留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

功能梯度板中Griffith裂纹尖端应力场的三维解析研究

孙烨丽 沈璐璐 杨博

孙烨丽, 沈璐璐, 杨博. 功能梯度板中Griffith裂纹尖端应力场的三维解析研究[J]. 应用数学和力学, 2021, 42(1): 36-48. doi: 10.21656/1000-0887.410143
引用本文: 孙烨丽, 沈璐璐, 杨博. 功能梯度板中Griffith裂纹尖端应力场的三维解析研究[J]. 应用数学和力学, 2021, 42(1): 36-48. doi: 10.21656/1000-0887.410143
SUN Yeli, SHEN Lulu, YANG Bo. 3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates[J]. Applied Mathematics and Mechanics, 2021, 42(1): 36-48. doi: 10.21656/1000-0887.410143
Citation: SUN Yeli, SHEN Lulu, YANG Bo. 3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates[J]. Applied Mathematics and Mechanics, 2021, 42(1): 36-48. doi: 10.21656/1000-0887.410143

功能梯度板中Griffith裂纹尖端应力场的三维解析研究

doi: 10.21656/1000-0887.410143
基金项目: 国家自然科学基金 (11872336);浙江省自然科学基金(LY18A020009)
详细信息
    作者简介:

    孙烨丽(1995—),女,硕士生(E-mail: 2692124689@qq.com);沈璐璐(1990—),女,讲师(E-mail: lulushen@zstu.edu.cn);杨博(1979—),男,教授,硕士生导师(通讯作者. E-mail: youngbo@zstu.edu.cn).

  • 中图分类号: O343.1

3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates

Funds: The National Natural Science Foundation of China(11872336)
  • 摘要: 基于推广后的England-Spencer板理论,研究了横观各向同性功能梯度板中Griffith裂纹尖端的三维应力场.假定材料参数沿板厚方向可以任意连续变化,利用复变函数解法和保角变换技术分别给出了受无穷远处荷载作用和受均匀内压时裂纹尖端应力的三维解析解.当材料退化为各向同性均匀材料时,将该解答与经典二维解进行了比较,进而验证了该解答的有效性.通过数值算例,进一步讨论了材料梯度因子和荷载条件等因素对裂纹尖端三维应力场的影响.
  • [1] 仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展[J]. 力学进展, 2010,40(5): 528-541.(ZHONG Zheng, WU Linzhi, CHEN Weiqiu. Research progress on some mechanical problems of functionally graded materials and structures[J]. Advances in Mechanics,2010,40(5): 528-541.(in Chinese))
    [2] 柯燎亮, 汪越胜. 功能梯度材料接触力学若干基本问题的研究进展[J]. 科学通报, 2015,60(17): 1565-1573.(KE Liaoliang, WANG Yuesheng. Research progress on some basic problems of contact mechanics of functionally graded materials[J]. Chinese Science Bulletin, 2015,60(17): 1565-1573.(in Chinese))
    [3] 张冠军, 李文栋, 刘哲, 等. 介电功能梯度材料在电气绝缘领域的研究进展[J]. 中国电机工程学报, 2017,37(14): 4232-4245.(ZHANG Guanjun, LI Wendong, LIU Zhe, et al. Research progress of dielectric functional gradient materials in the field of electrical insulation[J]. Proceedings of the CSEE,2017,37(14): 4232-4245.(in Chinese))
    [4] ESKANDARI H. Three-dimensional investigations of stress intensity factors in a rotating thick-walled FGM cylinder[J]. Jordan Journal of Mechanical and Industrial Engineering,2016,10(2): 105-113.
    [5] NOJUMI M M, WANG X D. Dynamic analysis of crack problems in functionally graded materials using a new graded singular finite element[J]. Theoretical and Applied Fracture Mechanics,2018,93: 183-194.
    [6] CHENG J X, SUN B, WANG M Y, et al. Analysis of Ⅲ crack in a finite plate of functionally graded piezoelectric/piezomagnetic materials using boundary collocation method[J]. Archive of Applied Mechanics,2019,89(2): 231-243.
    [7] BOUCHIKHI A S. Numerical investigation of fracture in double-edge notched FGM plates under tension load[J]. International Journal of Structural Integrity,2019,10(6): 838-849.
    [8] CHENG Z Q, ZHONG Z. Fracture analysis of a functionally graded strip under plane deformation[J]. Acta Mechanica Solida Sinica,2006,19(2): 114-121.
    [9] 薛雁, 聂辉, 冯文杰. 磁电弹性功能梯度板共线Griffith裂纹断裂行为[J]. 工程力学, 2008,25(4): 70-74.(XUE Yan, NIE Hui, FENG Wenjie. Fracture behaviors of collinear Griffith cracks in a functionally gradient magneto-electro-elastic strip[J]. Engineering Mechanics,2008,25(4): 70-74.(in Chinese))
    [10] 程站起, 高丹盈, 仲政. 任意梯度分布功能梯度涂层平面裂纹分析[J]. 固体力学学报, 2011,32(4): 426-432.(CHENG Zhanqi, GAO Danying, ZHONG Zheng. Plane crack problem for functionally graded strip with arbitrarily distributed material properties[J]. Chinese Journal of Solid Mechanics,2011,32(4): 426-432.(in Chinese))
    [11] 刘俊俏, 苗福生, 李星. 带功能梯度材料的压电底层中周期裂纹对SH波的散射[J]. 固体力学学报, 2014,35(1): 15-20.(LIU Junqiao, MIAO Fusheng, LI Xing. The scattering of SH wave on the array of periodic cracks in a piezoelectric substrate bonded a half-plane of functionally graded materials[J]. Chinese Journal of Solid Mechanics,2014,35(1): 15-20.(in Chinese))
    [12] 蒋正文, 沈孔健, 万水. 基于分层线性离散模型的FGM板断裂力学分析[J]. 华南理工大学学报(自然科学版), 2014,42(4): 77-84.(JIANG Zhengwen, SHEN Kongjian, WAN Shui. Fracture mechanics analysis of FGM plate based on layered linear discrete model[J]. Journal of South China University of Technology (Natural Science Edition),2014,42(4): 77-84.(in Chinese))
    [13] 杨博. 横观各向同性功能梯度板弯曲问题的弹性力学解[D]. 博士学位论文. 杭州: 浙江大学, 2011.(YANG Bo. Elasticity solutions for bending problems of functionally graded plates with transverse isotropy[D]. PhD Thesis. Hangzhou: Zhejiang University, 2011.(in Chinese))
    [14] YANG B, CHEN W Q, DING H J. 3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holes[J]. Acta Mechanica,2015,226(5): 1571-1590.
    [15] YANG B, DING H J, CHEN W Q. Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported[J]. Applied Mathematical Modelling,2012,36(1): 488-503.
    [16] YANG B, CHEN W Q, DING H J. Equilibrium of transversely isotropic FGM plates with an elliptical hole: 3D elasticity solutions[J]. Archive of Applied Mechanics,2016,86(8): 1391-1414.
    [17] 范天佑. 固体与软物质缺陷与断裂理论基础(上册)[M]. 北京: 科学出版社, 2014.(FAN Tianyou. Theoretical Basis for Defects and Fracture of Solid and Soft Materials(Vol 〖STBX〗1) [M]. Beijing: Science Press, 2014.(in Chinese))
  • 加载中
计量
  • 文章访问数:  931
  • HTML全文浏览量:  118
  • PDF下载量:  215
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-05-19
  • 修回日期:  2020-06-05
  • 刊出日期:  2021-01-01

目录

    /

    返回文章
    返回