1 Introduction
2 Peridynamics formulation and crack modelling
2.1 PD formulation for 3D structures
2.2 Crack modelling
3 Optimization procedure
3.1 Optimization problem definition
3.2 Proportional topology optimization method
3.3 Optimality criteria method
3.4 Filter scheme and stabilization
4 Topology optimization examples
4.1 Cantilever beam
4.2 Hanger beam
5 Dynamic analyses for the assessment of fracture toughness enhancement
5.1 Dynamic analysis setup
5.2 Comparison strategies
5.3 Numerical results: dynamic behaviour of the optimized structures
Case | PD-OC | PD-PROP | ||
---|---|---|---|---|
No crack | Front crack | No crack | Front crack | |
Max disp. (mm) | 4.894 | 9.067 | 4.897 | 8.839 |
Diff (%) | 85.27 | 80.50 |
Case | PD-OC | PD-PROP | ||
---|---|---|---|---|
No crack | New crack | No crack | New crack | |
Max disp. (mm) | 1.645 | 1.797 | 1.522 | 1.631 |
Diff (%) | 9.24 | 7.16 |
6 Conclusions
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The final geometries obtained by PD-OC, and PD-PROP methods for all the scenarios are examined comprehensively. Although both methods show improvement in the optimized results to avoid crack propagation, it is revealed that the OC method is more sensitive to structural discontinuities and PROP creates fewer sub-branches between the main support arms.
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The performance of the PD-TO methods in fracture toughness enhancement is investigated. In this regard, the damage contours and fracture patterns of the optimized geometries are compared at certain time steps under dynamic load. These comparisons revealed that the suggested methods would produce superior designs that could support a greater load than the initial TO results by just embedding hypothetical (predicted by simulations) cracks into the regions that are determined to be critical under dynamic loading.