Minimum volume of trusses at shakedown – mathematical models and new solution algorithms

Abstract

Perfectly elastic-plastic truss of known geometry adapted to variable repeated load (only its lower and upper variation bounds are prescribed) is considered. Non-linear mathematical models of truss minimum volume problem are formulated. Not only strength and stiffness constraints are included in problem formulations, but also possible bar buckling is taken into account. As during volume minimization stiffness of truss elements is changing, non-linear optimization problem is solved step-by-step. Solution algorithm allows the evaluation of bar unloading phenomenon, which often occurs during shakedown process. The technique is illustrated by numerical example of pin-joined bar system calculation. The results are valid for the small displacement assumptions.