Evaluation of eigenfunctions from compound matrix variables in non-linear elasticity – I. Fourth order systems

We show how the compound matrix method can be used to produce eigenfunctions as well as eigenvalues for bifurcation problems in non-linear elasticity. For typical problems in elasticity the boundary conditions require a different treatment to that required for typical problems in fluid mechanics. For elasticity problems we have to use an additional shooting method to ensure that the boundary conditions are satisfied.