Material symmetry optimization by Kelvin modes

Pointwise optimization of the material symmetry of an anisotropic elastic material with respect to fixed and specified stress (or strain) states is accomplished. The conceptual variables in this problem are the type of material symmetry and the orientation of the canonical symmetry axis for the material at a point in the material. The actual variables are the coefficients of the elasticity (or compliance) matrix. The results are presented in the form of the elasticity (or compliance) matrices that minimize the strain energy with respect to specified, but arbitrary, stress (or strain) states.