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Journal articles on the topic 'Locking free finite elements'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Reddy, J. N. "On locking-free shear deformable beam finite elements." Computer Methods in Applied Mechanics and Engineering 149, no. 1-4 (October 1997): 113–32. http://dx.doi.org/10.1016/s0045-7825(97)00075-3.

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2

Falk, Richard S., and Tong Tu. "Locking-free finite elements for the Reissner-Mindlin plate." Mathematics of Computation 69, no. 231 (August 20, 1999): 911–29. http://dx.doi.org/10.1090/s0025-5718-99-01165-5.

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3

Krysl, P., and B. Zhu. "Locking-free continuum displacement finite elements with nodal integration." International Journal for Numerical Methods in Engineering 76, no. 7 (November 12, 2008): 1020–43. http://dx.doi.org/10.1002/nme.2354.

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4

Chinosi, C., C. Lovadina, and L. D. Marini. "Nonconforming locking-free finite elements for Reissner–Mindlin plates." Computer Methods in Applied Mechanics and Engineering 195, no. 25-28 (May 2006): 3448–60. http://dx.doi.org/10.1016/j.cma.2005.06.025.

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5

Belhachmi, Z., J. M. Sac-Epée, and S. Tahir. "Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity." Mathematical Modelling of Natural Phenomena 4, no. 1 (2009): 1–20. http://dx.doi.org/10.1051/mmnp/20094101.

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6

Xiao, Liu-Chao, Yong-Qin Yang, and Shao-Chun Chen. "Locking-free nonconforming finite elements for three-dimensional elasticity problem." Applied Mathematics and Computation 217, no. 12 (February 2011): 5790–97. http://dx.doi.org/10.1016/j.amc.2010.12.061.

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7

Izzuddin, B. A., and Y. Liang. "A hierarchic optimisation approach towards locking-free shell finite elements." Computers & Structures 232 (May 2020): 105839. http://dx.doi.org/10.1016/j.compstruc.2017.08.010.

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8

Heisserer, Ulrich, Stefan Hartmann, Alexander Düster, and Zohar Yosibash. "On volumetric locking-free behaviour of p-version finite elements under finite deformations." Communications in Numerical Methods in Engineering 24, no. 11 (June 5, 2007): 1019–32. http://dx.doi.org/10.1002/cnm.1008.

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9

Arnold, Douglas N., and Franco Brezzi. "Locking-free finite element methods for shells." Mathematics of Computation 66, no. 217 (January 1, 1997): 1–15. http://dx.doi.org/10.1090/s0025-5718-97-00785-0.

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10

Oyarzúa, Ricardo, and Ricardo Ruiz-Baier. "Locking-Free Finite Element Methods for Poroelasticity." SIAM Journal on Numerical Analysis 54, no. 5 (January 2016): 2951–73. http://dx.doi.org/10.1137/15m1050082.

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11

Chang, C. C. "Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (July 19, 2010): 280–91. http://dx.doi.org/10.1243/09544062jmes2072.

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In standard linear finite-element formulations, volumetric locking because of the incompressibility constraint that may occur in computational plasticity is often encountered. This study uses crossed patch arrangements of triangles to form quadrilateral elements in order to overcome the locking in the upper bound finite-element analysis of plane strain deformation problems. The velocity field is described in terms of linear triangular elements, while the incompressibility constraint is imposed by quadrilateral elements. Rigid, perfectly plastic materials, and strain hardening materials that form the von Mises model have been considered. The velocity formulation is presented and has been implemented in a finite-element code. Several examples, some benchmarks problems, are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field during the plastic deformation. Numerical results show that the crossed patch arrangements of linear triangular elements are free of volumetric locking and achieve well-defined limit loads. This study shows that the presented method can be used to simulate large plastic deformation under plane strain conditions.

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12

Minghini, F., N. Tullini, and F. Laudiero. "Buckling analysis of FRP pultruded frames using locking-free finite elements." Thin-Walled Structures 46, no. 3 (March 2008): 223–41. http://dx.doi.org/10.1016/j.tws.2007.09.001.

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13

Minghini, F., N. Tullini, and F. Laudiero. "Locking-free finite elements for shear deformable orthotropic thin-walled beams." International Journal for Numerical Methods in Engineering 72, no. 7 (2007): 808–34. http://dx.doi.org/10.1002/nme.2034.

