摘要
等几何拓扑优化方法将经典拓扑优化理论中的有限元分析过程更改为等几何分析计算,从而提高了拓扑优化的效率与稳定性。针对现有的等几何拓扑优化方法在处理复杂实体结构优化问题时具有一定的局限性,提出一种非结构化样条实体等几何拓扑优化方法。基于混合B样条构造技术,在非结构化六面体网格上构造具有复杂结构的样条实体,并将其作为拓扑优化问题的设计域。用于描述这一样条实体的基函数被直接应用于材料密度分布的表达以及等几何分析计算。在数值算例中,该方法表现出应用于复杂结构时的良好稳定性和鲁棒性。研究成果对等几何拓扑优化方法应用于实际工程问题具有一定的参考意义。
For isogeometric topology optimization(ITO)methods,isogeometric analysis(IGA)is adopted for topology optimization to address the limitation of the finite element method,which can improve the efficiency and stability of the optimization.However,it is of great challenge for existing ITO methods to manage arbitrarily shaped design domains,especially in three-dimensional solid problems.Therefore,a new ITO method was proposed to handle unstructured solid models.A spline solid with complex structures was obtained from an unstructured hexahedral mesh based on the blended B-spline construction.The basis functions describing the unstructured spline solid were applied to the representation of density distribution and the calculation of IGA.Several examples proved the flexibility and robustness of the proposed method in dealing with complex structures.These results may shed light on the application of ITO in practical engineering problems.
作者
杨佳明
赵罡
王伟
郭马一
杜孝孝
YANG Jia-ming;ZHAO Gang;WANG Wei;GUO Ma-yi;DU Xiao-xiao(School of Mechanical Engineering&Automation,Beihang University,Beijing 100191,China;Key Laboratory of Aeronautics Smart Manufacturing,Ministry of Industry and Information Technology,Beijing 100191,China;Beijing Engineering Technological Research Center of High-Efficient&Green CNC Machining Process and Equipment,Beijing 100191,China)
出处
《图学学报》
CSCD
北大核心
2021年第3期501-510,共10页
Journal of Graphics
基金
国家自然科学基金项目(61972011,61572056)。
关键词
拓扑优化
等几何分析
体参数化
B样条
非结构化样条
topology optimization
isogeometric analysis
volume parameterization
B-spline
unstructured splines
