应用扰动广义微分求积法的复合材料层合板剪切屈曲分析与优化

摘要/Abstract

摘要： 广义微分求积(GDQ)法求解复合材料层合板剪切屈曲时存在计算精度差、计算振荡不收敛问题，研究发现该现象源于载荷矩阵存在奇异,为此,提出扰动GDQ法，通过扰动主对角线权重系数以改善载荷矩阵的奇异性来消除计算振荡。数值算例验证了扰动策略的有效性，实现复合材料层合板剪切屈曲问题的高效稳定求解。在此基础上，结合直接搜索模拟退火算法，开展了含剪切载荷的复合材料层合板铺层顺序优化。结果表明：剪切工况时对称复合材料层合板的优化铺层不受铺层数和铺设形式影响，优化铺层角随长宽比增大而趋于60°；而剪切与轴压组合工况下较小的剪切力能改善层合板屈曲性能，随着剪切力的增大，优化屈曲性能逐渐降低，优化铺层趋同于剪切工况。研究结果为复合材料层合板的剪切屈曲性能设计提供了参考。

关键词: 剪切屈曲, 扰动广义微分求积法, 铺层顺序优化, 复合材料层合板

Abstract: There was poor accuracy, calculation oscillation and non|convergence for the cases of shear buckling responses of composite laminates by using GDQ method. The example study found that the problems came from the singular load matrix, therefore, the perturbation GDQ method was proposed to realize the stable and efficient solution of shear buckling problems for composite laminates, by disturbing the main diagonal weight coefficients to improve the singularity of the load matrix. Numerical examples demonstrate the validity of the perturbed GDQ method. The stacking sequence of composite laminates including shear loads was optimized combined perturbation GDQ method with the direct search simulated annealing algorithm. The results show that the ply numbers and lay forms of composite laminates have little effects on the optimum ply under shear loads, and optimized layup angle tends to 60° with the increasing of aspect ratio. Under combined loads of shear and axial compression, the relatively small shear forces may improve the buckling behavior of laminates, while the optimized buckling performances are gradually reduced and the optimum ply is converged to the ply of shear loads with the increasing of shear forces. The results provide a reference for the shear buckling performance design of composite laminates.

Key words: shear buckling, perturbation generalized differential quadrature(GDQ) method, stacking sequence optimization, composite laminate

中图分类号:

TB332

孙士平;张冰;胡政. 应用扰动广义微分求积法的复合材料层合板剪切屈曲分析与优化[J]. 中国机械工程.

SUN Shiping;ZHANG Bing;HU Zheng. Shear Buckling Analysis and Optimization of Composite Laminates Using Perturbation GDQ Method[J]. China Mechanical Engineering.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: http://www.cmemo.org.cn/CN/

