A multi-material topology optimization approach for wrinkle-free design of cable-suspended membrane structures

In order to eliminate stress-related wrinkles in cable-suspended membrane structures and to provide simple and reliable deployment, this study presents a multi-material topology optimization model and an effective solution procedure for generating optimal connected layouts for membranes and cables. On the basis of the principal stress criterion of membrane wrinkling behavior and the density-based interpolation of multi-phase materials, the optimization objective is to maximize the total structural stiffness while satisfying principal stress constraints and specified material volume requirements. By adopting the cosine-type relaxation scheme to avoid the stress singularity phenomenon, the optimization model is successfully solved through a standard gradient-based algorithm. Four-corner tensioned membrane structures with different loading cases were investigated to demonstrate the effectiveness of the proposed method in automatically finding the optimal design composed of curved boundary cables and wrinkle-free membranes.

[1]  Jing Cao,et al.  Layout optimization for multi-bi-modulus materials system under multiple load cases , 2016, Engineering with Computers.

[2]  Hiraku Sakamoto,et al.  Dynamic Wrinkle Reduction Strategies for Cable Suspended Membrane Structures , 2005 .

[3]  R. Tavakoli.  Optimal design of multiphase composites under elastodynamic loading , 2016 .

[4]  Wonsiri Punurai,et al.  Erratum to Implementation of genetic algorithm for optimum cutting pattern generation of wrinkle free finishing membrane structures Finite Elem. Anal. Des. 58 (2012) 84-90 , 2016 .

[5]  Z. Kang,et al.  A multi-material level set-based topology and shape optimization method , 2015 .

[6]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[7]  Michael Yu Wang,et al.  Optimal topology design of steel-concrete composite structures under stiffness and strength constraints , 2012 .

[8]  Bingen Yang,et al.  The modeling and numerical analysis of wrinkled membranes , 2003 .

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

[10]  Shiwei Zhou,et al.  Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition , 2006 .

[11]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[12]  Yasuyuki Miyazaki,et al.  Wrinkle/slack model and finite element dynamics of membrane , 2006 .

[13]  Xue Feng,et al.  Controllable wrinkle configurations by soft micro-patterns to enhance the stretchability of Si ribbons. , 2014, Soft matter.

[14]  Jingli Du,et al.  Optimization and experiment of an electrostatic forming membrane reflector in space , 2015 .

[15]  G. K. Ananthasuresh,et al.  Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme , 2001 .

[16]  John Wang,et al.  Effective Modeling and Nonlinear Shell Analysis of Thin Membranes Exhibiting Structural Wrinkling , 2005 .

[17]  T. Witten,et al.  Wrinkle to fold transition: influence of the substrate response , 2013 .

[18]  U. Kirsch,et al.  On singular topologies in optimum structural design , 1990 .

[19]  Wonsiri Punurai,et al.  Implementation of genetic algorithm for optimum cutting pattern generation of wrinkle free finishing membrane structures , 2012 .

[20]  Xu Guo,et al.  Stress-related topology optimization of continuum structures involving multi-phase materials , 2014 .

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

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

[23]  Xiaoming Wang,et al.  Color level sets: a multi-phase method for structural topology optimization with multiple materials , 2004 .

[24]  Michel Potier-Ferry,et al.  A multi-scale modeling framework for instabilities of film/substrate systems , 2015 .

[25]  Anand Ramani,et al.  A pseudo-sensitivity based discrete-variable approach to structural topology optimization with multiple materials , 2010 .

[26]  Salim Belouettar,et al.  Macroscopic simulation of membrane wrinkling for various loading cases , 2015 .

[27]  Fujikake Masahisa,et al.  Analysis of fabric tension structures , 1989 .

[28]  F. Peng,et al.  Tailoring the wrinkle pattern of a microstructured membrane , 2014 .

[29]  Jiao Shi,et al.  Optimal layout of multiple bi-modulus materials , 2016 .

[30]  Jae-Yeol Kim,et al.  A new technique for optimum cutting pattern generation of membrane structures , 2002 .

[31]  Gengdong Cheng,et al.  STUDY ON TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS , 1992 .

[32]  Seokwoo Kang,et al.  Finite element analysis of wrinkling membranes , 1997 .

[33]  David M. Murphy,et al.  A Method to Quantify the Thrust Degradation Effects of Structural Wrinkles in Solar Sails , 2002 .

[34]  Ali Rezaei,et al.  A shape optimization approach to integrated design and nonlinear analysis of tensioned fabric membrane structures with boundary cables , 2016 .

[35]  G. Cheng,et al.  ε-relaxed approach in structural topology optimization , 1997 .

[36]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[37]  Hiraku Sakamoto,et al.  Evaluation of membrane structure designs using boundary web cables for uniform tensioning , 2007 .

[38]  Martin M. Mikulas,et al.  Rapid Structural Assessment Approach for Square Solar Sails Including Edge Support Cords , 2003 .

[40]  Michihiro Natori,et al.  Sensitivity Analysis Method for Membrane Wrinkling Based on the Tension-Field Theory , 2008 .

[41]  S. Pellegrino,et al.  Prediction of Winkle Amplitudes in Square Solar Sails , 2003 .

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

[43]  C. Lim,et al.  Shape optimization of membrane structures based on finite element simulation , 2012 .