371–93. http://dx.doi.org/10.1007/s10236-010-0358-3.

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38

Mohsen, Marwah, Abdalnassre Abbas, and Ahmed Saadoon. "Effect of Loading Level and Span Length on Critical Buckling Load." Basrah journal for engineering science 16, no. 1 (February 1, 2016): 15–21. http://dx.doi.org/10.33971/bjes.16.1.3.

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An investigation was conducted to study the effect ofloading level with respect to shear center and span length onlateral torsional buckling of steel I-section beams using linearand nonlinear finite element analysis available in ANSYS(version 12.0) computer program. The steel beams which havebeen studied included prismatic beams and linearly web tapered beams with web tapering ratio of (0.5). The maximumheight of all beams was 300 mm with span length of 4, 6 and 8m. The critical buckling loads for prismatic and linearlytapered cantilever and simply supported beams subjected topoint load and uniformly distributed load were determined.The results showed that the bottom flange loading gives abuckling loads higher than that of the top flange loading withpercentage increases of 148% and 155% for the linear andnonlinear analysis respectively for the prismatic beams. Whilefor the tapered beams, these percentages increases were 61%and 67% respectively

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39

Klochkov, Yu V., S. D. Fomin, O. V. Vakhnina, T. A. Sobolevskaya, M. Yu Klochkov, and A. S. Andreev. "Finite element modeling of the processes of elastic-plastic deformation of reclamation objects of the agro-industrial complex." IOP Conference Series: Earth and Environmental Science 965, no. 1 (January 1, 2022): 012049. http://dx.doi.org/10.1088/1755-1315/965/1/012049.

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Abstract Annotation. To study the processes of nonlinear deformation of reclamation objects and engineering systems of the agro-industrial complex, taking into account the plastic stage of the used structural material, a finite element model was created based on a volumetric prismatic discretization element with quadrangular bases. The plastic stage of deformation of the applied structural material of the object is taken into account on the basis of the provisions of the deformation theory of plasticity. The plasticity matrix at the (j + 1)-th stage of sequential loading was compiled as a result of applying the operation of differentiating the stress tensor components accumulated over the j previous stages of sequential loading with respect to the strain tensor components. The stiffness matrix and the column of nodal forces of a prismatic discretization element with quadrangular bases at the (j + 1)-th stage of loading were obtained by minimizing the Lagrange functional. Numerical experiments on the calculation of a tubular outlet proved the adequacy of the developed finite element model and the accuracy of calculating the required strength parameters of the studied reclamation objects and other engineering systems of the agro-industrial complex, sufficient for engineering practice.

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40

Toh, Hoong Thiam. "Numerical Simulation of Hydraulic Jump Using the Improved Space-Time Conservation Element and Solution Element Method." Applied Mechanics and Materials 575 (June 2014): 790–99. http://dx.doi.org/10.4028/www.scientific.net/amm.575.790.

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This paper illustrates how Space-time Conservation Element and Solution Element (CE/SE) method which is developed for compressible flow can be used to solve the Saint-Venant equations numerically. The sharp shock-capturing capability of the scheme is demonstrated through the simulation of hydraulic jump phenomenon in prismatic open-channels. Two channel cross-section geometries are considered, viz rectangular and triangular cross sections. The code developed for the present study is validated by solving the benchmark problem of dam-break flow. The numerical solution of the Saint-Venant equations for the rectangular channel is found to be in good agreement with the experimental data available in the literature. The effect of channel wall slope on hydraulic jump in triangular channel is also discussed in this paper.

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41

Guliar, Oleksandr, Yurii Maksymiuk, Andrii Kozak, and Oleksandr Maksymiuk. "UNIVERSAL PRISMATIC FINITE ELEMENT OF GENERAL TYPE FOR PHYSI-CALLY AND GEOMETRICALLY NONLINEAR PROBLEMS OF DEFOR-MATION OF PRISMATIC BODIES." Building constructions. Theory and Practice, no. 6 (June 4, 2020): 72–84. http://dx.doi.org/10.32347/2522-4182.6.2020.72-84.