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14

Dasgupta, Gautam. "Locking-free compressible quadrilateral finite elements: Poisson’s ratio-dependent vector interpolants." Acta Mechanica 225, no. 1 (September 4, 2013): 309–30. http://dx.doi.org/10.1007/s00707-013-0927-x.

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15

Sulbhewar, Litesh N., and P. Raveendranath. "A locking-free coupled polynomial Timoshenko piezoelectric beam finite element." Engineering Computations 32, no. 5 (July 6, 2015): 1251–74. http://dx.doi.org/10.1108/ec-09-2013-0218.

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Purpose – Piezoelectric extension mode smart beams are vital part of modern control technology and their numerical analysis is an important step in the design process. Finite elements based on First-order Shear Deformation Theory (FSDT) are widely used for their structural analysis. The performance of the conventional FSDT-based two-noded piezoelectric beam formulations with assumed independent linear field interpolations is not impressive due to shear and material locking phenomena. The purpose of this paper is to develop an efficient locking-free FSDT piezoelectric beam element, while maintaining the same number of nodal degrees of freedom. Design/methodology/approach – The governing equations are derived using a variational formulation to establish coupled polynomial field representation for the field variables. Shape functions based on these coupled polynomials are employed here. The proposed formulation eliminates all locking effects by accommodating strain and material couplings into the field interpolation, in a variationally consistent manner. Findings – The present formulation shows improved convergence characteristics over the conventional formulations and proves to be the most efficient way to model extension mode piezoelectric smart beams, as demonstrated by the results obtained for numerical test problems. Originality/value – To the best of the authors’ knowledge, no such FSDT-based finite element with coupled polynomial shape function exists in the literature, which incorporates electromechanical coupling along with bending-extension and bending-shear couplings at the field interpolation level itself. The proposed formulation proves to be the fastest converging FSDT-based extension mode smart beam formulation.

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16

Wong, F. T., Adam Sulistio, and Hidayat Syamsoeyadi. "Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850064. http://dx.doi.org/10.1142/s0219876218500640.

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Kriging-based finite element method (K-FEM) is an enhancement of the FEM through the use of Kriging interpolation in place of the conventional polynomial interpolation. In this paper, the K-FEM is developed for static, free vibration, and buckling analyses of Timoshenko beams. The discrete shear gap technique is employed to eliminate shear locking. The numerical tests show that a Kriging-Based beam element with cubic basis and three element-layer domain of influencing nodes is free from shear locking. Exceptionally accurate displacements, bending moments, natural frequencies, and buckling loads and reasonably accurate shear force can be achieved using a relatively course mesh.

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17

Pechstein, Astrid S., Martin Meindlhumer, and Alexander Humer. "New mixed finite elements for the discretization of piezoelectric structures or macro-fiber composites." Journal of Intelligent Material Systems and Structures 29, no. 16 (July 5, 2018): 3266–83. http://dx.doi.org/10.1177/1045389x18781026.

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We propose a new three-dimensional formulation based on the mixed tangential-displacement normal-normal-stress method for elasticity. In elastic tangential-displacement normal-normal-stress elements, the tangential component of the displacement field and the normal component of the stress vector are degrees of freedom and continuous across inter-element interfaces. Tangential-displacement normal-normal-stress finite elements have been shown to be locking-free with respect to shear locking in thin elements, which makes them suitable for the discretization of laminates or macro-fiber composites. In the current paper, we extend the formulation to piezoelectric materials by adding the electric potential as degree of freedom.

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18

Bramble, James H., and Tong Sun. "A locking-free finite element method for Naghdi shells." Journal of Computational and Applied Mathematics 89, no. 1 (March 1998): 119–33. http://dx.doi.org/10.1016/s0377-0427(97)00234-3.

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19

Bletzinger, Kai-Uwe, Manfred Bischoff, and Ekkehard Ramm. "A unified approach for shear-locking-free triangular and rectangular shell finite elements." Computers & Structures 75, no. 3 (April 2000): 321–34. http://dx.doi.org/10.1016/s0045-7949(99)00140-6.

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20

Kuhl, D., and E. Ramm. "Time integration in the context of energy control and locking free finite elements." Archives of Computational Methods in Engineering 7, no. 3 (September 2000): 299–332. http://dx.doi.org/10.1007/bf02736211.

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21

Senjanović, Ivo, Marko Tomić, Smiljko Rudan, and Neven Hadžić. "Conforming shear-locking-free four-node rectangular finite element of moderately thick plate." Journal of the Mechanical Behavior of Materials 25, no. 5-6 (December 20, 2016): 141–52. http://dx.doi.org/10.1515/jmbm-2017-0001.

