Plastic limit analysis of plane frames and grids using GAMS

Abstract

This paper describes the implementation and solution on a microcomputer of the plastic limit analysis problem for the class of plane frame and grid structures with the help of the mathematical programming language GAMS. The formulation used is based on the well-known static theorem of limit analysis applied to a suitably discretized structure. It leads to a problem in constrained optimization which becomes one of linear programming only if the yield conditions are linear. After a review of the main features of GAMS, the limit analysis model is described and applied to solve frame and grid problems involving a variety of yield constraints. An important aspect of the work described is that is serves to show that a modeling system can efficiently remove many of the barriers associated with the practical application of mathematical programming for solving structural plasticity problems. In particular, capability for large model construction, generation of detailed reports, and ease of model maintenance and modification are provided in addition to automatic interfacing with a variety of powerful solvers.