Geometrically nonlinear buckling analysis of truss under mechanical and thermal load based on mixed finite element formulation

Abstract

This paper is concerned with the numerical method for the geometrically nonlinear buckling analysis of truss under mechanical load and thermal load due to constant temperature change. The solution of a geometrically nonlinear problem of the system under thermal load based on a displacement-based finite formulation requires the implementation of thermal deformation constraint depending on the incremental element length. The additional constraint of thermal expansion considerably increases the difficulty in finite element formulation and solving method of the nonlinear buckling problem. This research proposes a novel approach to formulate the nonlinear buckling problem of truss under thermal load based on mixed finite formulation. The mixed balanced equation of thermal loading truss considering large displacement is formulated using the principle of virtual work. Based on the formulated equation, the research develops an incremental-iterative algorithm and calculation program for solving the nonlinear buckling problem of thermal loading truss using the arc length technique. The numerical test is presented to investigate the effect of thermal load to buckling behaviour of plan truss.