Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum

Shengfeng Zhu; Chunxiao Liu; Qingbiao Wu

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Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum

机译：用于二密度非均质鼓的拓扑和形状优化的二进制水平集方法

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摘要

We optimize eigenvalues in optimal shape design using binary level set methods. The interfaces of sub-regions are represented implicitly by the discontinuities of binary level set functions taking two values 1 or -1 at convergence. A binary constraint is added to the original model problems. We propose two var-iational algorithms to solve the constrained optimization problems. One is a hybrid type by coupling the Lagrange multiplier approach for the geometry constraint with the augmented Lagrangian method for the binary constraint. The other is devised using the Lagrange multiplier method for both constraints. The two iterative algorithms are both largely independent of the initial guess and can satisfy the geometry constraint very accurately during the iterations. Intensive numerical results are presented and compared with those obtained by level set methods, which demonstrate the effectiveness and robustness of our algorithms.

机译：我们使用二进制水平集方法优化形状设计中的特征值。子区域的接口隐含地表示为二进制级别集函数的不连续性，收敛时取两个值1或-1。将二进制约束添加到原始模型问题。我们提出了两种变分算法来解决约束优化问题。一种是混合类型，通过将用于几何约束的拉格朗日乘数方法与用于二进制约束的增强拉格朗日方法耦合。另一个是使用拉格朗日乘数法设计的。两种迭代算法都很大程度上与初始猜测无关，并且可以在迭代过程中非常准确地满足几何约束。提出了密集的数值结果，并将其与通过水平集方法获得的数值结果进行了比较，证明了我们算法的有效性和鲁棒性。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2010年第48期|p.2970-2986|共17页
作者
Shengfeng Zhu; Chunxiao Liu; Qingbiao Wu;
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作者单位

Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;

Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;

Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
shape optimization; eigenvalue; topology optimization; binary level set method; augmented lagrangian method; projection lagrangian method;

机译：形状优化;特征值拓扑优化;二进制级别设置方法;增强拉格朗日法投影拉格朗日法;

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1. Variational piecewise constant level set methods for shape optimization of a two-density drum [J] . Zhu S., Wu Q., Liu C. Journal of Computational Physics . 2010,第13期

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2. Level set topology and shape optimization by density methods using cut elements with length scale control [J] . Structural and multidisciplinary optimization . 2020,第2期

机译：使用带有长度尺度控制的切割元素的密度方法级别设置拓扑和形状优化
3. Filter the shape sensitivity in level set-based topology optimization methods [J] . Benliang Zhu, Xianmin Zhang, Sergej Fatikow Structural and Multidisciplinary Optimization . 2015,第5期

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4. MULTI-STAGE DESIGN METHOD FOR PRACTICAL COMPLIANT MECHANISMS BY TOPOLOGY AND SHAPE OPTIMIZATIONS AND SHAPE CONVERSION METHOD UTILIZING LEVEL SET METHOD [C] . Mechanisms and robotics conference . 2009

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5. Shape and Topology Optimization with Parametric Level Set Method and Partition of Unity Method. [D] . Ho, Hon Shan. 2010

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6. Optimization of the Drum Drying Parameters and Citric Acid Level to Produce Purple Sweet Potato (Ipomoea batatas L.) Powder Using Response Surface Methodology [O] . Sri Sampath Janaka Senevirathna, Nurul Shazini Ramli, Ezzat Mohamad Azman, 2021

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7. Shape optimized design of microwave dielectric resonators by level set and topology gradient methods [O] . Khalil, Hassan, Bila, Stéphane, Aubourg, Michel, 2010

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Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum

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