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AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

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22

Bleyer, Jeremy, Canh Van Le, and Patrick de Buhan. "Locking-free discontinuous finite elements for the upper bound yield design of thick plates." International Journal for Numerical Methods in Engineering 103, no. 12 (May 29, 2015): 894–913. http://dx.doi.org/10.1002/nme.4912.

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23

Dasgupta, Gautam. "Incompressible and locking-free finite elements from Rayleigh mode vectors: quadratic polynomial displacement fields." Acta Mechanica 223, no. 8 (May 1, 2012): 1645–56. http://dx.doi.org/10.1007/s00707-012-0654-8.

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24

Pitkäranta, Juhani. "The first locking-free plane-elastic finite element: historia mathematica." Computer Methods in Applied Mechanics and Engineering 190, no. 11-12 (December 2000): 1323–66. http://dx.doi.org/10.1016/s0045-7825(00)00163-8.

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25

Carstensen, C., G. Dolzmann, S. A. Funken, and D. S. Helm. "Locking-free adaptive mixed finite element methods in linear elasticity." Computer Methods in Applied Mechanics and Engineering 190, no. 13-14 (December 2000): 1701–18. http://dx.doi.org/10.1016/s0045-7825(00)00185-7.

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26

Chilton, Lawrence, and Manil Suri. "Locking-free mixed hp finite element methods for curvilinear domains." Computer Methods in Applied Mechanics and Engineering 190, no. 26-27 (March 2001): 3427–42. http://dx.doi.org/10.1016/s0045-7825(00)00277-2.

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27

Erkmen, R. Emre, and Mark A. Bradford. "Locking-free finite element formulation for steel-concrete composite members." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012239. http://dx.doi.org/10.1088/1757-899x/10/1/012239.

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28

Onishi, Yuki, Ryoya Iida, and Kenji Amaya. "Accurate Viscoelastic Large Deformation Analysis Using F-Bar Aided Edge-Based Smoothed Finite Element Method for 4-Node Tetrahedral Meshes (F-BarES-FEM-T4)." International Journal of Computational Methods 17, no. 02 (October 24, 2019): 1845003. http://dx.doi.org/10.1142/s0219876218450032.

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A state-of-the-art tetrahedral smoothed finite element method, F-barES-FEM-T4, is demonstrated on viscoelastic large deformation problems. The stress relaxation of viscoelastic materials brings near incompressibility when the long-term Poisson’s ratio is close to 0.5. The conventional hybrid 4-node tetrahedral (T4) elements cannot avoid the shear locking and pressure checkerboarding issues, meanwhile F-barES-FEM-T4 can suppress these issues successfully by adopting the edge-based smoothed finite element method (ES-FEM) with the aid of the F-bar method and the cyclic smoothing procedure. A few examples of analyses verify that F-barES-FEM-T4 is locking-free and pressure oscillation-free in viscoelastic analyses as well as in nearly incompressible hyperelastic or elastoplastic analyses.

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29

Gilewski, W. "Extended Penalty Coefficients For Elimination The Locking Effects In Moderately Thick Beam And Plate Finite Elements." Archives of Civil Engineering 60, no. 3 (September 1, 2014): 367–85. http://dx.doi.org/10.2478/ace-2014-0025.

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AbstractThe present paper is dedicated to presentation and energy verification of the methods of stabilization the strain energy by penalty coefficients. Verification of the methods is based on the consistency and ellipticity conditions to be satisfied by the finite elements. Three methods of stabilization are discussed. The first does not satisfy the above requirements. The second is consistent but cannot eliminate parasitic energy terms. The third method, proposed by the author, is based on the decomposition of the element stiffness matrix. The method can help to eliminate locking of the finite elements. For two-noded beam element with linear shape functions and exact integration a stabilized free of locking (and elliptical) element is received (equivalent to reduced integration element). Two plate finite elements are analyzed: four-noded rectangular element and DSG triangle. A new method of stabilization with the use of four independent parameters is proposed. The finite elements with this kind of stabilization satisfy the consistency condition. In the rectangular element it was not possible to eliminate one parasitic term of energy which appears during the procedure. For DSG triangle all parasitic terms of energy are eliminated. The penalty coefficients depends on the geometry of the triangle.

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30

Bošanský, Michal, and Bořek Patzák. "PARALLELIZATION OF ASSEMBLY OPERATION IN FINITE ELEMENT METHOD." Acta Polytechnica 60, no. 1 (March 2, 2020): 25–37. http://dx.doi.org/10.14311/ap.2020.60.0025.

