Computation and solution procedures for non-linear analysis by combined finite element — finite difference methods

Abstract This paper begins with the basic principle of virtual work and derives expressions for the pseudo forces and contributions to the tangent stiffness matrix for geometric and material nonlinearities. For this formulation a computional procedure is presented which evaluates the effects of nonlinearities through the use of finite difference expressions. This computational procedure is an order of magnitude faster than reported by other researchers and permits the solution for complex nonlinear behavior in reasonable times on the computer. Examples are presented for the large elastic-plastic deflections of shells of revolution under both static and dynamic loading and computer times are reported.

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