Optimal shakedown design of trusses: strenght, stiffness and stability constraints

Abstract

Known geometry perfectly elastic-plastic truss subjected by cyclic load defined by its upper and lower variation bounds is considered. Non-linear mathematical model of truss minimum volume problem is formulated, where strength, stiffness and stability constraints are included. Stiffness constraints are realized via restriction of truss deflection, i.e. displacements of truss joints. In this paper a new technique is proposed for calculation of maximal and minimal values of residual displacements of truss joint, which depend on loading history. Stability constraints are related with recommendations of EUROCODE 3, when admissible forces of compressive bars are obtained by reduction of their material yield limit. Problem of truss optimization is difficult optimal operating problem: not always it is possible to apply dual theory of mathematical programming directly for stress and strain determination (analysis problem) of structure at shakedown. During solution of the main non-linear problem of truss optimization, stiffness of truss elements (together with that truss stress and strain state) is changing. That is why this problem is solved step-by-step. In this research Kuhn-Tucker optimality conditions of mathematical programming are widely applied. Rozen project gradient method is applied for non-linear problem solution. Proposed technique is illustrated by solution of pin-joined bar structure optimization problem. The results are valid for the small displacement assumptions.