| Abstract: | This article presents an explicit solution of the thermal stresses in a one-sided composite patch repair, with the patch being orthotropic in both mechanical and thermal properties. The emphasis is placed on the analysis of the bending deformation of the reinforced structure resulting from thermal loading. The reinforced region is represented by an equivalent inclusion that undergoes a combination of in-plane extension and out-of-plane extension. Explicit formulae are derived for the thermal expansion coefficients as well as the bending stiffness and the in-plane extensional stiffness of the equivalent inclusion. The Eshelby inclusion analogy is first extended by postulating uniform bending curvatures and mean strains throughout the inclusion. The correctness of this conjecture is then proved by the satisfaction of force, bending moment, and displacement continuity conditions. Explicit solutions are finally derived for the bending and membrane stresses resulting from thermal loading of an isotropic plate reinforced by a circular patch. It is shown that the present solutions correlate well with the numerical results obtained using fully three-dimensional finite element analysis. |
