Optimization approach for designing free-orientation of orthotropic materials of a shell structure

In this study, we propose a parameter-free optimization method of material orientation for a shell structure consisting of orthotropic materials. We consider the compliance as an objective function and minimize it under the state equation constraint. The material orientation distribution is the design variables to be determined. This optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function with respect to the orientation variation is theoretically derived based on the variational method. The optimum orientation variations are determined by the H1 gradient method with the Poisson's equation, where the sensitivity function is applied as the internal heat generation on the shell surface, a driving force to vary the orientation in order to reduce the objective function while maintaining the smooth material orientation distribution. The optimum and continuously distributed orientation variations are determined as the temperature distribution of this fictitious heat transfer analysis without design parameterization. The optimum design examples show that the optimum the material orientation for the minimum compliance can be effectively obtained with the proposed optimization method.