Volume 43 Issue 4
Apr.  2022
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GE Renyu, ZHANG Jiachen, MA Guoqiang, LIU Xiaoshuang, NIU Zhongrong. Analysis on Stress Singularity of Plane Joints With the Differential Quadrature Method[J]. Applied Mathematics and Mechanics, 2022, 43(4): 382-391. doi: 10.21656/1000-0887.420218
 Citation: GE Renyu, ZHANG Jiachen, MA Guoqiang, LIU Xiaoshuang, NIU Zhongrong. Analysis on Stress Singularity of Plane Joints With the Differential Quadrature Method[J]. Applied Mathematics and Mechanics, 2022, 43(4): 382-391.

Analysis on Stress Singularity of Plane Joints With the Differential Quadrature Method

doi: 10.21656/1000-0887.420218
• Received Date: 2021-07-28
• Accepted Date: 2021-07-28
• Rev Recd Date: 2021-09-19
• Available Online: 2022-03-24
• Publish Date: 2022-04-01
• A novel differential quadrature method (DQM) for analysis of the stress singularity index was proposed. Firstly, the radial asymptotic expansion scheme of the displacement field at the connection point of the plane joint was substituted into the governing equation of plane elasticity, and the eigenvalue problem of ordinary differential equations (ODEs) about the stress singularity index was obtained. Then, based on the DQM theory, the eigenvalue problem of ordinary differential equations was transformed into the eigenvalue problem of standard generalized algebraic equations. The stress singularity index at the connection point of the bi-material plane joint was calculated at one time, and the corresponding displacement and stress characteristic functions at the connection point were obtained at the same time. The numerical results show that, the DQM is correct in calculation of the stress singularity index at the connection point of the plane joint.

•  [1] LIU C I, CHUE C H. On the stress singularity of dissimilar anisotropic wedges and junctions in anti-plane shear[J]. Composite Structures, 2006, 73(4): 432-442. [2] 张志春, 强洪夫, 周伟. 基于粘结界面模型的三维裂纹扩展研究[J]. 计算物理, 2010, 27(4): 586-592. (ZHANG Zhichun, QIANG Hongfu, ZHOU Wei. 3D crack propagation in cohesive zone models[J]. Chinese Journal of Computational Physics, 2010, 27(4): 586-592.(in Chinese) [3] HEIN V L, ERDOGAN F. Stress singularities in a two-material wedge[J]. International Journal of Fracture, 1971, 7: 317-330. [4] BOGY D B. On the problem of edgebonded elastic quarteroplanes loaded at the boundary[J]. International Journal of Solids & Structures, 1970, 6(9): 1287-1313. [5] BOGY D B. Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions[J]. Journal of Applied Mechanics, 1971, 38(2): 377-386. [6] WILLIAMS M L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension[J]. Journal of Applied Mechanics, 1952, 19(4): 526-528. [7] ENGLAND A H. On stress singularities in linear elasticity[J]. International Journal of Engineering Science, 1971, 9(6): 571-585. [8] STERN M, SONI M L. On the computation of stress intensities at fixed-free corners[J]. International Journal of Solids & Structures, 1976, 12(5): 331-337. [9] CARPENTER W C, BYERS C. A path independent integral for computing stress intensities for V-notched cracks in a bi-material[J]. International Journal of Fracture, 1987, 35: 245-268. [10] PAGGI M, CARPINTERI A. On the stress singularities at multi-material interfaces and related analogies with fluid dynamics and diffusion[J]. Applied Mechanics Reviews, 2008, 61(2): 1-22. [11] PICU C R, GUPTA V. Stress singularities at triple junctions with freely sliding grains[J]. International Journal of Solids & Structures, 1996, 33(11): 1535-1541. [12] LIU X H, SUO Z, MA Q. Split singularities: stress field near the edge of a silicon die on a polymer substrate[J]. Computer Methods in Applied Mechanics and Engineering, 1999, 47(1): 67-76. [13] BONIFACE V, SIMHA K R Y. Suppression of complex singularity using wedge interphase in interface fracture[J]. International Journal of Solids and Structure, 2001, 38(30/31): 5411-5420. [14] 张金轮, 葛仁余, 韩有民, 等. 各向同性材料接头和界面相交裂纹应力奇异性特征分析[J]. 应用力学学报, 2017, 34(1): 14-19. (ZHANG Jinlun, GE Renyu, HAN Youmin, et al. Analysis of the stress singularity of the junctions and plane cracks terminating at the interface in bonded dissimilar isotropic materials[J]. Chinese Journal of Applied Mechanics, 2017, 34(1): 14-19.(in Chinese) [15] SATOR C, BECKER W. Closed-form solutions for stress singularities at plane bi- and trimaterial junctions[J]. Archive of Applied Mechanics, 2012, 82(5): 643-658. [16] CARPINTERI A, PAGGI M. Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems[J]. Engineering Fracture Mechanics, 2007, 74(1/2): 59-74. [17] CHO S B, CARPENTER W C. The complex potential approach to power-logarithmic stress singularities for V-notched cracks in a bi-material[J]. KSME International Journal, 1999, 13(1): 19-25. [18] BELLMAN R, CASTI J. Differential quadrature and long-term integration[J]. Journal of Mathematical Analysis and Applications, 1971, 34: 235-238. [19] BERT C W, WANG X, STRIZ A G. Differential quadrature for static and free vibration analysis of anisotropic plates[J]. International Journal of Solids and Structures, 1993, 30(13): 1737-1744. [20] BERT C W, JANG S K, STRIZ A G. Two new approximate methods for analyzing free vibration of structural components[J]. AIAA Journal, 2015, 26(5): 612-618. [21] LIEW K M, TEO T M, HAN J B. Three-dimensional static solutions of rectangular plates by variant differential quadrature method[J]. International Journal of Mechanical Sciences, 2001, 43(7): 1611-1628. [22] YANG J, KITIPORNCHAI S, LIEW K M. Non-linear analysis of thermos-electro-mechanical behavior of shear deformable FGM plates with piezoelectric actuators[J]. International Journal for Numerical Methods in Engineering, 2004, 59(12): 1605-1632. doi: 10.1002/nme.932 [23] 许金泉. 界面力学[M]. 1版. 北京: 科学出版社, 2006. XU Jinquan. The Mechanics of Interface[M]. 1st ed. Beijing: Science Press, 2006. (in Chinese)

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沈阳化工大学材料科学与工程学院 沈阳 110142

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