2018 – 2021 Principal Investigator: Alejandro Ortiz-Bernardin. Project funded by CONICYT-FONDECYT (Grant Nº 1181192) Meshfree methods have several attributes that make them attractive for simulation in mechanics. Two important ones are summarized as follows. The meshfree approximation is independent of the definition of a finite element mesh — the approximation is constructed based solely on nodal locations.
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Paper Accepted for Publication in the International Journal for Numerical Methods in Engineering A. Ortiz-Bernardin, A. Russo, N. Sukumar, “Consistent and stable meshfree Galerkin methods using the virtual element decomposition.” ABSTRACT Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to
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International Journal for Numerical Methods in Engineering Vol. 112, No. 7, pp 655-684, 2017 A. Ortiz-Bernardin, A. Russo, N. Sukumar Abstract Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth
Read More » Read MoreA. Ortiz-Bernardin, A. Russo, N. Sukumar, “Consistent and stable meshfree Galerkin methods using the virtual element decomposition,” submitted. ABSTRACT Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree method are smooth (nonpolynomial functions),
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Paper Accepted for Publication in International Journal for Numerical Methods in Engineering A. Francis, A. Ortiz-Bernardin, SPA. Bordas, S. Natarajan, “Linear smoothed polygonal and polyhedral finite elements.” ABSTRACT It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as
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International Journal for Numerical Methods in Engineering Vol. 109, No. 9, pp. 1263–1288, 2017
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Computer Methods in Applied Mechanics and Engineering Vol. 119, No. 25-28, pp. 1859-1871, 2010 A. Ortiz , M.A. Puso, N. Sukumar 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
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Finite Elements in Analysis and Design Vol. 47, No. 6, pp. 572-585, 2011 A. Ortiz , M.A. Puso, N. Sukumar Abstract A novel maximum-entropy meshfree method that we recently introduced in Ortiz et al. (2010) [1] is extended to Stokes flow in two dimensions and to three-dimensional incompressible linear elasticity. The numerical procedure is aimed
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