A Compact Linear Programming Procedure for Optimal Design in Plane Stress∗

Abstract

Abstract Two-dimensional problems in plane stress are considered, with a view toward obtaining the optimal distribution of thickness under the condition that there be no collapse. Geometrical constraints on the shape of the structure are included for the purpose of meeting practical limitations. The aim of the paper is to give a new theoretical formulation to the problem in order to effect greater savings in computer time. In particular, the number of constraints is shown to be significantly reduced, and static admissibility is guaranteed even when dealing with a reduced formulation of the problem. This is done by linearizing the yield surface and by expressing the stress vectors as linear nonnegative combinations of the vertices of the yield polyhedron, and by enforcing plastic conformity in a simple compact way. Known static and kinematic formulations are rederived by invoking the properties of linear programming. The effectiveness of the procedure is demonstrated through applications at the end of the ...