~ Beam4 MPC MPC184 5

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1 Mechanical Science and Technology for Aerospace Engineering March Vol No. 3 姜成, 赵又群, 阮米庆, 汪伟在保证结构与实际车轮模型结构相同的条件下, 建立机械弹性车轮的有限元模型, 实现了车轮受力时的结构协调性和弹簧的回位功能利用 ANSYS 软件对车轮进行了有限元分析, 得出车轮的径向刚度根据结构优化问题的特点, 以轮辐的每段长度作为设计变量, 轮胎径向刚度为优化目标, 利用序列二次规划 ( SQP) 算法, 对车轮结构进行优化设计结果表明 : 基于 SQP 算法的机械弹性车轮的结构优化, 在允许范围内有效的增大了车轮的径向刚度序列二次规划算法 ; 机械弹性车轮 ; 有限元分析 ; 结构优化 U A Structure Optimization of the Mechanical Elastic Wheel Based on the Sequential Quadratic Programming Algorithm Jiang Cheng Zhao Youqun Ruan Miqing Wang Wei College of Energy and Power Engineering Nanjing University of Aeronautics and Astronautics Nanjing Abstract The finite element model of mechanical elastic wheel which was similar to the practical one at most was built. The coordination of structural deformation under pressure was ensured and the function of the restoring spring was realized. The ANSYS software was adopted to calculate the radial stiffness of the wheel. According to the characteristics of structural optimization Using the length of each wheel rib as the design variables and radial stiffness as optimization objective the wheel structure was optimized with the sequential quadratic programming SQP algorithm. The results showed that the radical stiffness of the wheel was increased effectively within the allowable range. Key words algorithms calculations computer software constrained optimization finite element analysis flowcharting mechanical elastic wheel multiobjective optimization quadratic programming springs components SQP algorithm stiffness structural optimization 1 2 SQP 3 SQP CXLX13 _ @ qq. com yqzhao@ nuaa. edu. cn SQP QP SQP

2 ~ Beam4 MPC MPC184 5

3 Combin14 Solid 45 Solid185 Mooney-Rivlin P 1 P 2 P Rivlin X = P 1 P 2 P 3 X min = X W = n max = X 0 = 232 C ijk I 1-3 i I 2-3 j I 3-3 k i j k = 0 W C ijk Rivlin I 1 I Green C 10 = E / C 01 = 0. 25E / E = MPa 6 C 10 = C 01 = I minf x N ANSYS G x mm f x G x = G Z = df g 1 X g 2 X g n X T Z 5 dz X = x 1 x 2 x 3 T N /mm W = C 10 I C 01 I Mooney-Rivlin 5-5 C 10 C 01 Rivlin 150% f z = min disp z C 10 C SQP SQP X k S K X k +1 = X k + α k S k 8 α k k X k X k SQP X k QP S

4 min QP S = f X k T S ST A k S s. t. C v x k + C v x k T S = 0 C j x k + C j x k T S 0 H k ΔH k = - Hk ΔX k ΔX k T H k ΔX k T H k ΔX k + 9 v = 1 2 p 10 j = 1 2 m 11 S = S 1 S 2 S n T f X k C v X k C v X k C j X k C j X k A k S A k L X λx Hessian L X λ = f X + p 7 SQP λ v C v X 12 v = 1 A k = 2 f X k + p λ v 2 C v X k 13 Marotos v = 1 X * 2 f X * A k X k X * d k = α k S k SQP k f X k + α k S k < f X k H k H k +1 Hessian A k Marotos Marotos H k +1 = H k + H k 14 Δgk Δg k T ΔX k T Δg k 15 ΔX k = X k +`1 - X k 16 Δg k = L X k +1 λ k +1 - L X k λ k 17 H 0 = I 11 1 X 0 λ 0 ε H 0 = I 2 QP 3 λ k S k 4 S k α k 8 X k +1 = X k + α k S k f X 5 k +1 - f X K ε f X k 6 6 BFGS H k H k +1 2 SQP 7 9 d k SQP Marotos 3. 4 SQP P 1 P 2 P 3 8 ~ 10 P 1 P 2

3 427 10 P 3 4. P. 200510089076. 7. P 1 P 2 P 3 2009-05-27 2009-05-27 in Chinese 9. 708 mm 5 Meschke G Helnwein P. Large-strain 3D analysis of fi- composites using rebar element hyerelas- 700.

5 P 3 4. P P 1 P 2 P in Chinese mm 5 Meschke G Helnwein P. Large-strain 3D analysis of fi- composites using rebar element hyerelas N /mm 11 bre-reinforced mm tic formulation for cord J. Computational Mechanics N /mm mm N /mm D Li H. 3-D nonlinear FEA of radial tires under inflation and contacting load D. Wuhan Huazhong University of Science and Technology 2006 in Chinese 7. M Yuan Y X Sun W Y. Theory and methods of optimization M. Beijing Beijing Science and Technology Press 2001 in Chinese 8. - M Liu Y Tang L S Chen Y P. Nonlinear parallel algorithm second copies -genetic algorithm M. Beijing 11 Science Press 1995 in Chinese 9. J Shen S S Fang Z D Zhang X J et al. Optimal design of guiding mechanism and rubber bushing based on riding smoothness of air suspension J. Mechanical Sci- ence and Technology in Chinese SQP 10. J SQP D. 1. M Zhuang J D. Technology of vehicle tire M. Beijing Beijing Institute of Technology Press 2011 in Chinese 2 Michael M. A run-flat future R. SAE 100 Futures Look in Celebration of SAE' s Centennial in 2005 Detroit USA SQP J Mao H P Wu Y Z Chen L P. SQP paral lel optimization algorithm based on multi-domain simulation J. China Mechanical Engineering in Chinese Zhao Z D. Spring elastic wheel P. China Wu K G Yan Y J Jiang J S. Structural dynamics optimization research frame and plate combination J. Mechanical Science and Technology Supplement in Chinese Sun F C. Research on aero-engine performance seeking control D. Nanjing Nanjing University of Aeronautics and Astronautics 2007 in Chinese

JOURNAL OF EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol. 31 No. 6 Dec

31 6 2011 12 JOURNAL OF EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION Vol. 31 No. 6 Dec. 2011 1000-1301 2011 06-0159 - 08 1 1 1 1 2 1. 150080 2. 100124 1 2 3 P315. 93 TU 43 TU41 A Shaking table test