任意分布载荷下两对边简支单向非均匀变厚度矩形板的弯曲问题*
Bending Problem of Rectangular Plates of UnidirectionalNonhomogeneity and Variable Thickness with Two Opposite Edges Simply Supported underArbitrary Distributed Loads
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摘要: 本文使用阶梯折算法[1,2],研究了任意分布载荷下两对边简支(x=0和x=a边)单向非均匀变厚度(D=D(y))矩形板的弯曲问题,得到了问题的阶梯近似解,文末对静水压力作用下四边简支线性变厚度正方形板的弯曲作了数值计算,所得结果与[3]一致,这样便验证了阶梯折算法的准确性.Abstract: Using the step reduction method[1,2] suggested by the first author of this paper, we investigate the problem indicated in the title and obtain the stepped approximate solutions. As an example, the case of a square plate of linearly varying thickness with four edges simply supported under linearly distributed loads is calculated. The obtained results agree well with those given in [3] and thus the exactness of the new method is verified.
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[1] 叶开沅、许剑云,非均匀变厚度弹性体力学若干问题的一般解 I.在非均匀定常温度场下的非均匀变厚度高速度旋转圆盘的弹塑性应力分析,兰州大学学报(自然科学版),力学专号,1(1979),60-74;力学学报,专号(1981),7B-89;在第十六届ICTAM上宣读,Toronto(1980). [2] 叶开沅、郭建虎,同上I.在任意定常温度场和任意分布载荷下的任意轴对称非均匀变厚度环形板的弯曲.兰州大学学报(自然科学版),力学专号,1(1979),75-114, [3] Timoshenko,S,and S,Woinowsky-Krieger,Theorp of Plates and Shells,McGraw-Hill Book Company.Inc.,New York(1959). -
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