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Based on a bond-based peridynamics theory for dynamic crack propagation problems, this paper presents a design sensitivity analysis and optimization method. Peridynamics has a peculiar advantage over the existing continuum theory in the mathematical modelling of problems where discontinuities arise. For the design optimization of the crack propagation problems, a non-shape design sensitivity is derived using the adjoint variable method. The obtained adjoint sensitivity of displacement and strain energy turns out to be very accurate and efficient compared to the finite different sensitivity. The obtained design sensitivities are futher utilized to optimally control the position of bifurcation point in the design optimization of crack propagation in a plate under tension. A numerical experiment demonstrates that the optimal distribution of material density could delay the position of bifurcation.

Structural Design Optimization of Dynamic Crack Propagation Problems Using Peridynamics