基于等几何分析的离散变量拓扑优化方法研究

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胡清元,李小渔,梁缘.基于等几何分析的离散变量拓扑优化方法研究[J].,2022,62(3):221-227

基于等几何分析的离散变量拓扑优化方法研究

Research on discrete variable topology optimization method based on isogeometric analysis

DOI：10.7511/dllgxb202203001

中文关键词:等几何分析有限元曲边单元拓扑优化离散变量

英文关键词:isogeometric analysis finite element curved element topology optimization discrete variable

基金项目:中央高校基本科研业务费专项资金资助项目(JUSRP12038)；江苏省自然科学基金资助项目(BK20200611)；国家自然科学基金资助项目(12102146).

作者	单位
胡清元,李小渔,梁缘

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中文摘要:

基于等几何分析框架，采用离散变量优化算法，针对平面问题展开拓扑优化方法研究．在等几何分析框架内引入了离散变量优化算法，使得所提出的拓扑优化方法结合了两者的优势：一方面等几何分析允许曲边单元存在，另一方面离散变量优化计算所得到的单元只存在0/1(白/黑)两个状态，因此所得优化结果在整体上更加清晰、在局部上更加光滑．此外，针对等几何曲边单元，采用了基于Helmholtz方程的隐式过滤方法，保证了过滤效果，节省了计算量．在给出了算法实现的关键细节后，通过数值算例展示了方法的效果，验证了方法的有效性．

英文摘要:

Based on the isogeometric analysis framework, adopting discrete variable optimization algorithm, the topology optimization methods for plane problems are studied. In the framework of isogeometric analysis, the discrete variable optimization algorithm is introduced, so that the proposed topology optimization method combines the advantages of them: isogeometric analysis allows the presence of curved elements, moreover, elements obtained by the discrete variable optimization method are restricted to have only two states of 0/1 (white/black), thus the obtained optimized results are clearer globally and smoother locally. In addition, for isogeometric curved elements, an implicit filtering method based on the Helmholtz equation is adopted to ensure filtering effect, the calculation effort is also saved. After providing implementation details of the algorithm, the performance of the proposed algorithm is tested by numerical examples, the effectiveness of the proposed algorithm is also verified.

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基于等几何分析的离散变量拓扑优化方法研究

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