Material symmetry optimization by Kelvin modes

Pointwise optimization of the material symmetry of an anisotropic elastic m aterial with respect to fixed and specified stress (or strain) states is ac complished. The conceptual variables in this problem are the type of materi al symmetry and the orientation of the canonical symmetry axis for the mate rial 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 en ergy with respect to specified, but arbitrary, stress (or strain) states.