Continuum Sensitivity Analysis for Structural Shape Design Variables Using Finite-Volume Method

Two of the most important requirements when using gradient-based optimization for fluid-structure interaction problems are efficiency and accuracy in calculating the sensitivities. As a result, analytical continuum sensitivity formulations are finding their place due to their lower cost and accuracy. However, the necessary computation of mesh sensitivities in shape optimization is becoming a bottleneck, especially when handling complex geometries. In this research, an algorithm based on continuum sensitivity analysis for structural shape design variables is developed. In the proposed method, regularized Heaviside functions are used to modify the properties of mesh cells. Therefore, mesh dependency is removed from the sensitivity equations. This method does not require moving or modifying the mesh to handle the shape changes. This method is applied to two different validation cases where continuum sensitivity equations are formulated and solved. Validation cases are selected as a structural and thermal problem to show the applicability of this method for different physics. The results demonstrate the efficiency of the proposed algorithm for design-optimization framework.