求解厚矩形板弯曲问题的功的互等定理法
Reciprocal Theorem Method for Solving the Problems of Bending of Thick Rectangular Plates
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摘要: 在本文中,功的互等定理法(RTM)被推广于求解基于Reissner理论的厚矩形板弯曲问题。首先,本文绘出了厚矩形板弯曲的基本解;其次,给出了三边固定一边自由在均布载荷作用下厚矩形板弯曲的精确解析解;最后,我们分析了本文解的数值结果。
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关键词:
- 功的互等定理法 /
- 基本解 /
- 厚矩形板的弯曲 /
- Reissner理论
Abstract: In this paper,reciprocal theorem method(RTM) is generalized to solve theof bending of thick rectangular plates based on Reissner's theory.First,the paper gives the basic solution of the bending of thick rectangular platesand then the exact analytical solution of the bending of thick rectangular plate with three clamped edges and one free edge under umiformly distributed load is found by RTM, finally, we analyze numerical results of the solution. -
[1] 付宝连,一个求解位移方程的新方法,东北重型机械学院第三届学术报告会(1981). [2] 付宝连,应用功的互等定理求解具有复杂边界矩形板的挠曲面方程,应用数学和力学,3(3)(1982), 315-325. [3] Reissner, E., The effect of transverse shear deformation on the bending of elastic plates, Journal Applied Mechanics, 12, June(1945), 69-77. [4] 程昌钧、杨晓,三边夹紧一边自由的矩形厚板的弯曲,应用数学和力学,11(6)(1990), 505-520. [5] Salerno, V. L. and A. Goldberg, Effect of shear deformation on bending of rectangular plates, J. Appl. Mech., 27, March(1960), 54-58. -
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