Finite strains and displacements of elastic membranes by the finite element method

Abstract This paper presents a consistent finite element formulation for the analysis of large displacements and finite strains in elastic membranes of general shape. A continuous membrane is divided into a number of flat triangular elements and the behavior of a typical element is described in terms of the displacements of its nodes. It is assumed that the node points are sufficiently close that the displacement fields within each element can be approximated by linear functions of the local coordinates. On the basis of this assumption, the Lagrangian strain tensor is expressed in terms of the node displacements and a nonlinear stiffness relation between node forces and displacements is derived. Group transformations are introduced which re-assemble the elements and apply appropriate boundary conditions. These lead to systems of nonlinear algebraic equations in the generalized displacements. Numerical examples are included to demonstrate the procedure.