Closed form solution for rectangular inclusions with quadratic eigenstrains

The problem of a rectangular inclusion in an infinite isotropic elastic domain is solved in closed form for the case of a quadratic eigenstrain within the inclusion. The eigenstrain represents a stress free strain such as would occur with a quadratic temperature field. The problem is formulated in terms of fundamental point load solutions yielding a Green's function based integral expression. This integral is singular for interior points of the inclusion and non-singular for exterior points. For both cases closed form formulae are obtained. A non-uniformly heated rectangular region and a rectangular region with a non-uniform shear distortion are solved as examples. (C) 1999 Elsevier Science Ltd. All rights reserved.