ANALYTICAL SOLUTIONS FOR BENDING OF CLAMPED ORTHOTROPIC RECTANGULAR PLATES UNDER A CONCENTRATED FORCE
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摘要: 采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分：集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。Abstract: For a clamped orthotropic rectangular plate, the bending deflection due to a concentrated force can be treated as the superposition of deflections of simply supported plate under three load cases, a concentrated force, moments along two opposite edges and moments along the other two opposite edges. The solution satisfies the boundary conditions of the clamped plate. Matlab program is developed for calculating the deflections of four plates with different thickness and concentrated force positions. The analytical solutions are compared with Finite Element Method results, demonstrating the accuracy of the proposed solution. Finally, the reasonability of Kirchhoff plate assumptions is discussed through the case of clamped plate under a concentrated force.
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Keywords:
- method of superposition /
- concentrated force /
- clamped rectangular plate /
- orthotropic /
- deflection
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[1] Timoshenko S, Woinowsky-Krieger S. Theory of plates and shells [M]. 2nd ed. New York: McGraw-Hill, 1959: 105―225. [2] Lekhnitskii S G. Anisotropic plates [M]. 2nd ed. New York: Gordon and Breach, 1968: 241―345. [3] Mbakogu F C, Pavlović M N. Bending of clamped orthotropic rectangular plates: A variational symbolic solution [J]. Computers & Structures, 2000, 77(2): 117―128. [4] 杨加明, 孙良新, 雷呈凤. 三边夹紧一边铰支正交各向异性矩形薄板的几何非线性分析[J]. 工程力学, 2002, 19(3): 39―43. Yang Jiaming, Sun Liangxin, Lei Chengfeng. Geometrically nonlinear analysis of orthotropic rectangular thin plates with three edges clamped and one edge simply supported [J]. Engineering Mechanics, 2002, 19(3): 39―43. (in Chinese) [5] Green A E. Double Fourier series and boundary value problems [C]// Dunajski M, Kryński W. Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge: Cambridge University Press, 1944, 40(3): 222―228. [6] Dickinson S M. The flexural vibration of rectangular orthotropic plates [J]. Journal of Applied Mechanics, 1969, 36(1): 101―106. [7] Whitney J M. Fourier analysis of clamped anisotropic plates [J]. Journal of Applied Mechanics, 1971, 38: 530―532. [8] Hencky H. Über ein einfaches näherungsverfahren zur bestimmung des spannungszustandes in rechteckig begrenzten scheiben, auf deren umfang nur normalspannungen wirken [M]// Von Karman T. Beiträge Zur Technischen Mechanik und Technischen Physik. Heidelberg, Springer Berlin Heidelberg, 1924: 62―73. [9] Galerkin B G. Rectangular plates supported by edges [M]. Moscow: Collected Papers, 1953: 3―42. [10] Bhaskar K, Kaushik B. Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges [J]. Composite Structures, 2004, 63(1): 63―68. [11] Bhaskar K, Kaushik B. Analysis of clamped unsymmetric cross-ply rectangular plates by superposition of simple exact double Fourier series solutions [J]. Composite Structures, 2005, 68(3): 303―307. [12] Baraigi N K. A text book of plate analysis [M]. Delhi: Khanna Publishers, 1986: 2―6. -
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