Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum Compliance Problems and Its Implementation in MATLAB

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-sensitivity method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing optimality criteria method which computes sensitivities. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org.

[1]  Kumar Vemaganti,et al.  Parallel methods for optimality criteria-based topology optimization , 2005 .

[2]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[3]  G. Dantzig,et al.  Linear Programming and Its Extensions. , 1966 .

[4]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[5]  Guan-Chun Luh,et al.  Multi-modal topological optimization of structure using immune algorithm , 2004 .

[6]  C. S. Jog,et al.  Optimization of vibrating structures to reduce radiated noise , 2012 .

[7]  W Prager,et al.  Optimality criteria in structural design. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[9]  Sui Yunkang,et al.  Topology optimization design of continuum structures under stress and displacement constraints , 2000 .

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

[11]  G. Paulino,et al.  PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab , 2012 .

[12]  Chun-Yin Wu,et al.  Topology optimization of structures using modified binary differential evolution , 2010 .

[13]  SigmundOle.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[14]  A. Michell.  LVIII. The limits of economy of material in frame-structures , 1904 .

[15]  V. Braibant,et al.  Structural optimization: A new dual method using mixed variables , 1986 .

[16]  M. Bendsøe,et al.  Topology optimization of continuum structures with local stress constraints , 1998 .

[17]  LiuKai,et al.  An efficient 3D topology optimization code written in Matlab , 2014 .

[18]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[19]  John E. Renaud,et al.  Comparative Study of Topology Optimization Techniques , 2008 .

[20]  Vivien J. Challis,et al.  A discrete level-set topology optimization code written in Matlab , 2010 .

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

[22]  Angelika Foerster,et al.  An Introduction To Structural Optimization , 2016 .

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

[24]  Andres Tovar,et al.  An efficient 3D topology optimization code written in Matlab , 2014 .

[25]  J. T. Pereira,et al.  Topology optimization of continuum structures with material failure constraints , 2004 .

[26]  F. Navarrina,et al.  Stress constraints sensitivity analysis in structural topology optimization , 2010 .

[27]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[28]  Julián A. Norato,et al.  Stress-based topology optimization for continua , 2010 .

[29]  M. Bruggi.  On an alternative approach to stress constraints relaxation in topology optimization , 2008 .

[30]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .

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

[32]  F. Navarrina,et al.  Topology optimization of continuum structures with local and global stress constraints , 2009 .

[33]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[34]  Krister Svanberg,et al.  Sequential integer programming methods for stress constrained topology optimization , 2007 .

[35]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[36]  Jianbin Du,et al.  Microstructural topology optimization with respect to sound power radiation , 2013 .

[37]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

[38]  Glaucio H. Paulino,et al.  PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes , 2012 .

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

[40]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[41]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[42]  Albert C. To,et al.  Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation , 2015 .

[43]  Souran Manoochehri,et al.  GENERATING OPTIMAL CONFIGURATIONS IN STRUCTURAL DESIGN USING SIMULATED ANNEALING , 1997 .

[44]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[45]  Erik Holmberg,et al.  Stress constrained topology optimization , 2013, Structural and Multidisciplinary Optimization.

[46]  Kai A. James,et al.  Structural and Multidisciplinary Optimization Manuscript No. Stress-constrained Topology Optimization with Design- Dependent Loading , 2022 .

[47]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

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