LimitS—A system for limit state analysis and optimal material layout

Abstract

A system Limits for limit state analysis and material optimization has been developed and implemented in a PC environment. The program is formulated in a general finite element format with stress-based elements. The solution method is based on the lower-bound theorem, where an optimal stress distribution or an optimal material layout is determined. Through linearization of the yield criteria the optimization problem is stated as a linear programming problem. Within the formulation of the discretized model the optimal lower-bound solution is shown to be an upper-bound solution, and thereby both the statics and kinematics of the collapse mode are determined via the dual variables of the LP-problem. In Limits the following element types are implemented: two- and three-dimensional beam elements; truss elements; triangular slab elements; and shear and stringer elements for plates with in-plane loading. Examples of all three problem types are given including both limit state analysis and material optimization.