A computationally efficient method for considering a large number of nonlinear multi-point constraints within the finite element method

Abstract

Nonlinear constraints are crucial in modeling various problems in computational mechanics. Among other things, they can be used for the subsequent consideration of rigid inclusions in a body originally modeled as deformable, without requiring a remeshing of the considered domain and thus contributing to a rapid modeling building. Unlike Lagrange multipliers and the penalty method, the master-slave elimination reduces the problem dimension but is limited to linear constraints. We introduce a new master-slave elimination method for arbitrary nonlinear multi-point constraints. It is compared to existing methods through analysis of the resulting equations and numerical examples. Results indicate that the method is as accurate, robust, and flexible as Lagrange multipliers, with improved efficiency due to reduced degrees of freedom, which is particularly advantageous when a large number of constraints have to be considered.

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