Local Unilateral Contact Problems of Beams and Plates Undergoing Large Deflections (Post-Buckling).

Abstract

Local unilateral contact problems involving beams and plates undergoing large deflections are studied using incremental formulations, with particular interest in the post-buckling behavior of these structural members. Finite element formulations are obtained from the discretization procedure of incremental Lagrangian forms based on the principle of virtual work. Formulation for a plate follows from a higher order theory by Lo, Christensen and Wu which contains Mindlin's theory as a special case. It is further simplified for beams using the Essenburg, the Timoshenko and the classic beam theories. For the finite element formulations, computer codes are developed to solve problems of bending and buckling of beams with unilateral constraints, with emphasis on post-buckling behavior and possibility of the secondary bifurcation. Numerical solutions are obtained using an incremental procedure.