Computer analysis of slackened-elastic-plastic beams under non-proportional loads

Abstract

A computer method for elastic-plastic continuous beams with rotation constraints is proposed. Such structures belong to a particular class of slackened systems, i.e. systems with gaps at structural joints. The mathematical model of slackened structures represents a discrete form of the Kuhn-Tucker's conditions, and is equivalent to dual Quadratic Programming Problems (QPPs). The uniqueness of a solution to the problem of the beams under considerations is assured, excluding cases where the structure converts into a mechanism, and the solution corresponds to dual Linear Programming Problems (LPPs). In order to calculate both the structure and mechanism a concept of the finite element with elastic rotation supports is used in the computer program. The uniqueness of solutions makes it possible to use a pure elastic analysis with some additional constraints superimposed on state variables. It allows us to avoid the time-consuming mathematical programming methods. Several examples illustrate the behaviour of beams under multiparameter loads. Results relate the cyclic loading (shakedown) as well as elastic, sublimit and limit surfaces. The work presents the characteristic features of slackened structural systems.