A new method based on adaptive volume constraint and stress penalty for stress-constrained topology optimization

This paper focuses on the stress-constrained topology optimization of minimizing the structural volume and compliance. A new method based on adaptive volume constraint and stress penalty is proposed. According to this method, the stress-constrained volume and compliance minimization topology optimization problem is transformed into two simple and related problems: a stress-penalty-based compliance minimization problem and a volume-decision problem. In the former problem, stress penalty is conducted and used to control the local stress level of the structure. To solve this problem, the parametric level set method with the compactly supported radial basis functions is adopted. Meanwhile, an adaptive adjusting scheme of the stress penalty factor is used to improve the control of the local stress level. To solve the volume-decision problem, a combination scheme of the interval search and local search is proposed. Numerical examples are used to test the proposed method. Results show the lightweight design, which meets the stress constraint and whose compliance is simultaneously optimized, can be obtained by the proposed method.

[1]  Jian Zhang,et al.  Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons , 2016 .

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

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

[4]  Michael Yu Wang,et al.  Shape and topology optimization of compliant mechanisms using a parameterization level set method , 2007, J. Comput. Phys..

[5]  Chyi-Yeu Lin,et al.  Adaptive volume constraint algorithm for stress limit-based topology optimization , 2009, Comput. Aided Des..

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

[7]  G. Qiu,et al.  A note on the derivation of global stress constraints , 2009 .

[8]  P. Pedersen.  On optimal shapes in materials and structures , 2000 .

[9]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[10]  Gil Ho Yoon,et al.  Stress-based topology optimization method for steady-state fluid–structure interaction problems , 2014 .

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

[12]  Ole Sigmund,et al.  New Developments in Handling Stress Constraints in Optimal Material Distributions , 1998 .

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

[14]  Xu Guo,et al.  Stress-related Topology Optimization via Level Set Approach , 2011 .

[15]  Ole Sigmund,et al.  Stress-constrained topology optimization for compliant mechanism design , 2015 .

[16]  Jian Zhang,et al.  A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model , 2016 .

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

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

[19]  E. L. Cardoso,et al.  Stress-based topology optimization of continuum structures under uncertainties , 2017 .

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

[21]  Fred van Keulen,et al.  Damage approach: A new method for topology optimization with local stress constraints , 2016 .

[22]  Dong-Hoon Choi,et al.  Development of a novel phase-field method for local stress-based shape and topology optimization , 2014 .

[23]  I. Colominas,et al.  Block aggregation of stress constraints in topology optimization of structures , 2007, Adv. Eng. Softw..

[24]  J. Korvink,et al.  Adaptive moving mesh level set method for structure topology optimization , 2008 .

[25]  Ren-Jye Yang,et al.  Stress-based topology optimization , 1996 .

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

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

[28]  M. Wang,et al.  A level set‐based parameterization method for structural shape and topology optimization , 2008 .

[29]  J. N. Reddy,et al.  A new multi-p-norm formulation approach for stress-based topology optimization design , 2016 .

[30]  Matteo Bruggi,et al.  Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance , 2017 .

[31]  E. Fancello,et al.  A level set approach for topology optimization with local stress constraints , 2014 .

[32]  Ting Ting Xiao,et al.  Continuum structural topological optimizations with stress constraints based on an active constraint technique , 2016 .

[33]  Michael Yu Wang,et al.  PDE-Driven Level Sets, Shape Sensitivity and Curvature Flow for Structural Topology Optimization , 2004 .

[34]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[35]  T. Shi,et al.  A level set solution to the stress-based structural shape and topology optimization , 2012 .

[36]  Kyung K. Choi,et al.  Structural sensitivity analysis and optimization , 2005 .

[37]  Edward J. Haug,et al.  Design Sensitivity Analysis of Structural Systems , 1986 .

[38]  Z. Kang,et al.  An enhanced aggregation method for topology optimization with local stress constraints , 2013 .

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

[40]  M. Bruggi,et al.  A mixed FEM approach to stress‐constrained topology optimization , 2008 .

[41]  Jeonghoon Yoo,et al.  A novel P-norm correction method for lightweight topology optimization under maximum stress constraints , 2016 .

[42]  Duc T. Nguyen,et al.  Numerical Methods with Applications , 2011 .

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

[44]  C. G. Lopes,et al.  Topology design of compliant mechanisms with stress constraints based on the topological derivative concept , 2016 .