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  • Open Access


    Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

    Arash Mehraban1, Henry Tufo1, Stein Sture2, Richard Regueiro2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1283-1303, 2021, DOI:10.32604/cmes.2021.017476

    Abstract Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive. To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with respect to strain energy error are investigated for polynomial order p = 1, 2, 3, 4 for compressible elasticity, and p = 2, 3, 4 for nearly-incompressible elasticity, on different number More >

  • Open Access


    Growth, Anisotropy, and Residual Stresses in Arteries

    K. Y. Volokh 1, 2 , Y. Lev3

    Molecular & Cellular Biomechanics, Vol.2, No.1, pp. 27-40, 2005, DOI:10.3970/mcb.2005.002.027

    Abstract A simple phenomenological theory of tissue growth is used in order to demonstrate that volumetric growth combined with material anisotropy can lead to accumulation of residual stresses in arteries. The theory is applied to growth of a cylindrical blood vessel with the anisotropy moduli derived from experiments. It is shown that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery \textit {in vitro} as it is observed in experiments. It is emphasized that the mode of the arterial ring opening More >

  • Open Access


    Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

    S. Kshrisagar1, A. Francis1, J. J. Yee2, S. Natarajan1, C. K. Lee3,*

    CMC-Computers, Materials & Continua, Vol.61, No.2, pp. 481-502, 2019, DOI:10.32604/cmc.2019.07967

    Abstract In this paper, the node based smoothed-strain Abaqus user element (UEL) in the framework of finite element method is introduced. The basic idea behind of the node based smoothed finite element (NSFEM) is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell [Liu, Dai and Nguyen-Thoi (2007)]. Therefore, the numerical integration is globally performed over smoothing domains. It is demonstrated that the proposed UEL retains all the advantages of the NSFEM, i.e., upper bound solution, overly soft stiffness and free from More >

  • Open Access


    Application of the MLPG Mixed Collocation Method for Solving Inverse Problems of Linear Isotropic/Anisotropic Elasticity with Simply/Multiply-Connected Domains

    Tao Zhang1,2, Leiting Dong2,3, Abdullah Alotaibi4, Satya N. Atluri2,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 1-28, 2013, DOI:10.3970/cmes.2013.094.001

    Abstract In this paper, a novel Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed for solving the inverse Cauchy problem of linear elasticity, wherein both the tractions as well as displacements are prescribed/measured at a small portion of the boundary of an elastic body. The elastic body may be isotropic/anisotropic and simply connected or multiply-connected. In the MLPG mixed collocation method, the same meshless basis function is used to interpolate both the displacement as well as the stress fields. The nodal stresses are expressed in terms of nodal displacements by enforcing the constitutive relation between… More >

  • Open Access


    A New and Simple Meshless LBIE-RBF Numerical Scheme in Linear Elasticity

    E.J. Sellountos1, D. Polyzos2, S.N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.6, pp. 513-551, 2012, DOI:10.3970/cmes.2012.089.513

    Abstract A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral representation for displacements is considered. At the local circular boundaries tractions are eliminated with the aid of companion solution, while at the intersections between the local domains and the global boundary displacements and tractions are treated as independent variables avoiding thus More >

  • Open Access


    Numerical Solutions of 2-D Linear Elastostatic Problems by Network Method

    J.L. Morales1, J.A. Moreno2, F. Alhama3

    CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 1-18, 2011, DOI:10.3970/cmes.2011.076.001

    Abstract Following the rules of the network simulation method, a general purpose network model is designed and numerically solved for linear elastostatic problems formulated by the Navier equations. Coupled and nonlinear terms of the PDE, as well as boundary conditions, are easily implemented in the model by means of general purpose electrical devices named controlled current (or voltage) sources. The complete model is run in the commercial software PSPICE and the numerical results are post-processed by MATLAB to facilitate graphical representation. To demonstrate the reliability and efficiency of the proposed method two applications are presented: a More >

  • Open Access


    Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm

    Liviu Marin1

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.060.221

    Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical More >

  • Open Access


    A Galerkin Boundary Node Method for Two-Dimensional Linear Elasticity

    Xiaolin Li1, Jialin Zhu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.1, pp. 1-30, 2009, DOI:10.3970/cmes.2009.045.001

    Abstract In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin scheme for numerical analysis, thus boundary conditions in the GBNM can be satisfied easily and directly in the weak formulation of the boundary integral equation. Another advantage with the Galerkin scheme is that the More >

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