SOLUTION OF CONTACT PROBLEM USING "MIXED" MLPG FINITE VOLUME METHOD WITH MLS APPROXIMATIONS

Year 2016, Volume: 12 Issue: 1, 90 - 104, 24.04.2016

Cengiz Erdönmez

Abstract

Meshless methods are became an alternative to most popular numerical
methods used to solve engineering problems such as Finite Difference and Finite
Element Methods. Because of element free nature, problems are solved using
meshless methods depending on the general geometry and conditions of the
problem. Mixed Meshless Local Petrov-Galerkin (MLPG) approach is based on
writing the local weak forms of PDEs. Moving least squares (MLS) is used as the
interpolation schemes. In this study contact analysis problem is modelled using
Meshless Finite Volume Method (MFVM) with MLS interpolation and solved for beam
contact problem. Meshless discretization and linear complementary equation of
the 2-D frictionless contact problems are described first. Then the problem is converted
to a linear complementary problem (LCP) and solved using Lemke’s algorithm. An
elastic cantilever beam contact to a rigid foundation is considered as an
example problem.

Keywords

Mixed Meshless Local Petrov-Galerkin, Moving least squares, Meshless Finite Volume Method, Linear Complimentary Problem, Cantilever beam contact.

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