Computational procedures for plastic shakedown design of structures

Abstract

The minimum volume design problem of elastic perfectly plastic finite element structures subjected to a combination of fixed and perfect cyclic loads is studied. The design problem is formulated in such a way that incremental collapse is certainly prevented. The search for the structural design with the required limit behaviour is effected following two different formulations, both developed on the grounds of a statical approach: the first one operates below the elastic shakedown limit and is able to provide a suboptimal design; the second one operates above the elastic shakedown limit and is able to provide the/an optimal design. The Kuhn–Tucker conditions of the two problems provide useful information about the different behaviour of the obtained structures. An application concludes the paper; the comparison among the designs is effected, pointing out the different behaviour of the obtained structures as well as the required computational effort related to the numerical solutions

An extended shakedown theory on an elastic–plastic spherical shell

“…The multi-extremity of problem (37)-(46) is determined by complementary slackness conditions for mathematical programing (42). Problem (37)- (46) has to be solved in an iterative manner [35,[42][43][44]. A vector of limit forces of the first iteration S Ãð1Þ 0 is obtained in the first solution to the problem with the initial data (initial elemental flexibility matrix D).…”

Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

“…In such case the application of mathematical programing is very narrowly adapted -as a tool for the solution of extremum problems only. Therefore the formulation of the rational solution algorithms for the nonlinear analysis problems of the stresses, deformations and displacements of the structures at shakedown, remains important in the theory of shakedown of plastic structures [21,24,32].…”

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

“…For an assigned value of the cyclic load multiplier ξ a c (Fig. 2), the fixed load multiplier at the elastic/plastic shakedown limit ξ 0 ξ a c can be determined solving the following problem [25,26]:…”