[1] Xu Qilou*, Ji Tonggeng, Jiang Rui, Tang Guoming, et al. Unified Solution Method of Rectangular Plate Elastic Bending [J]. Journal of Southeast University (English Edition), 2002, 18 (3): 241-248. [doi:10.3969/j.issn.1003-7985.2002.03.010]
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Unified Solution Method of Rectangular Plate Elastic Bending(
)
矩形薄板弹性弯曲统一求解方法
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 18
- Issue:
- 2002 3
- Page:
- 241-248
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2002-09-30
Info
- Title:
- Unified Solution Method of Rectangular Plate Elastic Bending
- 矩形薄板弹性弯曲统一求解方法
- Author(s):
- Xu Qilou1*; Ji Tonggeng2; Jiang Rui1; Tang Guoming3; Ji Hongen4
-
1Civil Engineering Institute, Zhengzhou University, Zhengzhou 450002, China
2Henan Provincial Communication Planning Survey and Design Institute, Zhengzhou 450052, China
3Zhaoqing Planning and Design Institute, Zha
- 许琪楼1; 姬同庚2; 姜锐1; 唐国明3; 姬鸿恩4
- 1郑州大学土木工程学院, 郑州 450002; 2河南省交通厅勘察设计院, 郑州 450052; 3广东肇庆市城市规划设计院, 肇庆 526040; 4郑州工程学院, 郑州 450052
- PACS:
- TU311.4
- DOI:
- 10.3969/j.issn.1003-7985.2002.03.010
- Abstract:
- The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of boundary, such as simply supported edge, clamped edge, free edge, free corner point and pillar support corner point, can be solved under arbitrary loads, such as the loads on plate, the loads in plate edge, the load at free corner point, and when the plate edge and the pillar support corner point have settlement or when the plate edge has rotation. The method can organically unite the Navier solution and the Levy solution and has the advantages of rapid convergence and high precision.
- 在分析角点求解条件完备性的基础上将矩形板弯曲划分为广义静定问题和广义超静定问题.广义静定弯曲可以由板的平衡微分方程及四边边界条件直接求解, 广义超静定弯曲可以由叠加法求解.这种求解方法可以解决各种边界条件下(包括简支边、固定边、自由边、自由角点、支柱角点)的矩形板在任意荷载作用下(包括板面上作用任意法向荷载, 板边界上作用任意荷载, 板自由角点上作用集中力, 板边界及支柱角点发生任意位移)的弯曲.本方法可以将经典的纳维叶解和李维解法有机地统一起来, 且收敛速度快, 计算精度高.
References:
[1] Timoshenko S, Woinowski S. Theory of plates and shells. 2nd ed.[M].Beijing: Science Publishing House, 1977.110-238.(in Chinese)
[2] Xu Qilou, Ji Tonggeng. Bending solution of rectangular plates with two adjacent supported edges and two free edges subjected to uniform load[J]. China Civil Engineering Journal, 1995, 28(3):32-41.(in Chinese)
[3] Xu Qilou, Ji Tonggeng. Bending solution of a rectangular plates with one edge built-in and one corner point supported subjected to uniform load [J]. Applied Mathematics and Mechanics(English Edition), 1996, 17(12):1153-1163.
[4] Xu Qilou. New solution of rectangular plate with one edge built-in subjected to uniform load [J]. Journal of Zhengzhou Institute of Technology, 1996, 17(2):42-47.(in Chinese)
[5] Xu Qilou, Ji Tonggeng. Bending of rectangular plate with one simply supported edge and two corner point supported [J]. Chinese Journal of Applied Mechanics, 1997, 14(4):56-63.(in Chinese)
[6] Xu Qilou, Ji Tonggeng. Bending of rectangular plate with one simply supported edge and one corner point supported [J]. China Civil Engineering Journal, 1997, 30(5):76-79.(in Chinese)
[7] Xu Qilou, Jiang Rui. Rectangular plate bending with three edges supported and one edge free[J]. Journal of Zhengzhou University of Technology, 1997, 18(3):5-15.(in Chinese)
[8] Xu Qilou, Jiang Rui, Tang Guoming. United solution method on rectangular plate bending with one simply supported edge and one or two corner points supported [J]. Journal of Zhengzhou University of Technology, 1998, 19(1):52-59.(in Chinese)
[9] Xu Qilou, Jiang Rui, Tang Guoming. United solution method on rectangular plate bending with one edge clamped and one or two corner points supported[J]. Chinese Journal of Computational Mechanics, 1999, 16(2):210-215.(in Chinese)
[10] Xu Qilou, Li Mingsheng, Jiang Rui, et al. United solution method on rectangular plate bending with three edges supported and one edge free[J]. Journal of Southeast University, 1999, 29(2):87-92.(in Chinese)
[11] Xu Qilou, Jiang Rui, Tang Guoming. United solution method on rectangular plate bending with four edges supported — discussion on unification of Navier solution and Levy solution[J]. Engineering Mechanics, 1999, 16(3): 90-99.(in Chinese)
[12] Xu Qilou, Jiang Rui, Tang Guoming. United solution method on rectangular plate bending with two adjacent edges supported and two free edges[J]. Journal of Southeast University, 2000, 30(2): 138-142.(in Chinese)
[13] Xu Qilou, Jiang Rui, Tang Guoming. United solution method on rectangular plate bending with three corner points resting or four corner points resting [J]. Journal of Zhengzhou University of Technology, 2000, 21(3):19-22.(in Chinese)
[14] Xu Qilou, Ji Hongen, Jiang Rui, et al. United solution method of rectangular plate bending with two opposite supported edges and two free edges[A]. In: Cui Jinghao, ed. Proceedings of the Tenth National Conference on Structural Engineering[C]. 2001.427-431.
[15] Ji Hongen. United solution method of rectangular plate bending with boundary displacements[D]. Zhengzhou: Zhengzhou University, 2001.(in Chinese)
Memo
- Memo:
- * Born in 1944, male, professor.