Isogeometric Optimization of Structural Shapes for Robustness Based on Biomimetic Principles

New challenges in shape optimization design under uncertainties lead to inspiration from nature. In this paper, we choose trees as the inspiration resource and apply the axiom of uniform strains, a governing principle of tree design, to avoid material overloading or under-utilizing. The hypothesis of the uniform strains is formulated as the mean and standard deviation of strains which are defined as the optimization objectives. Then we use the isogeometric analysis (IGA) method to establish the numerical models. To take the geometric uncertainties into account, the coordinates of control points are defined as design variables. In the optimization process, the non-dominated sorting genetic algorithm II (NSGA-II) is applied to update design variables to figure out the optimal geometry. The Pareto front is obtained after iterative computation. The results based on bio-inspired criteria show that structural resistance can be increased significantly. This research provides new criteria for structural robust design under uncertainties.