• Mode Shapes

    To assess quadrature errors in the integration of weak form integrals

  • Damage Assessment Algorithm

    Algorithm based on the maximum-entropy principle

  • Meshfree Basis Functions

    Plots of the maximum-entropy basis functions for different support sizes

  • Indentation of a Nearly-Incompressible Block

    Solution based on the linear volume-averaged nodal projection (VANP) method

  • Deflection of a 3-D Cantilever Beam

    Solution based on the linear volume-averaged nodal pressure technique

  • 3-D Compression of a Hyperelastic Rubber Block

    Solution based on the nonlinear volume-averaged nodal projection (VANP) method

  • Virtual Element Analysis

    Using the Veamy open-source library for the virtual element method (VEM)

  • Debonding Assessment of Sandwich Panels

    Algorithm uses damage indices derived from the modal strain energy method and the maximum-entropy linear approximation

  • Skew Plate Subjected to a Uniform Load

    Solution based on the volume-averaged nodal projection method for Reissner-Mindlin plates

  • Simulation of Colliding Flow

    Solution obtained using the volume-averaged nodal pressure technique

  • 2-D Compression of a Hyperleastic Rubber Block

    Solution obtained using the nonlinear volume-averaged nodal projection (VANP) method

Latest News

A Meshfree Nodal Integration Method for Elastic and Elastoplastic Applications Using The Virtual Element Decomposition

A Meshfree Nodal Integration Method for Elastic and Elastoplastic Applications Using The Virtual Element Decomposition

A talk given by A. Ortiz-Bernardin at COMPLAS 2019, September 3, 2019, Barcelona, Spain. A MESHFREE NODAL INTEGRATION METHOD FOR…

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

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

Paper Accepted for Publication in International Journal for Numerical Methods in Engineering R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli, …

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Accepted Paper: A MINI element over star convex polytopes

Accepted Paper: A MINI element over star convex polytopes

Paper Accepted for Publication in Finite Elements in Analysis and Design Amrita Francis, Alejandro Ortiz-Bernardin, Stéphane P. A. Bordas, Sundararajan…

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VEMLab

The free and open source library for the Virtual Element Method

Latest Journal Articles

Some of our latest research efforts are tailored to devise new nodal integration techniques by combining meshfree Galerkin methods with the relatively new numerical technology offered by the Virtual Element Method. Nodal integration schemes formulated in this manner are stable and convergent by construction. In this approach, state variables such as strains, stresses, and other internal variables in nonlinear computations can be stored at the nodes just like the displacements.

Some nodal cells used in nodal integration.

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

R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli,  N. Hitschfeld-Kahler

A MINI element over star convex polytopes

A. Francis, A. Ortiz-Bernardin, S. P. A. Bordas, S. Natarajan

Impact identification using nonlinear dimensionality reduction and supervised learning

V. Meruane, C. Espinoza, E. Lopez Droguett, A. Ortiz-Bernardin

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

A. Ortiz-Bernardin, C. Alvarez, N. Hitschfeld-Kahler, A. Russo, R. Silva-Valenzuela, E. Olate-Sanzana