Limit Analysis of Curved Grids

Abstract

The limit analysis of a class of grillages consisting of essentially two main circular arc girders connected by a number of straight cross beams is formulated as a mathematical programming problem using the static or lower bound theorem of plasticity. Discretization of both the structure into finite elements and of the nonlinear bending‐torsion yield surface into a piecewise linear polygon converts the formulation into an easy‐to‐solve linear programming problem. Sufficient details on how to enforce the necessary requirements of equilibrium and yield conformity are given to allow a direct computer implementation. The use of a mathematical programming based formulation is shown to overcome various shortcomings of existing methods to solve the same problem, the main ones being lack of generality, need for prior knowledge of collapse modes, and computational difficulty. Finally, an example is presented primarily to illustrate the application of method, and also to show how useful design‐oriented charts can be developed through parametric studies.