Optimization Approach for Free-Orientation of a Laminated Shell Structure with Orthotropic Material

In this study, we propose a non-parametric material orientation optimization method for optimum design of laminated composite shell structures consisting of orthotropic materials. We consider a single objective in terms of the compliance in the present work and minimize it under the state equation constraint. The material orientation in all layers are taken as design variables. The optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function which respect to the material orientation variation is theoretically derived. The optimum orientation variations are determined by using the H¹ gradient method with the Poisson’s equation, where the sensitivity functions are applied as the fictitious internal heat generation with the Robin condition to vary the material orientation. With the propped method, we can obtain the arbitrary and smooth distribution of the material orientations of all layers to reduce the compliance without design parametrization. The optimum design examples show that the proposed optimization method can effectively obtain the optimum distribution of the material orientation.