[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()

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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

Author(s):

Xu Qilou^1*;  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

Keywords:

bending of elastic thin plate;  rectangular plate;  unified solution method

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.

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.

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