Nonlinear equation approach for inequality elastostatics: a two-dimensional BEM implementation

The numerical solution of variational inequality problems in elastostatics is investigated by means of recently proposed equivalent nonlinear equations. Symmetric and nonsymmetric variational inequalities and linear or nonlinear, but monotone, complementarity problems can be solved this way without explicit use of nonsmooth (nondifferentiable) solvers. As a model application, two-dimentional unilateral contact problems with and without friction effects approximated by the boundary element method are formulated as nonsymmetric variational inequalities, or, for the two-dimensional case as linear complementarity problems, and are numerically solved. Performance comparisons using two standard, smooth, general purpose nonlinear equation solvers are included.