A finite-variation method in the nonlinear shell mechanics

A numerical algorithm is proposed for calculating the coefficients of the first and second order variations of the strain energy of a nonlinear finite element model of a shell, which are necessary to determine the equilibrium states of a shell and investigate their stability. Several numerical schemes based on various finite difference approximations are considered. For these schemes, the accuracy, convergence, and computation time are studied using popular geometrically-nonlinear problems of elastic plates and shells.