A simplified finite element method for large deformation, post‐buckling analyses of large frame structures, using explicitly derived tangent stiffness matrices

Abstract

Abstract In this paper, a simplified, economical and highly accurate method for large deformation, post‐buckling, analyses of frame‐type structures is presented. Using the concepts of polar‐decomposition of deformation, an explicit expression for the tangent stiffness matrix of a member/element of the frame, that accounts for the nonlinear bending‐stretching coupling, is derived in closed form, at any point in the load‐deformation path. The ranges of validity of the present simplified approach are discussed. Several example problems to demonstrate the feasibility of the present approach, over ranges of deformation that are well beyond those likely to occur in practical large frame structures, are included.