Abstract
In this study, we propose a material orientation optimization method for optimum design of laminated composite shell structures. Tsai-Hill criterion is employed for evaluating the strength, and its maximum value is minimized. The issue of non-differentiability inherent in this min-max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional using the Kreisselmeier-Steinhauser function. The optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function with respect to the material orientation variation is theoretically derived based on the variational method. The optimal material orientation variations are determined by using the H1 gradient method with Poisson's equation, where the sensitivity functions aforementioned are applied as the Robin condition to vary and optimize the material orientation. The optimal design example shows that the proposed method can effectively obtain the optimal smooth material orientation distribution and maximum strength measured by the Tsai-Hill failure criterion.
