Elastostatics in the presence of a temperature distribution or inhomogeneity

The equilibrium of an inhomogeneous elastic body is analyzed theoretically and numerically, with special emphasis on the case when the inhomogeneity arises from a given temperature distribution. The case when the inhomogeneity (or variation in temperature) is small is treated via linearization, the corresponding expansion of the solution in terms of an appropriate small parameter e{open} being justified by means of the implicit function theorem. For certain stored-energy functions suggested by the problem of cooling basalt rock, an exact solution to the linearized problem is found. A direct minimization of the energy using a finite-element algorithm is found to agree with the linearized solution as e{open} ? 0. © 1992 Birkhäuser Verlag.