The eigenstrain formulation for classical plates

Abstract

In the present paper, the eigenstrain formulation is developed for classical plates. By employing this approach. Green's function of an isotropic plate is obtained in closed form. The solution for a plate with semi-infinite hinge is derived, which shows a l/r singularity near the tip of the hinge. The Eshelby-type problem, an elliptic inclusion with uniform eigenstrain. is studied and the result has the same features as that of the Eshelby solution for ellipsoidal inclusion in threedimensional elasticity, i.e., the general stress Mαβ and strain Wαβ are uniform inside the inclusion. By using the equivalent inclusion method outlined in this paper, an elliptic inhomogeneity which has different material properties from the matrix can be made equivalent to an elliptic inclusion with appropriate uniform eigenstrain. and can therefore be solved readily.