%A Francis Tin-Loi
%A Michael C. Ferris
%T Complementarity Problems in Engineering and Mechanics: Models and Solution
%D February 1999
%R 99-02
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
A large class of problems in engineering mechanics involves a
so-called "complementarity" relationship representing the
orthogonality of two sign-constrained vectors. Typical instances are
plasticity laws and contact-like conditions. For state problems, the
formulation leads to a mixed complementarity problem (MCP) whereas in
synthesis (e.g. minimum weight design) or identification problems, a
mathematical program with equilibrium constraints (MPEC) is
obtained. The aim of this paper is two-fold. Firstly, it describes,
through two typical models, how some important engineering mechanics
problems can be formulated elegantly and naturally as either an MCP or
an MPEC. Secondly, it describes a powerful computer-oriented
environment for constructing and solving these mathematical
programming problems, with features such as sparsity and automatic
differentiation facilities being transparently accessible. This
involves the use of the modeling language GAMS (an acronym for General
Algebraic Modeling System) and its associated mathematical programming
solvers (e.g. the industry standard MCP solver PATH). A simple generic
model suitable for solving the state problem for trusses is used to
clarify the syntax of GAMS models and to illustrate the ease with
which they can be built and solved.