Optimal Design of Plastic Structures for Fixed and Shakedown Loadings

Abstract

Optimal (minimum weight) solutions for plastic framed structures under shakedown conditions are found by linear programming. Designs that are optimal for two failure criteria (collapse under fixed loads and collapse under variable repeated loads) are then investigated. It is found that these designs are governed by the ratio of the specified factors defining the two failure criteria, i.e., for shakedown, λs and for collapse under fixed loading, λ. Below a certain value (λs /λ)min the optimal solution under fixed loading is also optimal for fixed and shakedown loading. Above a value (λs /λ)max the optimal design for variable loading is also optimal under the two loading conditions. For intermediate values of λs /λ the optimal design that simultaneously satisfies the two criteria is different from the optimal designs for each independent loading condition. An example illustrates the effect of λs /λ on the nature of the design solution.