Thermal stresses in a plate with a circular reinforcement

An analytical method is presented based on an inclusion analogy for determining the thermal residual stresses in an isotropic plate reinforced with a circular orthotropic patch. Explicit formulae are obtained for both the elastic properties and the thermal expansion coecients of the equivalent inclusion. Exact solutions are derived for the thermal stresses in a circular orthotropic composite reinforcement bonded to an isotropic plate. To quantify the ®nite size e€ect, approximate solutions have also been obtained for a circular plate reinforced by a concentric circular patch. The present solutions are compared with ®nite element results, demonstrating a very good agreement with the numerical results. These explicit solutions provide a convenient tool for evaluating the residual thermal stresses when designing bonded repairs