Shakedown Analysis of Elastoplastic Arches

The use of mathematical programming methods proves to be of interest in the formulation and the solution of some rather tedious problems of structural plasticity. This paper extends the application of linear programming techniques to elastoplastic arches under variable repeated loadings by adopting linearized models for the arch shape and the yield criteria of its sections. The concept of M and M + N mechanisms proves convenient in formulating the equilibrium equations by the static approach. With nonlinear yield conditions the formulations presented will still hold, but the solution of corresponding nonlinear programming problems will likely become more complex. In addition to their practical applications, the linear programming approaches suggested and illustrated have the advantage of allowing the incremental collapse load to be derived by a direct, algorithmic procedure, rather than by the trial and error procedures suggested in earlier investigations.