Shape Design Sensitivity Analysis of Dynamic Crack Propagation using Peridynamics

Abstract

The shape design sensitivity analysis based on the mesh-free method for the bond-based peridynamics theory is developed for the solution to dynamic crack propagation problems. The methods may serve for the following two purposes. First, for the shortcomings of the Finite Difference Method that is involved. Specifically, the FDM is very sensitive to the amount of design perturbation. Second, it may serve for the foundation of the basis in proceeding shape design optimization. To solve large scale problems and to improve numerical efficiency, the binary decomposition method is employed for parallel computation. A shape design sensitivity analysis method is developed by using the direct differentiation method (DDM) and the adjoint variable method (AVM). Shape design sensitivity is developed using the Lagrangian approach since the geometry and finite grids perturb together during the shape variation. -continuous volume fraction that arises from numerical discretization is necessary for accurate analytical shape design sensitivity. The accuracy of the analytical design sensitivity is verified by comparing it with the Finite Difference Method.