Adaptive isogeometric topology optimization maximizing natural frequency for multi-patch vibrating structures
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This work presents an adaptive multi-patch isogeometric topology optimization (ITO) approach for vibrating structures, where the fundamental eigenfrequency is treated as the optimization objectives, respectively. In particular, we propose a novel algorithm to perform structural vibration for the complex structures by exploiting the local refinement capabilities of suitably graded truncated hierarchical B-splines (THB) under multi-patch configuration. The presented ITO method is based on the separation of uniform multi-patch design mesh from adaptive multi-patch isogeometric analysis (IGA) mesh, with the physical response of finest multi-patch design mesh obtained by multiplying eigenvector by THB transformation matrix. This formulation is characterized by the sensitivity analysis of multi-patch nodal design variables derived from the tensor product decomposed implicit filter, by considering the equality constraints of control design variables of adjacent patches along the patch interface, and the hierarchical multi-patch IGA mesh is adaptively refined based on an indicator by combining a geometric-based estimator with a residual-based estimator, with a sound balance between efficiency and accuracy. In all numerical examples, we can perform adaptive multi-patch ITO for vibrating structures in a robust and efficient manner. Therefore, the proposed methodology is a promising approach in implementing the integrated design of vibrating engineering structures.
