Limit state analysis of thin plates and slabs by a numerical pseudo-lower yield design approach

Abstract

The prediction of failure load, collapse mechanism and moment distribution at limit state plays a crucial role in structural design. For plates and slabs, numerical lower bound solutions and associated limit moment distribution are rarely reported due to the difficulties in constructing moment-based plate elements used in the static formulation. In this paper, a novel numerical limit state analysis procedure, which uses pseudo-static theorem and conic programming, is developed. The total moment fields are decomposed into parts involving a fictitious elastic moment and a self-equilibrated residual moment. Equilibrium equations for the self-equilibrated residual moment field are satisfied in a weak sense by means of the displacement-based elements. Numerical solutions are obtained rapidly with the use of second-order cone programming. Various plates and slabs with arbitrary geometries and boundary conditions are examined, providing accurately estimated collapse load factors and the moment distribution at limit state.