An Incremental Method for the Solution of Static Boundary Value Problems in Finite Elasticity

Abstract

A method is proposed for the solution of boundary value problems in finite elasticity. In this method successive small increments of the prescribed surface displacements and/or stresses and/or body forces are applied until the final prescribed values of these quantities are reached. The method lends itself to straightforward numerical analysis because the differential equations and boundary conditions that must be satisfied, at each increment, are linear in the incremental displacements. The problem is formulated in cartesian as well as curvilinear coordinates and in the material as well as in the spatial coordinate system. No restrictions are placed on the form of the strain energy function, but specific forms of the equations are given for a Neo-Hookean material.