A practical method for the evaluation of eigenfunctions from compound matrix variables in finite elastic bifurcation problems

Abstract

We show how the compound matrix method can be extended to give eigenfunctions as well as generalised eigenvalues to bifurcation problems in non-linear elasticity. When the incremental problem is formulated in terms of displacements only there are significant difficulties that arise from the non-trivial boundary conditions. In order to avoid these problems we adopt a Stroh formulation of the incremental problem. This then produces trivial boundary conditions for the compound matrix eigenvalue problem and more importantly known initial conditions for the compound matrix eigenfunction problem. This results in a straightforward and robust calculation for the eigenfunctions.