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The efficient codes can take an advantage of multiple threads and/or processing nodes to partition a work that can be processed concurrently. This can reduce the overall run-time or make the solution of a large problem feasible. This paper deals with evaluation of different parallelization strategies of assembly operations for global vectors and matrices, which are one of the critical operations in any finite element software. Different assembly strategies for systems with a shared memory model are proposed and evaluated, using Open Multi-Processing (OpenMP), Portable Operating System Interface (POSIX), and C++11 Threads. The considered strategies are based on simple synchronization directives, various block locking algorithms and, finally, on smart locking free processing based on a colouring algorithm. The different strategies were implemented in a free finite element code with object-oriented architecture OOFEM [1].

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31

Lee, Hong-Woo, Jin-Rae Cho, and Do-Young Kim. "Locking-free robust finite element approximation of thin shell-like structures." Journal of Mechanical Science and Technology 34, no. 9 (September 2020): 3701–8. http://dx.doi.org/10.1007/s12206-020-0822-z.

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32

Senjanović, Ivo, Nikola Vladimir, and Neven Hadžić. "Modified Mindlin plate theory and shear locking-free finite element formulation." Mechanics Research Communications 55 (January 2014): 95–104. http://dx.doi.org/10.1016/j.mechrescom.2013.10.007.

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33

NGUYEN-THOI, T., G. R. LIU, and H. NGUYEN-XUAN. "ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 06, no. 04 (December 2009): 633–66. http://dx.doi.org/10.1142/s0219876209001954.

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A node-based smoothed finite element method (NS-FEM) for solving solid mechanics problems using a mesh of general polygonal elements was recently proposed. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh, and a number of important properties have been found, such as the upper bound property and free from the volumetric locking. The examination was performed only for two-dimensional (2D) problems. In this paper, we (1) extend the NS-FEM to three-dimensional (3D) problems using tetrahedral elements (NS-FEM-T4), (2) reconfirm the upper bound and free from the volumetric locking properties for 3D problems, and (3) explore further other properties of NS-FEM for both 2D and 3D problems. In addition, our examinations will be thorough and performed fully using the error norms in both energy and displacement. The results in this work revealed that NS-FEM possesses two additional interesting properties that quite similar to the equilibrium FEM model such as: (1) super accuracy and super-convergence of stress solutions; (2) similar accuracy of displacement solutions compared to the standard FEM model.

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34

Kabir, Humayun R. H., and Abdullateef M. Al-Khaleefi. "Frequency Response of a Three-Node Finite Element for Thick and Thin Plates." Journal of Vibration and Control 8, no. 8 (August 2002): 1123–53. http://dx.doi.org/10.1177/107754602029584.

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A shear-locking free isoparametric three-node triangular finite element is presented to study the frequency response of moderately thick and thin plates. Reissner/Mindlin theory that incorporates shear deformation effects is included into the element formulation. A shear correction term is introduced in transverse shear strain components to avoid the shear-locking phenomenon. The element is developed with a full integration scheme, hence, the element remains kinematically stable. Natural frequencies and mode shapes are obtained and compared with the available analytical and finite element solutions.

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35

Gellert, M. "A new method for derivation of locking-free plate bending finite elements via mixed/hybrid formulation." International Journal for Numerical Methods in Engineering 26, no. 5 (May 1988): 1185–200. http://dx.doi.org/10.1002/nme.1620260512.

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36

CHAPELLE, D., and R. STENBERG. "AN OPTIMAL LOW-ORDER LOCKING-FREE FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES." Mathematical Models and Methods in Applied Sciences 08, no. 03 (May 1998): 407–30. http://dx.doi.org/10.1142/s0218202598000172.

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We propose a simple modification of a recently introduced locking-free finite element method for the Reissner–Mindlin plate model. By this modification, we are able to obtain optimal convergence rates on numerical benchmarks. These results are substantiated by a complete mathematical analysis which provides optimal a priori error estimates.

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37

Coda, Humberto Breves, and Rodrigo Ribeiro Paccola. "Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells." Mathematical Problems in Engineering 2009 (2009): 1–32. http://dx.doi.org/10.1155/2009/575131.

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This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.

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38

Hui, Y., G. De Pietro, G. Giunta, S. Belouettar, H. Hu, E. Carrera, and A. Pagani. "Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements." Mathematical Problems in Engineering 2018 (November 27, 2018): 1–22. http://dx.doi.org/10.1155/2018/4821385.

