Maximum-entropy meshfree method for compressible and near-incompressible elasticity |
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| Authors: | A. Ortiz M.A. Puso N. Sukumar |
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| Affiliation: | 1. Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA 95616, USA;2. Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551, USA;1. Dip. di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Italy;2. Fakultät für Mathematik, Universität Wien, Austria;1. Department of Civil Engineering and Computer Science, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy;2. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Via G. Di Biasio 43, 03043 Cassino, Italy;3. Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy;1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;2. IUSS, Piazza della Vittoria 15, 27100 Pavia, Italy;3. IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy;4. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy;5. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi 53, 20153 Milano, Italy |
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| Abstract: | Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation. |
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