SEQUENTIAL QUADRATIC-PROGRAMMING FOR NONLINEAR ELASTIC, CONTACT PROBLEMS

The physical problem considered in this paper is that of a non-linear elastic body being indented by a rigid punch. The treatment is based o n finite element discretization and sequential quadratic programming ( SQP). The finite element formulation is obtained through a variational formulation, which generalizes to frictionless contact a three-field principle which involves deformation, volume strain and hydrostatic pr essure as independent fields. We compare an incremental load method an d a method where the indentation for the final load is sought directly . Crucial for the second method is the use of a line search with respe ct to a merit function which measures the infeasibility in the optimal ity criteria for the problem; this line search also includes a check o f the orientation-preserving condition of a positive determinant of th e deformation gradient. Each iteration within an SQP method requires t he solution of a quadratic programming (QP) subproblem, and four diffe rent methods for the solution of these subproblems are compared. The p erformance of the overall procedure is also compared to that of a comm ercially available system. Test examples ranging from 23 to 770 displa cement degrees of freedom are treated. The computational results show that the proposed solution concept is feasible and efficient. Furtherm ore, it can be applied to general non-linear elastic contact problems, since it does not include any ad hoc rules.