GEOMETRICALLY NONLINEAR-ANALYSIS OF PLATES AND SHALLOW SHELLS BY DYNAMIC RELAXATION

This paper investigates the application of dynamic relaxation (DR) met hod to the geometrically non-linear analysis of plates and shells invo lving large deflections, small rotations and strains. The merits and d emerits of two types of approaches suggested for the evaluation of par ameters of the DR method are reviewed. An accurate shallow shell eleme nt is developed in the present work using Marguerre's shallow shell th eory. Total Lagrangian (TL) approach is used for an explicit derivatio n of element internal force vector by energy approach considering all higher-order terms both in the membrane strain-displacement relations and in curvature expressions. The efficiency of the proposed shallow s hell element in combination with the DR method for pre-and post-buckli ng analysis of structures is illustrated through various numerical exa mples. Also, the effect of these higher-order terms in membrane and cu rvature expressions on overall accuracy of the solution is studied for the class of geometrically non-linear problems considered in the pres ent study.