Geometrically non-linear analysis of plates and shallow shells by dynamic relaxation Original Research Article

This paper investigates the application of dynamic relaxation (DR) method to the geometrically non-linear analysis of plates and shells involving large deflections, small rotations and strains. The merits and demerits of two types of approaches suggested for the evaluation of parameters of the DR method are reviewed. An accurate shallow shell element is developed in the present work using Marguerreʹs shallow shell theory. Total Lagrangian (TL) approach is used for an explicit derivation 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 shell element in combination with the DR method for preand post-buckling analysis of structures is illustrated through various numerical examples. Also, the effect of these higher-order terms in membrane and curvature expressions on overall accuracy of the solution is studied for the class of geometrically non-linear problems considered in the present study.