The optimum shape of orthotropic inclusion in infinite orthotropic plate. The equi-stressed shape of inclusion in a biaxial stress field.

An analytical method to determine the optimum shapes of orthotropic inclusions in orthotropic infinite plates (matrix) to which are applied uniformly biaxial tension or compression at infinity, is proposed. The method is based on the solution of an anisotropic plate with an elliptic inclusion found by Yang and Chou. The optimum inclusions, which have the optimum length ratios between the principal axes of the ellipses under the applied stress ratios, produce uniform stress distributions along the boundary between the inclusion and the matrix. Optimum shape diagrams for deciding the axis ratios of ellipses, which are plotted numerically for models with typical elastic stiffness ratios of inclusion to the matrix, show quantitatively the relationship between the effect of the anisotropic factors and the shapes. From the diagrams, it is appeared that the ellipse becomes more slender as the applied stress ratio or the anisotropic factors become larger or smaller than unit ; and that the factor of the inclusion produces an opposite effect on the shape, in comparison with that of the matrix