结构优化半解析灵敏度及误差修正改进算法

张力丹; 张盛; 陈飙松; 李云鹏

doi:10.6052/0459-1879-18-058

结构优化半解析灵敏度及误差修正改进算法

大连理工大学工业装备结构分析国家重点实验室, 大连 116024

基金项目: 国家重点研发计划(2016YFB0201602)和国家自然科学基金(11372064)资助项目.

详细信息

通讯作者:
陈飙松

中图分类号: TB12;
计量
- 文章访问数: 1233
- HTML全文浏览量: 204
- PDF下载量: 279
出版历程
- 刊出日期: 2018-07-17

MODIFIED SEMI-ANALYTICAL SENSITIVITY ANALYSIS AND ITS ERROR CORRECTION TECHNIQUES

State Key Laboratory of Industrial Equipment , Dalian University of Technology , Dalian 116024, China

摘要

摘要: 提出结构半解析灵敏度分析及其针对刚体位移的误差修正方法的改进算法, 构建灵敏度分析与误差修正项可分离形式. 该方法实现简便, 数值精度不受摄动步长与单元数目的影响. 首先从总体角度推得静力问题的误差修正半解析灵敏度分析方法, 提出了位移误差修正灵敏度列式, 并给出算法实施途径; 然后将此思路推广于自振频率、屈曲临界载荷问题, 提出了相应的计算步骤. 随后, 给出梁单元与壳单元误差修正项的具体推导方法, 并分别使用两种单元构建有限元模型进行算例测试. 结果表明, 该方法适用于多种分析类型, 数值精度不受单元数目与摄动步长的影响. 由于灵敏度分析与误差修正项可以分开计算, 该方法支持将误差修正项直接叠加于灵敏度求解结果进行误差修正, 使已有灵敏度分析程序得到充分利用. 尤其对于复杂工程结构的优化设计, 特别是形状优化设计以及尺寸、形状混合优化设计, 相比于原误差修正方法, 实现更为简便, 效率有所提升, 能为半解析灵敏度分析方法及其程序实现提供新的思路.
- 结构优化 /
- 半解析灵敏度分析法 /
- 误差修正 /
- 形状优化 /
- 改进算法
Abstract: Modified semi-analytical sensitivity analysis algorithm and its error correction term method are presented, where the sensitivity analysis terms and the error correction term can be separated. The method can facilitates program implementation and the accuracy of the method won’t be influenced by perturbation step length and number of elements. Firstly, a modified semi-analytical sensitivity analysis technique with its error correction term is presented for static displacement, which is based on global structure equations of the sensitivity analysis, and its program implementations are provided. Then, the modified method is implemented on other analysis tasks including natural frequency and linear buckling analysis. Consequently, the error correction terms of both beam elements and shell elements are derived. Then, the specific deducing process of error correction terms concerning beam and shell elements is described. Next, the modified method is verified by typical finite element models with beam and shell elements. The results highlight the applicability of the modified method to various analysis types mentioned above, and the accuracy is not influenced by the number of elements and perturbation step length. Since sensitivity analysis parts and error correction term can be computed respectively, the error correction term can becomputed independently and added directly to the results of sensitivity analysis, which can make full use of existing sensitivity analysis programming. This modified method can help complex engineering structural design. Especially, compared to the original semi-analytical sensitivity analysis and error correction methods, the computational efficiency of the modified method is enhanced with respect to shape optimization design variables or shape combined with size optimization, which can provide new ideas for sensitivity analysis and its program implementation.
- structural optimization /
- semi-analytical technique /
- error correction /
- shape optimization /
- modified method

HTML全文

参考文献(1)

