Limit Analysis and Optimal Design of Plates with Equilibrium Elements

Abstract

A finite‐element formulation is developed for limit analysis of perfectly plastic plates using triangular equilibrium elements and linear programming. The equilibrium elements are formulated in terms of three moment components at each corner. Equivalent corner forces including shear and torsion moment contributions are derived in a simple vector format. For a linearized yield surface the duality theorem of linear programming leads to dual static and kinematic representation of the solution, whereby the traditional lower bound must be interpreted in terms of the admissibility of the static field. Optimization of material properties, such as the distribution of reinforcement in concrete plates, is also considered. The algorithms are implemented in compact form in a personal computer (PC) environment using a specially developed simplex algorithm for infinite intervals, and examples illustrate the capability of the approach.