G. Bjorkman et al., SEQUENTIAL QUADRATIC-PROGRAMMING FOR NONLINEAR ELASTIC, CONTACT PROBLEMS, International journal for numerical methods in engineering, 38(1), 1995, pp. 137-165
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.