[1]	程耿东, 汪榴. 旋转体形状优化及敏度分析的拟解析法. 大连工学院学报,1986, 25(3): 19-25
[1]	(Cheng Gengdong, Wang Liu.Shape optimization of axisymmetric body and sensitivity analysis by quasi-analytical method.Journal of Dalian Institute of Technology, 1986, 25(3): 19-25 (in Chinese))
[2]	Bletzinger KU, Firl M, Daoud F.Approximation of derivatives in semi-analytical structural optimization.Computers & Structures, 2008, 86(13): 1404-1416
[3]	Van Keulen F, Haftka RT, Kim NH.Review of options for structural design sensitivity analysis.Computer Methods in Applied Mechanics and Engineering, 2005, 194(30): 3213-3243
[4]	Takezawa A, Kitamura M.Sensitivity analysis and optimization of vibration modes in continuum systems.Journal of Sound and Vibration, 2013, 332(6): 1553-1566
[5]	Liu ST, Cheng GD, Gu Y, et al.Mapping method for sensitivity analysis of composite material property.Structural and Multidisciplinary Optimization, 2002, 24(3): 212-217
[6]	张升刚, 王彦伟, 黄正东. 等几何壳体分析与形状优化. 计算力学学报, 2014, 31(1): 115-119
[6]	(Zhang Shenggang, Wang Yanwei, Huang Zhengdong.Isogeometric shell analysis and shape optimization.Chinese Journal of Computational Mechanics, 2014, 31(1): 115-119(in Chinese))
[7]	Cheng GD, Liu YW.A new computation scheme for sensitivity analysis.Engineering Optimization, 1987, 12(3): 219-234
[8]	顾元宪, 程耿东. 结构形状优化设计数值方法的研究和应用. 计算结构力学及其应用,1993, 10(3): 321-335
[8]	(Gu Yuanxian, Cheng Gengdong.Research and applications of numerical methods of structural shape optimization.Computational Structural Mechanics and Applications, 1993, 10(3): 321-335 (in Chinese))
[9]	易龙, 彭云, 孙秦. 基于改进的灵敏度分析的有限元优化技术研究. 机械强度,2008, 30(3): 483-487
[9]	(Yi Long, Peng Yun, Sun Qin.Research of the optimal design based on the fem and improved sensitivity analysis.Journal of Mechanical Strength, 2008, 30(3): 483-487 (in Chinese))
[10]	Haftka RT.Semi-analytical static nonlinear structural sensitivity analysis.AIAA Journal, 1993, 31(4): 1307-1312
[11]	Fenyes P, Lust RV.Error analysis of semianalytic displacement derivatives for shape and sizing variables,AIAA Journal, 1991, 29(2): 271-279
[12]	Olho N, Rasmussen J.Study of inaccuracy in semi-analytical sensitivity analysis—a model problem,Structural Optimization, 1991, 3(4): 203-213
[13]	Barthelemy B, Chon CT, Haftka RT.Accuracy problems associted with semi-analytical derivatives of static response.Finite Elements in Analysis and Design, 1988, 4(3): 249-265
[14]	Pauli P, Cheng GD, Rasmussen. On accuracy problems for semi-analytical sensitivity analyses.Journal of Structural Mechanics, 1989, 17(3): 373-384
[15]	程耿东, 刘英卫. 梁的半解析法计算灵敏度的误差分析. 大连理工大学学报, 1989, 29(4): 415-422
[15]	(Cheng Gengdong, Liu Yingwei.Study of error of semi-analytic sensitivity analysis in beam problems.Journal of Dalian University of Technology, 1989, 29(4): 415-422 (in Chinese))
[16]	Barthelemy B, Haftka RT.Accuracy analysis of the semi-analytical method for shape sensitivity calculation.Mechanics of Structures and Machines, 1990, 18(3): 407-432
[17]	Cheng GD, Olhoff N.Rigid body motion test against error in semi-analytical sensitivity analysis.Computers & Structures, 1993, 46(3): 515-527
[18]	Van Keulen F, De Boer H.Rigorous improvement of semi-analytical design sensitivities by exact differentiation of rigid body motions.International Journal for Numerical Methods in Engineering, 1998, 42(1): 71-91
