A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

International Journal for Numerical Methods in Engineering Accepted Manuscript. R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler Abstract In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of…

A MINI element over star convex polytopes

Finite Elements in Analysis and Design Accepted Manuscript. Amrita Francis, Alejandro Ortiz-Bernardin, Stéphane P. A. Bordas, Sundararajan Natarajan. Abstract In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain…

Impact identification using nonlinear dimensionality reduction and supervised learning

Smart Materials and Structures Volume 28, Issue 11, 1 October 2019, Pages 115005 V. Meruane, C. Espinoza, E. Lopez Droguett, A. Ortiz-Bernardin Abstract Real-time monitoring systems that can automatically locate and identify impacts as they occur have become increasingly attractive for ensuring safety and preventing catastrophic accidents in aerospace structures. In most cases, a set…

Veamy: an extensible object-oriented C++ library for the virtual element method

Numerical Algorithms Volume 82, 2019, Pages 1189-1220 Alejandro Ortiz-Bernardin, Catalina Alvarez, Nancy Hitschfeld-Kahler, Alessandro Russo, Rodrigo Silva-Valenzuela, Edgardo Olate-Sanzana. Abstract This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson problems in…

On the behaviour of spherical inclusions in a cylinder under tension loads

Ingenius Vol. 19, 2018, pp. 69-78 S. Montero, R. Bustamante, A. Ortiz-Bernardin Abstract In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modelled as nonlinear elastic bodies that undergo small strains….

A volume-averaged nodal projection method for the Reissner-Mindlin plate model

Computer Methods in Applied Mechanics and Engineering Volume 341, Issue 1, 2018, Pages 827-850 A. Ortiz-Bernardin, Philip Köbrich, Jack S. Hale, Edgardo Olate-Sanzana, Stéphane P. A. Bordas, Sundararajan Natarajan. Abstract We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e.,…

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