Large Deformation, Post-Buckling Analyses of Large Space Frame Structures, Using Explicitly Derived Tangent Stiffness Matrices

Abstract

Large deformation and post-buckling analyses of structures have been studied by many researchers as an important subject in structural mechanics in the past decade or so. In all their studies, an incremental approach, either of the total Lagragean type or the updated Lagragean type, is employed. As the incremental approach is often based on the so-called tangent stiffness matrix, which reflects all the non-linear geometrical and mechanical effects, the majority of non-linear analyses of typical engineering structures, and especially truss- and frame-type large space structures, will be vastly simplified if an explicit expression (i.e., without involving assumed basis functions for displacements/stresses, and without involving element-wise numerical integrations) for the tangent stiffness matrix of an element can be derived.