Topology Optimization of Thermoelastic Structures with Global Stress Constraints
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摘要: 针对静强度失效问题，提出一种基于全局应力约束的热弹性结构拓扑优化设计方法。考虑热载荷和机械载荷共同作用下，以结构的体积最小化为目标函数，利用应力松弛方法来消除奇异解现象，采用改进的P范数方法将所有的单元应力凝聚化为一个近似等于结构最大应力的全局应力，利用全局应力作为约束，建立热弹性结构全局应力约束拓扑优化模型，采用移动近似线算法进行拓扑优化问题的求解。数值算例表明热弹性结构全局应力约束拓扑优化设计方法是有效的。随着温度载荷增大，应力约束拓扑优化获得的拓扑结构不同，最优结构的用材有所增加。Abstract: For the static strength requirement, an approach for topology optimization design of thermoelastic structures with global stress constrains is proposed. The minimization of the structure volume is developed as the objective function under the combined action of thermal and mechanical loads. The stress relaxation method is adopted to avoid the singularity phenomena for the stress based topology optimization problem. All elemental stresses are aggregated into a global stress using the modified P-norm method. The global stress is approximately equal to the maximum stress and used as the constraint. The model for topology optimization of the thermoelastic structures with the global stress constraints is established. The method of moving asymptotes is performed to solve the optimization problems. The results of numerical examples show that the proposed method is effective. As the thermal load increases, optimal structure obtained by the stress-constrained topology optimization is different and leads to more materials used.
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表 1 不同温度变化的L型梁结构拓扑优化结果
温度变化/℃ 体积分数/% 最大应力/MPa 0 25.2 275.781 10 28.6 274.545 20 29.5 274.896 30 30.1 275.017 
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表 2 不同温度变化的悬臂梁结构拓扑优化结果
温度变化/℃ 体积分数/% 最大应力/MPa 0 14.9 275.422 10 16.0 275.179 30 17.2 275.055 50 20.8 275.000
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[1] Pedersen P, Pedersen N L. Interpolation/penalization applied for strength design of 3D thermoelastic structures[J]. Structural and Multidisciplinary Optimization, 2012, 45(6):773-786 doi: 10.1007/s00158-011-0755-3 [2] Rodrigues H, Fernandes P. A material based model for topology optimization of thermoelastic structures[J]. International Journal for Numerical Methods in Engineering, 1995, 38(12):1951-1965 doi: 10.1002/nme.1620381202 [3] Li Q, Steven G P, Xie Y M. Thermoelastic topology optimization for problems with varying temperature fields[J]. Journal of Thermal Stresses, 2001, 24(4):347-366 doi: 10.1080/01495730151078153 [4] 左孔天, 钱勤, 赵雨东, 等.热固耦合结构的拓扑优化设计研究[J].固体力学学报, 2005, 26(4):447-452 doi: 10.3969/j.issn.0254-7805.2005.04.011Zuo K T, Qian Q, Zhao Y D, et al. Research on the topology optimization about thermo-structural coupling field[J]. Acta Mechanica Solida Sinica, 2005, 26(4):447-452(in Chinese) doi: 10.3969/j.issn.0254-7805.2005.04.011 [5] Du Y X, Luo Z, Tian Q H, et al. Topology optimization for thermo-mechanical compliant actuators using mesh-free methods[J]. Engineering Optimization, 2009, 41(8):753-772 doi: 10.1080/03052150902834989 [6] Gao T, Xu P L, Zhang W H. Topology optimization of thermo-elastic structures with multiple materials under mass constraint[J]. Computers & Structures, 2016, 173:150-160 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=3c23f1258e114eeaf186ecce632d4efe [7] Yang X W, Li Y M. Structural topology optimization on dynamic compliance at resonance frequency in thermal environments[J]. Structural and Multidisciplinary Optimization, 2014, 49(1):81-91 doi: 10.1007/s00158-013-0961-2 [8] Deng J D, Yan J, Cheng G D. Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material[J]. Structural and Multidisciplinary Optimization, 2013, 47(4):583-597 doi: 10.1007/s00158-012-0849-6 [9] Liu X J, Wang C, Zhou Y H. Topology optimization of thermoelastic structures using the guide-weight method[J]. Science China Technological Sciences, 2014, 57(5):968-979 doi: 10.1007/s11431-014-5521-5 [10] Pedersen P, Pedersen N L. Strength optimized designs of thermoelastic structures[J]. Structural and Multidisciplinary Optimization, 2010, 42(5):681-691 doi: 10.1007/s00158-010-0535-5 [11] Deaton J D, Grandhi R V. Stiffening of restrained thermal structures via topology optimization[J]. Structural and Multidisciplinary Optimization, 2013, 48(4):731-745 doi: 10.1007/s00158-013-0934-5 [12] Deaton J D, Grandhi R V. Stress-based design of thermal structures via topology optimization[J]. Structural and Multidisciplinary Optimization, 2016, 53(2):253-270 doi: 10.1007/s00158-015-1331-z [13] 王选, 刘宏亮, 龙凯, 等.基于改进的双向渐进结构优化法的应力约束拓扑优化[J].力学学报, 2018, 50(2):385-394 http://d.old.wanfangdata.com.cn/Periodical/lxxb201802018Wang X, Liu H L, Long K, et al. Stress-constrained topology optimization based on improved bi-directional evolutionary optimization method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2):385-394(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/lxxb201802018 [14] 荣见华, 葛森, 邓果, 等.基于位移和应力灵敏度的结构拓扑优化设计[J].力学学报, 2009, 41(4):518-529 doi: 10.3321/j.issn:0459-1879.2009.04.008Rong J H, Ge S, Deng G, et al. Structural topological optimization based on displacement and stress sensitivity analyses[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4):518-529(in Chinese) doi: 10.3321/j.issn:0459-1879.2009.04.008 [15] 张永红, 桑阳, 葛文杰, 等.多相材料的柔性机构拓扑优化设计[J].机械科学与技术, 2017, 36(9):1320-1326 doi: 10.13433/j.cnki.1003-8728.2017.0902Zhang Y H, Sang Y, Ge W J, et al. Topology optimization design of compliant mechanisms for multiphase materials[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(9):1320-1326(in Chinese) doi: 10.13433/j.cnki.1003-8728.2017.0902 [16] Le C U, Norato J, Bruns T, et al. Stress-based topology optimization for continua[J]. Structural and Multidisciplinary Optimization, 2010, 41(4):605-620 doi: 10.1007/s00158-009-0440-y [17] Holmberg E, Torstenfelt B, Klarbring A. Stress constrained topology optimization[J]. Structural and Multidisciplinary Optimization, 2013, 48(1):33-47 doi: 10.1007/s00158-012-0880-7 [18] Oest J, Lund E. Topology optimization with finite-life fatigue constraints[J]. Structural and Multidisciplinary Optimization, 2017, 56(5):1045-1059 doi: 10.1007/s00158-017-1701-9 [19] Bruns T E, Tortorelli D A. Topology optimization of non-linear elastic structures and compliant mechanisms[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(26-27):3443-3459 doi: 10.1016/S0045-7825(00)00278-4 [20] Svanberg K. The method of moving asymptotes-a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2):359-373 doi: 10.1002/nme.1620240207 -
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