Finite element analysis for the elastic stability of thin walled open section columns under generalized loading

The current interest in collapse characteristics brought about by crashworthiness requirements ýas shown the need for a better understanding and predictive capability for the thin walled open section structures. In general three possible modes exist in which a loaded thin walled open section column can buckle: 1) they can bend in the plane of one of the principal axes; 2) they can twist about the shear. centre; 3) or they can bend and twist simultaneously. The following study was undertaken to investigate the general failure of thin walled open section structures. A literature survey was conducted and it prevailed that a basic fundamental theoretical study was vital in describing the behaviour of thin walled structural members. The following stages of theoretical study have been completed: 1) Formulation of the stiffness matrix to predict the generalised force-displacement relationships assuming the small displacement theory in the linear elastic range. 2) Formulation of the geometric stiffness matrix to predict the buckling criteria under generalised loading and end constraints in the linear elastic range. 3) Formulation of the compound coordinate transformation matrix to relate local and global displacements or forces. 4) Preparation of the associated finite element computer program to solve general thin walled open sections structural problems.