Generalization of Newton-Type Methods of Inelastic Contact Problems
Just as for elastic contact problems one can state for the elastoplastic one a minimization problem in terms of stress- and strain-rates. After a discretization in time by finite differences and in space by finite elements one has to solve either a sequence of nonlinear optimization problems with constraints or a sequence of Kuhn-Tucker inequalities. For this, sequential quadratic programming algorithms (as the natural extension of Newton-methods to problems with constraints) have proved best. So far, these methods were restricted to problems with small dimension and thus not suited for problems in the field of structural mechanics.
It is shown how to implement this method in general finite element codes by help of an algorithm given by Bertsekas. In the case that contact appears on the boundary of the body it is demonstrated how to accelerate the convergence substantially by a condensation of the linearized problems to the contact-variables.
KeywordsContact Problem Sequential Quadratic Programming Contact Node Sequential Quadratic Programming Algorithm Quadratic Programming Method
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