点简支正交各向异性矩形薄板弯曲的精确解
An Exact Solution for the Bending of Point-Supported Orthotropic Rectangular Thin Plates
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摘要: 本文利用迭加原理,给出了点简支正交各向异性短形薄板弯曲问题的封闭的级数式解答.简支点的位置和横向载荷的分布均可任意.用本文的级数解给出的算例与以往的数值解是十分一致的.
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关键词:
- 精确解 /
- 点支承 /
- 正交各向异性矩形薄板
Abstract: A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates.The positions of support points and the distribution of transverse loadare arbitrary.If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution.For the square plate simply supported on the middle of each edge and free at each corner,the results are very close to the numerical solutions in the past.-
Key words:
- exact solution /
- point supports /
- orthotropic rectangular thin plate
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[1] Thorne,C.J,,Square plates fixed at points,ASME Journal of Applied Mechanics,15(1948),420-425. [2] Yoshiki,M.,and T.Kawai,On the method of applicati0n of energy principles to problems of elastic plates,Proceedings of Eleventh International Congress of Applied Mechanics,Munich(1966),461-468. [3] Rajaiah,K.and A.K.Rao,Collocation solution for point-supported square plates,ASME Journal of Applied Mechanics,45(1978),424-425. [4] 吴兹潜、张佑敏、范寿昌,《结构分析的样条有限条法》,广东科学技术出版社(1986). [5] Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plates and Shells,2nd ed.,McGraw-Hill,New York(1959). -
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