Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p-norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.

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

[2]  Antonio André Novotny,et al.  Topological optimization of structures subject to Von Mises stress constraints , 2010 .

[3]  Volker Ulbricht,et al.  On boundary conditions for homogenization of volume elements undergoing localization , 2018 .

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

[5]  B. Niu,et al.  On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation , 2018 .

[6]  Olivier Bruls,et al.  Topology and generalized shape optimization: Why stress constraints are so important? , 2008 .

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

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

[9]  Shi Li,et al.  Stress-constrained topology optimization based on maximum stress measures , 2018 .

[10]  Raphael T. Haftka,et al.  Requirements for papers focusing on new or improved global optimization algorithms , 2016 .

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

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

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

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

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

[16]  N. Olhoff,et al.  Generalized incremental frequency method for topological designof continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency , 2016 .

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

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

[19]  A. Ramani.  Multi-material topology optimization with strength constraints , 2011 .

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

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

[22]  Erik Holmberg,et al.  Fatigue constrained topology optimization , 2014 .

[23]  Xuan Wang,et al.  Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm , 2018 .

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

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

[26]  B. Bourdin.  Filters in topology optimization , 2001 .

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

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

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

[30]  Qi Xia,et al.  Optimization of stresses in a local region for the maximization of sensitivity and minimization of cross—sensitivity of piezoresistive sensors , 2013 .

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

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

[33]  Erik Lund,et al.  Topology optimization with finite-life fatigue constraints , 2017 .

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

[35]  André T. Beck,et al.  Topology optimization of continuum structures with stress constraints and uncertainties in loading , 2018 .

[36]  Xianguang Gu,et al.  Concurrent topology optimization for minimization of total mass considering load-carrying capabilities and thermal insulation simultaneously , 2018 .

[37]  Hu Liu,et al.  A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations , 2015 .

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

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

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

[41]  Dong-Hoon Choi,et al.  Separable stress interpolation scheme for stress-based topology optimization with multiple homogenous materials , 2014 .

[42]  Eduardo Alberto Fancello,et al.  Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions , 2006 .

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

[44]  P. Duysinx,et al.  Topology optimization for minimum weight with compliance and stress constraints , 2012 .

[45]  Qi Xia,et al.  Shape and topology optimization for tailoring stress in a local region to enhance performance of piezoresistive sensors , 2013 .

[46]  Xianguang Gu,et al.  Local optimum in multi-material topology optimization and solution by reciprocal variables , 2018 .

[47]  Chao Hu,et al.  Sequential exploration-exploitation with dynamic trade-off for efficient reliability analysis of complex engineered systems , 2017 .

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

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

[50]  Niels Olhoff,et al.  Minimization of sound radiation from vibrating bi-material structures using topology optimization , 2007 .