Gradient‐Based Optimization of Linear Elasticity Mesh Deformation Quality

Mesh deformation based on the linear elasticity method is crucial in aerospace engineering research. However, maintaining mesh quality after significant deformations can be challenging. In this paper, the quality of mesh deformation in the linear elasticity method is improved by constructing a gradient optimization problem to solve for the optimal elastic modulus. The objective function is defined as the logarithmic sum of the quality of all mesh elements, and the gradient of the objective function is mathematically derived. Two case studies are used to analyze the influence of objective function improvement parameters and design space on the optimization results. To achieve higher efficiency in optimizing the mesh deformation quality of large‐scale viscous grids, a mesh deformation quality optimization process based on elastic modulus interpolation is established. This process is tested in two case studies, confirming the feasibility of the method.