Laminate elastostatics

A general formulation is presented for a class of plane elastostatic, laminated body problems which have the characteristic that the internal material interfaces and the external boundary are level surfaces of the same curvilinear coordinate system. The laminated body is regarded as a material continuum characterized by material property functions which possess finite jumps across material interfaces. The stress field within the body is considered as being induced by external boundary tractions and by temperature, the body being stress-free in the reference state. It is shown that the problem involves the determination of a single piecewise continuous stress function which is in turn expressed in terms of the material property functions and three continuous stress functions which have discontinuous normal derivatives at material interfaces. The theory reduces to that of ordinary elasticity when the material property functions become uniformly constant. In the case in which the number of material interfaces increases without limit, a correspondence principle is derived which relates the stress field in the laminated body to the stress field in a ‘corresponding’ homogeneous, anisotropic body.