多工况结构拓扑优化的灰色权重折衷规划模型法
|
摘要
针对多工况结构拓扑优化问题中的载荷病态现象,基于RAMP(Rational Approximation of Material Properties)拓扑优化模型,提出应用灰色理论确定工况权重系数,并将应变能目标函数归一化的折衷规划模型法.通过专家评价方法获得工况权重系数的灰色区间,结合灰色理论计算工况权重系数灰色区间的精确值,并采用导重法推导出多工况结构拓扑优化问题的求解迭代表达式.通过定义载荷比描述载荷病态的程度,对多工况结构拓扑优化典型算例在不同载荷比及不同工况权重系数下进行结构拓扑优化分析.优化结果表明,灰色权重折衷规划模型及求解方法对多工况结构拓扑优化问题具有高效、稳定的特点,能够克服载荷病态问题,并通过大跨度甲板强横梁的结构拓扑优化设计证明本文设计方法的有效性.
To avoid the phenomenon of load sickness in structural topology optimization under multiple load conditions, based on RAMP(rational approximation of material properties) method, the grey theory is applied to determine the weighting factor of load cases. The problem of load sickness is solved by the compromise programing approach, in which objective function is normalized. The weight factors' interval in compromise programming approach can be improved through the experts evaluation method, and the exact values of weight factors' interval are calculated by the grey theory. The Guide-Weight method is introduced to conduct the topology optimization, and the iterative formula of the Guide-Weight method for solving topology optimization is derived. The degree of load sickness is described by defining load case ratio. In this way, classical numerical examples of multiple load cases topology optimization are calculated, which optimal topological structures of numerical examples are analyzed through a serious of load ratios and weight factors. The optimization results demonstrate that combining the Guide-Weight method and compromise programming approach with grey weight factors can be used for structural topology optimization under multi load conditions with significant steady and efficiency, and can be able to overcome the problem of load sickness. Through the structural topology optimization design of large span web frame, the accuracy of the proposed method is validated.
To avoid the phenomenon of load sickness in structural topology optimization under multiple load conditions, based on RAMP(rational approximation of material properties) method, the grey theory is applied to determine the weighting factor of load cases. The problem of load sickness is solved by the compromise programing approach, in which objective function is normalized. The weight factors' interval in compromise programming approach can be improved through the experts evaluation method, and the exact values of weight factors' interval are calculated by the grey theory. The Guide-Weight method is introduced to conduct the topology optimization, and the iterative formula of the Guide-Weight method for solving topology optimization is derived. The degree of load sickness is described by defining load case ratio. In this way, classical numerical examples of multiple load cases topology optimization are calculated, which optimal topological structures of numerical examples are analyzed through a serious of load ratios and weight factors. The optimization results demonstrate that combining the Guide-Weight method and compromise programming approach with grey weight factors can be used for structural topology optimization under multi load conditions with significant steady and efficiency, and can be able to overcome the problem of load sickness. Through the structural topology optimization design of large span web frame, the accuracy of the proposed method is validated.
引文
[1]CAI Y,XU L,CHENG G.Novel numerical implementation of asymptotic homogenization method for periodic plate structures[J].International Journal of Solids and Structures,2014,51(1):284-292.
[2]SIGMUND O,MAUTE K.Topology optimization approaches[J].Structural and Multidisciplinary Optimization,2013,48(6):1031-1055.
[3]刘书田,胡瑞,周平,等.基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法[J].光学精密工程,2013,21(7):1803-1810.
[4]何林伟,蔡国平.Von Mises应力约束的连续结构的一种双向拓扑优化方法[J].力学季刊,2011,32(1):19-27.
[5]ALLAIRE G,DAPOGNY C,FREY P.A mesh evolution algorithm based on the level set method for geometry and topology optimization[J].Structural and Multidisciplinary Optimization,2013,48(4):711-715.
[6]叶红玲,隋允康.应力约束下三维连续体结构拓扑优化分析[J].力学季刊,2006,27(4):621-627.
[7]郝寨柳,刘祖源,冯佰威.多目标优化算法在船舶多学科设计优化中的应用[J].中国造船,2014,3:53-63.
[8]黄海燕,林志祥,王德禹.船艉结构静动态多目标优化设计[J].船舶力学,2011,15(11):1270-1277.
[9]朱金文,杨德庆.三种典型边界条件下受集中载荷梁大挠度弯曲精确解[J].力学季刊,2013,34(3):403-408.
[10]LIU X J,LI Z D,CHEN X.A new solution for topology optimization problems with multiple loads:the guide-weight method[J].Science China Technological Sciences,2011,54(6):1505-1514.
[11]苟鹏,崔维成.考虑依赖于结构形状的载荷的连续体结构拓扑优化[J].船舶力学,2006,10(1):62-70.
