Analytic investigation of stress coupling effects of spherically anisotropic functionally graded piezoelectric hollow spheres

We investigate the stress coupling effects of spherically anisotropic piezoelectric hollow spheres with functional gradients (represented by radial power law functions) under external uniform radial traction. By means of submatrix operations, we derive a dimensionless expression that signifies not only the characteristic (amplification/shielding) of the stress coupling, but also the magnitude of the effect. This should be very beneficial for structural design. When bounded strain energy conditions are assumed, the study extends to solid spheres under uniform radial traction on the surface. As in the case of pure elasticity, infinite stresses can occur at the center of the sphere regardless of the magnitude of the applied stress, but all have weaker stress singularities.