| 基于RKPM梁固有频率及薄板柔度的拓扑优化 |
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| 引用本文： | 张建平,蒋炎坤,龚曙光,刘欣.基于RKPM梁固有频率及薄板柔度的拓扑优化[J].华中科技大学学报(自然科学版),2011(6):101-105. |
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| 作者姓名： | 张建平 蒋炎坤 龚曙光 刘欣 |
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| 作者单位： | 华中科技大学能源与动力工程学院;湘潭大学机械工程学院; |
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| 基金项目： | 国家自然科学基金资助项目(50875223) |
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| 摘 要： | 以节点相对密度为设计变量,以固有频率最大为目标函数,通过修正低密度区质量矩阵建立了基于重构核粒子法(RKPM)的结构动力拓扑优化数学模型.采用罚函数法施加本质边界条件,利用直接微分法推导了结构固有频率灵敏度方程,同时研究了受横向载荷弯曲的基尔霍夫薄板柔度最小的拓扑优化问题.最后对比分析了节点依赖性以及设计变量对最优拓扑结构的影响,并结合以上算法和优化准则法编写程序完成了2个拓扑优化算例.优化结果表明:所建立的模型不仅能有效抑制局部模态和重特征频率的出现,而且因通过重构核近似提高了计算点密度场的连续性,棋盘格现象得以消除,可以得到清晰光滑的拓扑边界.
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| 关 键 词： | 动力拓扑优化 无网格法 重构核粒子法 基尔霍夫薄板 灵敏度分析 |
RKPM-based topology optimization for natural frequency of beam and compliance of thin plate |
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| Zhang Jianping Jiang Yankun Gong Shuguang Liu Xin.RKPM-based topology optimization for natural frequency of beam and compliance of thin plate[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2011(6):101-105. |
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| Authors: | Zhang Jianping Jiang Yankun Gong Shuguang Liu Xin |
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| Affiliation: | Zhang Jianping1 Jiang Yankun1 Gong Shuguang2 Liu Xin1(1 School of Energy and Power Engineering,Huazhong University of Science and Technology,Wuhan 430074,China,2 School of Mechanical Engineering,Xiangtan University,Xiangtan 411105,Hunan China) |
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| Abstract: | Relative density of node was chosen as design variable,and maximizing the natural frequency was the objective function,and then a numerical model of structural dynamic topology optimization based on reproducing kernel particle method(RKPM) was established through modifying the mass matrix in low density domain.The penalty method was employed into imposing the essential boundary conditions,and the sensitivity equation of structural natural frequency was deduced by using direct differentiation method.Meanwhil... |
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| Keywords: | dynamic topology optimization meshless method reproducing kernel particle method Kirchhoff thin plate sensitivity analysis |
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