[12]葛培明,李尧臣.改进的遗传算法在连续体结构多目标拓扑优化中的应用[J].力学季刊,2008,29(3):481-486.
[13]兰凤崇,赖番结,陈吉清,等.考虑动态特性的多工况车身结构拓扑优化研究[J].机械工程学报,2014,50(20):122-128.
[14]黄飞,彭高明,贺浩,等.多工况应力约束下刮板取料机输送链板的拓扑优化[J].力学与实践,2012,34(1):70-74.
[15]隋允康,彭细荣,叶红玲.ICM应力全局化方法克服连续体拓扑优化的载荷病态[J].工程力学,2009,26(6):1-9.
[16]王文平,邓聚龙.灰线性规划的灰解法[J].应用数学,1996,4:519-522.
[17]王连生,郝志勇,景囯玺.基于多目标形貌优化的缸盖罩低噪声设计[J].西南交通大学学报,2012,47(6):1064-1068.
[18]PAI T Y,HANAKI K,HO H H,et al.Using grey system theory to evaluate transportation effects on air quality trends in Japan[J].Transportation Research Part D:Transport and Environment,2007,12(3):158-166.
[19]陈树勋,韦齐峰,黄锦成,等.利用导重法进行结构轻量化设计[J].工程力学,2016,33(2):179-187.
[20]LIU X J,LI Z D,WANG L P,et al.Solving topology optimization problems by the guide-weight method[J].Frontiers of Mechanical Engineering,2011,6(1):136-150.
[2]SIGMUND O,MAUTE K.Topology optimization approaches[J].Structural and Multidisciplinary Optimization,2013,48(6):1031-1055.
[3]刘书田,胡瑞,周平,等.基于筋板式基结构的大口径空间反射镜构型设计的拓扑优化方法[J].光学精密工程,2013,21(7):1803-1810.
[4]何林伟,蔡国平.Von Mises应力约束的连续结构的一种双向拓扑优化方法[J].力学季刊,2011,32(1):19-27.
[5]ALLAIRE G,DAPOGNY C,FREY P.A mesh evolution algorithm based on the level set method for geometry and topology optimization[J].Structural and Multidisciplinary Optimization,2013,48(4):711-715.
[6]叶红玲,隋允康.应力约束下三维连续体结构拓扑优化分析[J].力学季刊,2006,27(4):621-627.
[7]郝寨柳,刘祖源,冯佰威.多目标优化算法在船舶多学科设计优化中的应用[J].中国造船,2014,3:53-63.
[8]黄海燕,林志祥,王德禹.船艉结构静动态多目标优化设计[J].船舶力学,2011,15(11):1270-1277.
[9]朱金文,杨德庆.三种典型边界条件下受集中载荷梁大挠度弯曲精确解[J].力学季刊,2013,34(3):403-408.
[10]LIU X J,LI Z D,CHEN X.A new solution for topology optimization problems with multiple loads:the guide-weight method[J].Science China Technological Sciences,2011,54(6):1505-1514.
[11]苟鹏,崔维成.考虑依赖于结构形状的载荷的连续体结构拓扑优化[J].船舶力学,2006,10(1):62-70.
[12]葛培明,李尧臣.改进的遗传算法在连续体结构多目标拓扑优化中的应用[J].力学季刊,2008,29(3):481-486.
[13]兰凤崇,赖番结,陈吉清,等.考虑动态特性的多工况车身结构拓扑优化研究[J].机械工程学报,2014,50(20):122-128.
[14]黄飞,彭高明,贺浩,等.多工况应力约束下刮板取料机输送链板的拓扑优化[J].力学与实践,2012,34(1):70-74.
[15]隋允康,彭细荣,叶红玲.ICM应力全局化方法克服连续体拓扑优化的载荷病态[J].工程力学,2009,26(6):1-9.
[16]王文平,邓聚龙.灰线性规划的灰解法[J].应用数学,1996,4:519-522.
[17]王连生,郝志勇,景囯玺.基于多目标形貌优化的缸盖罩低噪声设计[J].西南交通大学学报,2012,47(6):1064-1068.
[18]PAI T Y,HANAKI K,HO H H,et al.Using grey system theory to evaluate transportation effects on air quality trends in Japan[J].Transportation Research Part D:Transport and Environment,2007,12(3):158-166.
[19]陈树勋,韦齐峰,黄锦成,等.利用导重法进行结构轻量化设计[J].工程力学,2016,33(2):179-187.
[20]LIU X J,LI Z D,WANG L P,et al.Solving topology optimization problems by the guide-weight method[J].Frontiers of Mechanical Engineering,2011,6(1):136-150.