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Closed-Form Analysis of the Stress Field at Rectangular Corners of Reinforcement Patches

Laminate reinforcement patch corners are locations of stress localizations which may cause a premature failure of the structure. A closed-form approach for the calculation of the occurring interlaminar stress concentrations in the surroundings of rectangular reinforcement patch corners of thermally loaded composite cross-ply laminates is presented. The interlaminar stresses are obtained by the application of a perturbing stress field which comprises separable stress functions. The separation is of the kind that the dependency of the stress functions in transverse direction is assumed a priori to be known and that the stress functions' in-plane part is determined with the help of the principle of minimum complementary potential energy. Afterwards boundary conditions are applied using an expanded Ritz-approach with Lagrange multipliers in order to obtain the perturbing stress field. This stress field is then superposed to the results of the classical laminate plate theory. The method is in good agreement with results from a comparative finite element analysis, is easily applicable and requires very low computational effort.