Essential boundary conditions in meshfree methods via a modified variational principle. Applications to shell computations

Sebastian Skatulla; Carlo Sansour

Sebastian Skatulla The University of Nottingham
Carlo Sansour The University of Nottingham

Abstract

It has been recognized by many authors that the enforcement of the essential boundary conditions is not an easy task, when it comes to moving least square (MLS)-based meshfree methods. In particular, the modelling of non-linear problems requires high approximation accuracy in order to obtain a solution. This paper addresses the boundary approximation accuracy of MLS-based meshfree methods and shows more specifically its significance with respect to the imposition of essential boundary conditions by the penalty, the Lagrange multiplier method and their combination which results in a modified variational principle. The later is augmented by a stabilization term which uses individual stabilization parameters determined for each numerical integration point by an iteration procedure. This methodology is demonstrated on shell deformations in non-linear structural mechanics involving the Green strain tensor and two different hyper-elastic material laws.

Keywords

Meshfree methods; moving least square method; essential boundary conditions; shell analysis,

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