http://www.cmemo.org.cn/CN/Y2019/V30/I16/1931

参考文献

[1]唐俊. 剪切载荷作用下复合材料层合板优化分析[J]. 复合材料学报, 1980, 6(4): 48-56.
TANG Jun. On Optimum Analysis of Laminated Plates under Shear[J]. Acta Materiae Compositae Sinica, 1980, 6(4): 48-56.
[2]GRENESTEDT J L. Layup Optimization against Buckling of Shear Panels[J]. Structural & Multidisciplinary Optimization, 1991, 3(2):115-120.
[3]FUKUNAGA H, SEKINE H. A Laminate Design for Elastic Properties of Symmetric Laminates with Extension Shear or Bending-Twisting Coupling[J]. Journal of Composite Materials, 1994, 28(8): 708-731.
[4]KOSTELETOS S. Shear Buckling Response of Laminated Plates[J]. Composite Structures, 1992, 20(3): 147-154.
[5]LOUGHLAN J. The Shear Buckling Behaviour of Thin Composite Plates with Particular Reference to the Effects of Bend-Twist Coupling[J]. International Journal of Mechanical Sciences, 2001, 43(3): 771-792.
[6]LOPATIN A V, KORBUT Y B. Buckling of Clamped Orthotropic Plate in Shear[J]. Composite Structures, 2006, 76(1/2): 94-98.
[7]TARJAN G, SAPKAS A, KOLLAR L P. Stability Analysis of Long Composite Plates with Restrained Edges Subjected to Shear and Linearly Varying Loads[J]. Journal of Reinforced Plastics and Composites, 2010, 29(9):1386-1398.
[8]杨端生, 黄炎, 李广利. 各向异性矩形板的剪切屈曲分析[J]. 应用力学学报, 2012, 29(2):220-225.
YANG Duansheng, HUANG Yan, LI Guangli. Shear Buckling Analysis of Anisotropic Rectangular Plates[J]. Chinese Journal of Applied Mechanics, 2012, 29(2):220-225.
[9]SELYUGIN S. On Choice of Optimal Anisotropy of Composite Plates against Buckling, with Special Attention to Bending-Twisting Coupling[J]. Structural and Multidisciplinary Optimization, 2013, 48(2): 279-294.
[10]JUNG W Y, HAN S C. Shear Buckling Responses of Laminated Composite Shells Using a Modified 8-node ANS Shell Element[J]. Composite Structures, 2014, 109(1): 119-129.
[11]刘庆辉, 乔丕忠, 郭兴文, 等. 正交各向异性板剪切屈曲载荷的近似表达式研究[J]. 工程力学, 2014, 31(3): 32-38.
LIU Qinghui, QIAO Pizhong, GUO Xingwen, et al. Approximate Formulas for Shear Buckling of Orthotropic Plates[J]. Engineering Mechanics, 2014, 31(3): 32-38.
[12]LIU Q H, QIAO P Z, GUO X W. Buckling Analysis of Restrained Orthotropic Plates under Combined In-plane Shear and Axial Loads and Its Application to Web Local Buckling[J]. Composite Structures, 2014,111(11): 540-552.
[13]CHEN Q Y, QIAO P Z. Shear Buckling of Rotationally-restrained Composite Laminated Plates[J]. Thin-Walled Structures, 2015, 94: 147-154.
[14]SHU C, DU H J. A Generalized Approach for Implementing General Boundary Condition in the GDQ Free Vibration Analysis of Plates[J]. International Journal of Solids and Structures, 1997, 34(7): 837-846.
[15]SHU C. Differential Quadrature and Its Application in Enginerring[M]. London: Springer, 2000:95-120.
[16]KADKHODAYAN M, MAAREFDOUST M. Elastic/Plastic Buckling of Isotropic Thin Plates Subjected to Uniform and Linearly Varying In-plane Loading Using Incremental and Deformation Theories[J]. Aerospace Science and Technology, 2014, 32(1):66-83.
[17]李威，曾志松, 韩旭. 弹性地基上受切向力作用梁稳定性研究[J]. 振动与冲击, 2014, 33(8): 192-195.
LI Wei, ZENG Zhisong, HAN Xu. Stability of a Beam on Elastic Foundation Subjected to a Tangential Force[J]. Journal of Vibration and Shock, 2014, 33(8): 192-195.
[18]DARVIZEH M, DARVIZEH A, ANSARI R, et al. Buckling Analysis of Generally Laminated Composite Plates[J]. Composite Structures, 2004, 63(1): 69-74.
[19]MAAREFDOUST M, KADKHODAYAN M. Elastic/Plastic Buckling Analysis of Skew Plates under In-plane Shear Loading with Incremental and Deformation Theories of Plasticity by GDQ Method[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(2):761-776.
[20]孙士平, 曾庆龙, 吴建军. 基于改进模拟退火算法的复合材料层合板屈曲优化[J].中国机械工程, 2015, 26(12): 1676-1683.
SUN Shiping, ZENG Qinglong, WU Jianjun. Buckling Optimization of Composite Laminates Based on Improved Simulated Annealing[J]. China Mechanical Engineering, 2015, 26(12): 1676-1683.
[21]SMITH S T, BRADFORD M A, OEHLERS D J. Elastic Buckling of Unilaterally Constrained Rectangular Plates in Pure Shear[J]. Engineering Structures, 1999, 21(5): 443-453.
[22]KIM C W, LEE J S. Optimal Design of Laminated Composite Plates for Maximum Buckling Load Using Genetic Algorithm[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2005, 219(8):869-878.
[23]中国航空研究院.复合材料结构设计手册[M]. 北京：航空工业出版社, 2001:348-353.
Chinese Aeronautics Research Institute. Handbook of Composites Structures Design[M]. Beijing: Aviation Industry Press, 2001:348-353.