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42

Biswal, Alok Ranjan, Deepak Ranjan Biswal, Rasmi Ranjan Senapati, Abinash Bibek Dash, Poonam Prusty, Shibabrata Mohapatra, and Sanjeev Panda. "Finite Element Based Static and Dynamic Vibration Analysis of a Beam with Axial Variation of Material Properties." International Journal for Research in Applied Science and Engineering Technology 11, no. 6 (June 30, 2023): 4440–49. http://dx.doi.org/10.22214/ijraset.2023.54453.

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Abstract: The study examines the vibration analysis of a damped cantilever beam with nonuniform variation in material properties using finite element methods. With power modification of material parameters in the axial direction, the static and dynamic response of a prismatic rectangular beam with damping has been examined. For the finite element approach, two noded beam elements with two degrees of freedom at each node were evaluated. The power law variation of material properties was used throughout the investigation. This research investigated the effects of proportional damping on displacement, velocity, and acceleration responses. The proposed beam's mass, stiffness, and damping matrices were calculated using Hamilton's concept. In the temporal domain, the Newmark Method has been utilized

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43

Ping, Xuecheng, Mengcheng Chen, Wei Zhu, Yihua Xiao, and Weixing Wu. "Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method." International Journal of Computational Methods 14, no. 06 (August 2017): 1750065. http://dx.doi.org/10.1142/s0219876217500657.

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In order to consider corner configurations with straight corner fronts in three-dimensional (3D) solids, a super polygonal prismatic element containing a straight corner front is established by using the numerical eigensolutions of singular stress fields and the Hellinger–Reissner variational principle. Singular stresses near the corner front subject to far-field boundary conditions can be obtained by incorporating the super singular element with conventional 3D brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3D corner configurations and cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain that is necessary for conventional and enriched finite element methods, and lead to high accuracy and fast convergence. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects.

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44

Pinho, C. E. L., João M. P. Q. Delgado, V. Ferreira, R. Pilão, and C. Pinho. "Influence of Burner Geometry on Flame Characteristics of Propane-Air Mixture: Experimental and Numerical Studies." Defect and Diffusion Forum 273-276 (February 2008): 162–67. http://dx.doi.org/10.4028/www.scientific.net/ddf.273-276.162.

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This work describes an experimental and numerical study to determine the corresponding detailed thermal and fluid dynamic fields developed in a burner element for domestic water heaters. A three-dimensional burner element was designed in real scale and numerical studies using Fluent code were carried out in steady-state conditions to allow continuous observations and measurements of the influence of burner element geometry and fuel-air velocity on flame characteristics, namely colour, length and stability. Air has been used as a fluid. The computational results, specifically the velocity and flame characteristics were verified with experimental data obtained in order to ensure a stable flame. In order to evaluate the power generated and the emissions of CO2 and CO associated to different burner element geometries, some experiments were performed using single burner elements with a stainless steel prismatic tank covered with thermal insulation to minimize heat losses.

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45

Maksimyuk, Yurii, Mykola Kuzminets, Ivan Martyniuk, and Oleksandr Maksimyuk. "Research of the stressed and deformed state of metal stripin the broaching process." Strength of Materials and Theory of Structures, no. 109 (November 11, 2022): 229–38. http://dx.doi.org/10.32347/2410-2547.2022.109.229-238.

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In papers [2,4,5] the solution relations and the algorithm of the method of block iterations of solving linear and nonlinear equations by the semivanalytic finite element method for curvilinear inhomogeneous prismatic bodies are realized. In paper [1], a numerical study of the convergence of solutions was performed, and a wide range of test problems for bodies with smoothly and abruptly changing physical and geometric characteristics in elastic and resilient-plastic formulation was considered. In paper [6], to confirm the reliability of the results obtained on the basis of the semi-analytical finite element method, the effectiveness of this approach for the calculation of curvilinear inhomogeneous prismatic objects is shown. Solving control problems of the theory of elasticity, thermoelasticity and thermoplasticity, as well as problems of shape change makes it possible to draw conclusions about the reliability of the results of the study of a selected class of objects based on the developed methodology and implements its application package. In this work, using the methodology outlined in the above works, the solution of the spatial problem of plastic deformation of a prismatic body was solved on the basis of the semi-analytical method of finite elements, and the process of broaching a strip in the process of metal embossing was analyzed. The purpose of this study is to determine the spatial picture of the stress-strain state of the strip during drawing and to compare the spatial resolution with the flat one. A comparison of the parameters of the stress-strain state of the workpiece during the broaching process, obtained in flat and spatial settings, allows us to conclude that the research must be carried out on the basis of spatial calculation.

