Abstract
AbstractA new approach to enforce surface contact conditions in transient non‐linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss‐Seidel method in which non‐linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.
Highlights
Surface contact kinematic conditions can be enforced by prescribing displacement constraints to prevent structural or continuum domains from overlapping and to control surface contact sliding
A two dimensional finite element surface contact formulation based ·on the forward increment Lagrange multiplier method is developed in Sections 6, 7 and 8
It should be emphasized that the coupled system of equations involved in the forward increment Lagrange multiplier method is typically small
Summary
Surface contact kinematic conditions can be enforced by prescribing displacement constraints to prevent structural or continuum domains from overlapping and to control surface contact sliding. Lagrange multiplier methods and penalty function methods are the two most common used approaches to enforce finite element surface contact displacement constraints. A two dimensional finite element surface contact formulation based ·on the forward increment Lagrange multiplier method is developed in Sections 6, 7 and 8. The most significant contribution in the present paper is the formulation of an efficient method to solve the coupled forward increment Lagrange multiplier equations that arise in two dimensional surface contact
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