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Lagrange constraints for transient finite element surface contact
Author(s) -
Carpenter Nicholas J.,
Taylor Robert L.,
Katona Michael G.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620320107
Subject(s) - lagrange multiplier , finite element method , constraint algorithm , mathematics , compatibility (geochemistry) , penalty method , multiplier (economics) , unilateral contact , gauss , mathematical optimization , structural engineering , engineering , physics , quantum mechanics , chemical engineering , economics , macroeconomics
A 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.