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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39

Shi, Dongyang, Shipeng Mao, and Shaochun Chen. "A locking-free anisotropic nonconforming finite element for planar linear elasticity problem." Acta Mathematica Scientia 27, no. 1 (January 2007): 193–202. http://dx.doi.org/10.1016/s0252-9602(07)60017-4.

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40

Nascimbene, R. "An Arbitrary Cross Section, Locking Free Shear-flexible Curved Beam Finite Element." International Journal for Computational Methods in Engineering Science and Mechanics 14, no. 2 (February 2013): 90–103. http://dx.doi.org/10.1080/15502287.2012.698706.

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41

Lin, Tao, Dongwoo Sheen, and Xu Zhang. "A locking-free immersed finite element method for planar elasticity interface problems." Journal of Computational Physics 247 (August 2013): 228–47. http://dx.doi.org/10.1016/j.jcp.2013.03.053.

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42

Jung, Woo-Young, and Sung-Cheon Han. "An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions." Mathematical Problems in Engineering 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/276304.

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An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.

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43

Xia, Yiming. "Multiresolution Finite Element Method Based on a New Locking-Free Rectangular Mindlin Plate Element." World Journal of Mechanics 06, no. 06 (2016): 193–206. http://dx.doi.org/10.4236/wjm.2016.66016.

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44

Norouzzadeh, Amir, Reza Ansari, and Mansour Darvizeh. "Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis." Mathematics and Mechanics of Solids 24, no. 12 (June 12, 2019): 3753–78. http://dx.doi.org/10.1177/1081286519855111.

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In Part I of this study, a variational formulation was presented for the large elastic deformation problem of micromorphic shells. Using the novel matrix-vector format presented for the kinematic model, constitutive relations, and energy functions, an isogeometric analysis (IGA)-based solution strategy is developed, which appropriately estimates the macro- and micro-deformation field components. Due to the capability of constructing exact geometries and the powerful mesh refinement tools, IGA can be successfully applied to solve the equilibrium equations with dominant nonlinear terms. It is known that different types of locking phenomena take place in the conventional finite element analysis of thin shells based on low-order elements. Non-standard finite element models with mixed interpolation schemes and additional degrees of freedom (DOFs) or the ones used the high-order Lagrangian shell elements which require high computational costs, are the available solutions to tackle locking issues. The present 16-DOFs IGA is found to be efficient because of possessing a good rate of convergence and providing locking-free stable responses for micromorphic shells. Such a conclusion is found from several comparative studies with available data in the well-known macro-scale benchmark problems based on the classical elasticity as well as the corresponding numerical examples studied in nano-scale beam-, plate-, cylindrical shell- and spherical shell-type structures on the basis of the micromorphic continuum theory.

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45

Schulz, Matthias, and Markus Böl. "An objective and locking-free finite-element formulation for geometrically exact Kirchhoff rods." PAMM 17, no. 1 (December 2017): 347–48. http://dx.doi.org/10.1002/pamm.201710143.

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46

Lepe, Felipe, David Mora, and Rodolfo Rodríguez. "Locking-free finite element method for a bending moment formulation of Timoshenko beams." Computers & Mathematics with Applications 68, no. 3 (August 2014): 118–31. http://dx.doi.org/10.1016/j.camwa.2014.05.011.

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47

García-Vallejo, Daniel, Aki M. Mikkola, and José Luis Escalona. "A new locking-free shear deformable finite element based on absolute nodal coordinates." Nonlinear Dynamics 50, no. 1-2 (January 9, 2007): 249–64. http://dx.doi.org/10.1007/s11071-006-9155-4.

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48

Hansbo, Peter, and Mats G. Larson. "Locking free quadrilateral continuous/discontinuous finite element methods for the Reissner–Mindlin plate." Computer Methods in Applied Mechanics and Engineering 269 (February 2014): 381–93. http://dx.doi.org/10.1016/j.cma.2013.11.004.

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Onishi, Y., and K. Amaya. "A locking-free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems." International Journal for Numerical Methods in Engineering 99, no. 5 (May 14, 2014): 354–71. http://dx.doi.org/10.1002/nme.4684.

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Pham, Tien Dat, Quoc Hoa Pham, Van Duc Phan, Hoang Nam Nguyen, and Van Thom Do. "Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method." Symmetry 11, no. 5 (May 17, 2019): 684. http://dx.doi.org/10.3390/sym11050684.

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Abstract:

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.

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