A guide-weight criterion-based topology optimization method for maximizing the fundamental eigenfrequency of the continuum structure

This paper first introduces the guide-weight criterion into the topology optimization problems for maximization of the fundamental eigenfrequency of vibrating continuum structures. The traditional solid isotropic material with penalization model is modified to eliminate the artificial localized modes. Based on this modified model, the iteration formula of the design variables is derived using the guide-weight criterion. An iterative mass control strategy is adopted to satisfy the equality constraint on the final mass and to stabilize the iteration process. Additionally, a mass preserving density filter based on Heaviside function is used to solve the gray transition problem. Several typical examples are used to validate the proposed method. Numerical results show that the proposed method is capable of achieving iterative convergence and clear profiles of topologies; meanwhile, the optimal results obtained by the proposed method agree well with those obtained by the commonly used bi-directional evolutionary structural optimization (BESO) method. In particular, the proposed method has a faster convergence rate than the BESO method.

[1]  Grant P. Steven,et al.  A simple approach to structural frequency optimization , 1994 .

[2]  Sixue Chen,et al.  Criterion method for the optimal design of antenna structure , 1984 .

[3]  K. Svanberg,et al.  An alternative interpolation scheme for minimum compliance topology optimization , 2001 .

[4]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[5]  Yubao Chen,et al.  Study on the optimal design of engine cylinder head by parametric structure characterization with weight distribution criterion , 2011 .

[6]  Yi Min Xie,et al.  Evolutionary topological optimization of vibrating continuum structures for natural frequencies , 2010 .

[7]  M. Bogomolny.  Topology optimization for free vibrations using combined approximations , 2010 .

[8]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[9]  Gyung-Jin Park,et al.  Nonlinear dynamic response topology optimization using the equivalent static loads method , 2012 .

[10]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Structures with Multiple Displacement and Frequency Constraints , 2012 .

[11]  N. Olhoff,et al.  Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps , 2007 .

[12]  Shengli Xu,et al.  Volume preserving nonlinear density filter based on heaviside functions , 2010 .

[13]  Seog-Young Han,et al.  A modified ant colony optimization algorithm for dynamic topology optimization , 2013 .

[14]  Jianbin Du,et al.  Topology optimization of freely vibrating continuum structures based on nonsmooth optimization , 2017 .

[15]  Shuting Wang,et al.  Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency , 2019, Frontiers of Mechanical Engineering.

[16]  Liwen Guan,et al.  Guide-Weight method for topology optimization of continuum structures including body forces , 2013 .

[17]  Dmitri Tcherniak,et al.  Topology optimization of resonating structures using SIMP method , 2002 .

[18]  N. Olhoff,et al.  Multiple eigenvalues in structural optimization problems , 1994 .

[19]  Guan-Chun Luh,et al.  Structural topology optimization using ant colony optimization algorithm , 2009, Appl. Soft Comput..

[20]  Ye Shanghui,et al.  A GUIDE-WEIGHT CRITERION METHOD FOR THE OPTIMAL DESIGN OF ANTENNA STRUCTURES , 1986 .

[21]  Bin Liu.  Interpolation of Geodesic B-spline Curves on Manifold Triangulation , 2011 .

[22]  Xiaodong Huang,et al.  Concurrent topology optimization of macrostructures and material microstructures for natural frequency , 2016 .

[23]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Continuum Structures: Methods and Applications , 2010 .

[24]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[25]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[26]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[27]  Y. Xie,et al.  Bidirectional Evolutionary Method for Stiffness Optimization , 1999 .

[28]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[29]  N. Olhoff,et al.  Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps , 2007 .

[30]  Y. Xie,et al.  Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method , 2007 .

[31]  Liping Wang,et al.  Solving topology optimization problems by the Guide-Weight method , 2010 .

[32]  Y. Maeda,et al.  Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes , 2006 .

[33]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[34]  Xiaodong Huang,et al.  Smooth topological design of structures using the floating projection , 2020 .

[35]  G. Yoon.  Structural topology optimization for frequency response problem using model reduction schemes , 2010 .

[36]  Claude Fleury,et al.  CONLIN: An efficient dual optimizer based on convex approximation concepts , 1989 .

[37]  Xin-Jun Liu,et al.  A new solution for topology optimization problems with multiple loads: The guide-weight method , 2011 .

[38]  Chih-Chun Cheng,et al.  Structural design for desired eigenfrequencies and mode shapes using topology optimization , 2013 .

[39]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[40]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[41]  Liang Xia,et al.  Evolutionary topology optimization of continuum structures with smooth boundary representation , 2018 .

[42]  Xiaodong Huang,et al.  Topology optimization of dynamic acoustic–mechanical structures using the ersatz material model , 2020 .

[43]  G. Yoon.  Maximizing the fundamental eigenfrequency of geometrically nonlinear structures by topology optimization based on element connectivity parameterization , 2010 .

[44]  Junpeng Zhao,et al.  Dynamic response topology optimization in the time domain using model reduction method , 2016 .

[45]  N. L. Pedersen.  Maximization of eigenvalues using topology optimization , 2000 .

[46]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[47]  Sébastien Briot,et al.  Topology optimization of industrial robots: Application to a five-bar mechanism , 2018 .

[48]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[49]  Grant P. Steven,et al.  Topology Optimization for Frequencies Using an Evolutionary Method , 1999 .