Bounds on plastic deformations of trusses

Abstract

A technique to compute bounds on plastic deformations of truss structures is presented. Each element of the structure is constituted by an elastic-perfectly plastic material. The structure is subjected to a combination of loadings (i.e. a steady mechanical load and a cyclic mechanical and/or kinematical load) resulting slightly above the shakedown limit. The proposed technique utilizes a bounding principle by means of which it is possible to calculate a bound on a special proportionality factor. This characterizes the relation between the kinematical part of the solution to the Kuhn-Tucker equations relative to the shakedown cyclic load factor problem and the gradient (with respect to the cyclic load multiplier) of the kinematical part of the elastic-plastic steady-state response of the structure to loads at the shakedown limit. Bounds on any measure of real plastic deformation, in the structure subjected to the combination of loadings slightly above the shakedown limit, can be then easily computed by means of the knowledge of the bound on the above-mentioned proportionality factor as well as of the kinematical part of the solution to the shakedown cyclic load factor problem.