On multimodal optimization of circular arches against plane and spatial creep buckling

Abstract

The paper deals with the optimal design of circular arches against creep buckling in the Rabotnov-Shesterikov sense. The design vairable, i.e. the cross-sectional area function, is determined so as to minimize the total volume of an arch under given external load (radial pressure) and the critical time. Multimodal formulation of the problem is introduced, i.e. both symmetric and antisymmetric instability modes are considered for in-plane and out-of-plane buckling. The effect of the behaviour of loading in the course of buckling on optimal shapes is analysed. The problem is solved by the use of Pontryagin's maximum principle.