[19]	De Boer H, Van Keulen F, Vervenne K.Refined second order semi-analytical design sensitivities.International Journal for Numerical Methods in Engineering, 2002, 55(9): 1033-1051
[20]	Olhoff N, Rasmussen J, Lund E.A method of “exact” numerical differentiation for error elimination in finite-element-based semi-analytical shape sensitivity analyses.Journal of Structural Mechanics, 1993, 21(1): 1-66
[21]	Lund E, Olhoff N.Shape design sensitivity analysis of eigenvalues using ‘exact’ numerical differentiation of finite element matrices,Structural Optimization, 1994, 8(1): 52-59
[22]	Wang WJ, Clausen PM, Bletzinger KU.Improved semi-analytical sensitivity analysis using a secant stiffness matrix for geometric nonlinear shape optimization.Computers & Structures, 2015, 146: 143-151.
[23]	亢战, 罗阳军. 基于凸模型的结构非概率可靠性优化. 力学学报, 2006, 38(6): 807-815
[23]	(Kang Zhan, Luo Yangjun.On structural optimization for non-probabilistic reliability based on convex models,Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 807-815 (in Chinese))
[24]	亢战, 程耿东. 非确定性结构静动态特性稳健优化设计. 力学学报, 2006, 38(1): 57-65
[24]	(Kang Zhan, Cheng Gengdong.Structural robust design concerning static and dynamic performance based on perturbation stochastic finite element method.Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(1): 57-65 (in Chinese))
[25]	夏人伟, 刘鹏. 一种有效的结构优化设计方法. 力学学报, 1987, 19(3): 52-63
[25]	(Xia Renwei, Liu Peng.An efficient method for structural optimization.Acta Mechanica Sinica, 1987, 19(3): 52-63 (in Chinese))
[26]	吴曼乔, 朱继宏, 杨开科等. 面向压电智能结构精确变形的协同优化设计方法. 力学学报, 2017, 49(2): 380-389
[26]	(Wu Manqiao, Zhu Jihong, Yang Kaike, et al.Integrated layout and topology optimization design of piezoelectric smart structure in accurate shape control.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 380-389 (in Chinese))
[27]	龙凯, 王选, 韩丹. 基于多相材料的稳态热传导结构轻量化设计. 力学学报, 2017, 49(2): 359-366
[27]	(Long Kai, Wang Xuan, Han Dan.Structural light design for steady heat conduction using multi-material.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 359-366 (in Chinese))
[28]	王选, 胡平, 祝雪峰等. 考虑结构自重的基于NURBS插值的3D拓扑描述函数法. 力学学报, 2016, 48(6): 1437-1445
[28]	(Wang Xuan, Hu Ping, Zhu Xuefeng, et al.Topology description function approach using NURBS interpolation for 3D structures with self-weight loads.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1437-1445 (in Chinese))
[29]	郭旭, 顾元宪, 赵康. 广义变分原理的结构形状优化伴随法灵敏度分析. 力学学报, 2004, 36(3): 288-295
[29]	(Guo Xu, Gu Yuanxian, Zhao Kang.Adjoint shape sensitivity analysis based on generalized variational principle.Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 214-222 (in Chinese))
[30]	Haftka R T, Adelman H M.Recent developments in structural sensitivity analysis.Structural Optimization, 1989, 1(3): 137-151
[31]	Gu YX, Zhao GZ, Zhang HW, et al.Buckling design optimization of complex built-up structures with shape and size variables.Structural and Multidisciplinary Optimization, 2000, 19(3): 183-191

施引文献(8)

期刊类型引用(5)

1.	黄焱，孙策，田育丰. 气垫平台破冰阻力的模型试验研究. 力学学报. 2021(03): 714-727 . 本站查看
2.	王悦柔，王军锋，刘海龙. 电场作用下气泡上升行为特性的数值计算研究. 力学学报. 2020(01): 31-39 . 本站查看
3.	孙姣，周维，蔡润泽，陈文义. 垂直壁面附近上升单气泡的弹跳动力学研究. 力学学报. 2020(01): 1-11 . 本站查看
4.	邓斌，王孟飞，黄宗伟，伍志元，蒋昌波. 波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟. 力学学报. 2020(02): 408-419 . 本站查看
5.	王巍，唐滔，卢盛鹏，张庆典，王晓放. 主动射流控制水翼空化的数值模拟与分析. 力学学报. 2019(06): 1752-1760 . 本站查看