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46

Bai, Rui, Si-Wei Liu, and Siu-Lai Chan. "Modal and Elastic Time-History Analysis of Frames with Tapered Sections by Non-Prismatic Elements." International Journal of Structural Stability and Dynamics 18, no. 09 (September 2018): 1850106. http://dx.doi.org/10.1142/s0219455418501067.

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Low-cost robotic welding and wide availability of high strength steel plates of grades over 500[Formula: see text]MPa make the use of tapered members an economical alternative to conventional prismatic members for modern steel structures, as experienced by the authors in some practical projects in Hong Kong and Macau. This paper proposes a new and efficient numerical method for modal and elastic time-history analysis of the frames with tapered sections. A series of non-prismatic elements is derived on the basis of analytical expressions, and the exact consistent mass and tangent stiffness matrices are formulated. Five common types of tapered sections for practical applications, namely the circular solid, circular hollow, rectangular solid, rectangular hollow and doubly symmetric-I sections, are studied. Contrary to the conventional method using the approximate assumptions for the section properties along the member length, this research analytically expresses the flexural rigidity and cross-sectional area for the stiffness and mass matrices of an element. Further, the techniques for obtaining the dynamic performances, such as natural vibrations and time-history responses, of non-prismatic members are investigated. Finally, three examples are conducted for validating and verifying the accuracy of the proposed formulations. The present work can be used in the dynamic response analysis of frame structures with tapered sections in seismic zones.

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47

Zhao, Jing-Shan, Li Ye, Fulei Chu, and Jian S. Dai. "Synthesis and static analysis of the deployable frame for a morphing wing." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 3 (October 22, 2012): 565–79. http://dx.doi.org/10.1177/0954406212464728.

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This article proposes a deployable frame for a morphing wing. The frame is redundantly constrained in structure, and therefore it has both merits of high structural stiffness and strength of a truss structure and motion flexibility of a mechanism. The primary element of the foldable frame is synthesized from the viewpoint of identical strength principle. The major structures of previous deployable wings are mostly based on prismatic joints. However, the deflections of the cantilevered links might not satisfy the primary geometry requirements of the prismatic joint. Therefore revolute joints are used in our deployable frame to avoid violating the geometry conditions for prismatic joints resulting from the different deflections of its contacting two parts. The deflection and slope of every joint node of the foldable frame is investigated within the deploying/folding process. Numerical analysis indicates that the deployment ratio of the foldable frame can be designed much larger than that of the existing morphing wing even considering the allowable deflection under the completely unfolded situations.

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48

Wan, Jian-Hong, Si-Wei Liu, Xue-You Li, Li-Min Zhang, and Hai-Peng Zhao. "Buckling analysis of tapered piles using non-prismatic beam-column element model." Computers and Geotechnics 139 (November 2021): 104370. http://dx.doi.org/10.1016/j.compgeo.2021.104370.

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49

Chiozzi, Andrea, and Elena Benvenuti. "Extended virtual element method for the torsion problem of cracked prismatic beams." Meccanica 55, no. 4 (October 24, 2019): 637–48. http://dx.doi.org/10.1007/s11012-019-01073-5.

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50

Farid, Abed-Meraim, and Alain Combescure. "New prismatic solid-shell element: assumed strain formulation and hourglass mode analysis." Structural Engineering and Mechanics 37, no. 2 (January 25, 2011): 253–56. http://dx.doi.org/10.12989/sem.2011.37.2.253.

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