A finite-variation method in the nonlinear shell mechanics

V. V. Kuznetsov, S. V. Levyakov

Novosibirsk State Technical University

Abstract: 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.

Key words: finite-variation method, thin shell, large displacements, strain energy, finite element.

UDC: 539.3:519.6

Received: 06.06.2007
Revised: 10.07.2007

 English version: Numerical Analysis and Applications, 2008, 1:3, 269–279