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Nonlinear solution methods for infinitesimal perfect plasticity
Author(s) -
Wieners C.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200610339
Subject(s) - infinitesimal , sequential quadratic programming , mathematics , linearization , projection (relational algebra) , nonlinear system , context (archaeology) , convergence (economics) , mathematical optimization , nonlinear programming , mathematical analysis , quadratic programming , algorithm , paleontology , physics , quantum mechanics , economics , biology , economic growth
We review the classical return algorithm for incremental plasticity in the context of nonlinear programming, and we discuss the algorithmic realization of the SQP method for infinitesimal perfect plasticity. We show that the radial return corresponds to an orthogonal projection onto the convex set of admissible stresses. Inserting this projection into the equilibrium equation results in a semismooth equation which can be solved by a generalized Newton method. Alternatively, an appropriate linearization of the projection is equivalent to the SQP method, which is shown to be more robust as the classical radial return. This is illustrated by a numerical comparison of both methods for a benchmark problem.