A NEW METHOD FOR DEALING WITH PSEUDO MODES IN TOPOLOGY OPTIMIZATION OF CONTINUA FOR FREE VIBRATION
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摘要:
采用固体各向同性材料惩罚模型（solid isotropic material with penalization， SIMP） 进行动力拓朴优化通常在优化过程中会出现虚假的局部振动模态，为消除这种虚假模态产生的不利影响，提出了移频与虚假模态识别相结合的通用方法. 研究中考虑以材料体积为约束、结构基频最大化为目标的优化模型，并采用节点设计变量描述设计域内材料分布. 基于虚假模态的特性，首先在特征值分析中应用移频方法排除特征值接近于零的低阶虚假模态，然后再依据虚假模态识别准则判定并剔除其他可能存在的虚假模态，从而可以高效可靠地确定结构真实的固有振动模态. 数值算例表明，提出的方法可以有效地消除动力拓扑优化中虚假模态可能产生的不利影响，并保证优化解的可靠性.
Abstract:Pseudo modes may appear in topology optimization of continua when the SIMP (Solid Isotropic Material with Penalization) material model is used for eigenvalue problems. A new method based on the combined use of the frequency shift technique and pseudo mode identification is proposed to eliminate the detrimental effect of such pseudo modes. The topology optimization of continuum structures for maximum fundamental frequency subjected to volume constraint is considered in the study. The nodal densities are taken as design variables to describe the material distribution in the design domain. Based on an investigation of the characteristics of pseudo vibration modes, the eigenvalue shift technique is suggested for avoiding low-order pseudo modes with small eigenvalues from the eigenmode extraction, and further a pseudo mode identification criterion is constructed to exclude other high-order pseudo modes. A highly efficient and reliable algorithm for the topology optimization is then made possible. Numerical examples are presented illustrating the effectiveness of the proposed method.
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Bendsøe MP, Sigmund O. Topology Optimization: Theory, Methods and Applications. Berlin: Heidelberg: Springer-Verlag, 2003 Belblidia F, Bulman S. A hybrid topology optimization algorithm for static and vibrating shell structures. International Journal for Numerical Methods in Engineering, 2002, 54(6): 835-852 Pedersen NL. Maximization of eigenvalues using topology optimization. Structural and Multidisciplinary Optimization, 2000, 20(1): 2-11 Tcherniak D. Topology optimization of resonating structures using SIMP method. International Journal for Numerical Methods in Engineering, 2002, 54(11): 1605-1622 Du JB, Olhoff N. Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Structural and Multidisciplinary Optimization, 2007, 34(2): 91-110 Cheng G, Wang B. Constraint continuity analysis approach to structural topology optimization with frequency objective/constraints. In: Proceeding of the Seventh World Congress on Structural and Multidisciplinary Optimization, Seoul, Korea, 2007 朱继宏, 张卫红, 邱克鹏. 结构动力学拓扑优化局部模态现象分析. 航空学报, 2006, 27(4): 619-623 (Zhu Jihong, Zhang Weihong, Qiu Kepeng. Investigation of localized modes in topology optimization of dynamic structures. Acta Aeronautica et Astronautica Sinica, 2006, 27(4): 619-623 (in Chinese)) Neves MM, Rodrigues H, Guedes JM. Generalized topology design of structures with a buckling load criterion. Structural Optimization, 1995, 10: 71-78 Zhou M. Topology optimization for shell structures with linear buckling responses. In: Proceedings of the Sixth World Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress on Computational Mechanics, Beijing, China, 2004. 795-800 Rahmatalla SF, Swan CC. A Q4/Q4 continuum structural topology optimization implementation. Structural and Multidisciplinary Optimization, 2004, 27(1-2): 130-135 龙凯, 左正兴. 基于节点独立变量的连续体结构动态拓扑优化. 固体力学学报, 2008, 29(1): 91-97 (Long Kai, Zuo Zhengxing. Dynamic topological optimization method of continuum structures based on nodal independent design variables. Chinese Journal of Solid Mechanics, 2008, 29(1): 91-97 (in Chinese)) 李震, 孙宝元, 钱敏等. 基于节点密度的柔性机构的拓扑优化设计. 计算力学学报, 2007, 24(2): 130-134 (Li Zhen, Sun Baoyuan, Qian Min, et al. Topology optimization design for compliant mechanisms based on nodal density. Chinese Journal of Computational Mechanics, 2007, 24(2): 130-134 (in Chinese)) 赖云山, 马海涛. 考虑变厚度的杂交应力元. 科学技术与工程, 2010, 10(26): 6502-6504 (Lai Yunshan, Ma Haitao. Plane stress hybrid element for membrane with variable thickness. Science Technology and Engineering, 2010, 10(26): 6502-6504 (in Chinese)) 赖云山, 马海涛. 基于变厚度杂交元的二维连续体结构拓扑优化. 科学技术与工程, 2012, 20(6): 1352-1354 (Lai Yunshan, Ma Haitao. Topology optimization of 2D continuum structures using hybrid element of non-uniform thickness. Science Technology and Engineering, 2012, 20(6): 1352-1354 (in Chinese)) Deng X, Wei P, Ma H. Topology optimization of 2D continuum using nodal design variables. In: Proceedings of the Seventh China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China, 2012 Pian THH, Sumihara K. Rational approach for assumed stress finite elements. International Journal for Numerical Methods in Engineering, 1984, 20: 1685-1695 Seyranian AP, Lund E, Olhoff N. Multiple eigenvalues in structural optimization problems. Structural Optimization, 1994, 8: 207-227 Rodrigues HC, Guedes JM, Bendsøs MP. Necessary conditions for optimal design of structures with a non-smooth eigenvalue based criterion. Structural Optimization, 1995, 9: 52-56 Bathe KJ, Ramaswamy S. An accelerated subspace iteration method. Computer Methods in Applied Mechanics and Engineering, 1980, 23: 313-331 Brehm M, Zabel V, Bucher C. An automatic mode pairing strategy using an enhanced modal assurance criterion based on modal strain energies. Journal of Sound and Vibration, 2010, 329(25): 5375-5392 Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24: 359-373 Huang X, Zuo ZH, Xie YM. Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Computers and Structures, 2010, 88(5-6): 357-364 -
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