Lower bound limit analysis by quadrilateral elements

Abstract

This paper presents a quadrilateral element formulation of lower bound theorem. The formulation uses a four-noded quadrilateral element. The weak form of the equilibrium equations is performed to linearize the equilibrium equations. By Green’s theorem, the integral over quadrilateral element are transformed into boundary integral over the element boundary. The major advantage of using quadrilateral element, rather than triangular element, is that more accurate lower bound can be obtained with the same element size.Two numerical examples are given to illustrate the capability of the new method for computing lower bound. The accuracy of the quadrilateral element formulation is compared with that of three-noded triangular element formulation in detail.