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An augmented Lagrangian method for discrete large‐slip contact problems
Author(s) -
Heegaard J.H.,
Curnier A.
Publication year - 1993
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.1620360403
Subject(s) - augmented lagrangian method , mathematics , discretization , jacobian matrix and determinant , differentiable function , mathematical analysis , piecewise , lagrange multiplier , finite element method , penalty method , linearization , slip (aerodynamics) , nonlinear system , mathematical optimization , physics , quantum mechanics , thermodynamics
An augmented Lagrangian formulation is proposed for large‐slip frictionless contact problems between deformable discretized bodies in two dimensions. Starting from a finite element discretization of the two bodies, a node‐on‐facet element is defined. A non‐linear gap vector and its first variation are derived in terms of the nodal displacements. The relevant action and reaction principle is stated. The gap distance is then related to the conjugate pressure by a (multivalued non‐differentiable) unilateral contact law. The resulting inequality constrained minimization problem is transformed into an unconstrained saddle point problem using an augmented Lagrangian function. Large slip over several facets is possible and the effects of target convexity or concavity are investigated. A generalized Newton method is used to solve the resulting piecewise differentiable equations necessary for equilibrium and contact. The proper tangent (Jacobian) matrices are calculated. The primal (displacements) and dual (contact forces) unknowns are simultaneously updated at each iteration.