Yin Si-ming, Ruan Sheng-huang. Navier Solution for the Elastic Equilibrium Problems of Rectangular Thin Plates with Variable Thickness in Linear and Nonlinear Theories[J]. Applied Mathematics and Mechanics, 1985, 6(6): 519-530.
 Citation: Yin Si-ming, Ruan Sheng-huang. Navier Solution for the Elastic Equilibrium Problems of Rectangular Thin Plates with Variable Thickness in Linear and Nonlinear Theories[J]. Applied Mathematics and Mechanics, 1985, 6(6): 519-530.

# Navier Solution for the Elastic Equilibrium Problems of Rectangular Thin Plates with Variable Thickness in Linear and Nonlinear Theories

• Publish Date: 1985-06-15
• This paper discusses the elastic equilibrium problems of rectangular thin plates of varying thickness and simply supported on all four sides by linear and nonlinear theory, using the Navier method to seek an approach to the problem, and illustrates the solution with two examples. In conclusion, mention is made of scope of application and the convergency of the solution.
•  [1] 叶开沅等,非均匀变厚度弹性体勺学的若干问题的一般解(Ⅱ、任意分布荷载下两对边简支单向非均匀变厚度矩形板的弯曲问题),兰州大学学报(自然科学学报,力学专号,No1) (1979). [2] 中国科学院数学研究听力学研究室.《弹连圆薄板大挠度问题》,中国科学院出版(1954). [3] 范家让,变厚度矩形板,上海力学,3, 1 (1982). [4] Timoslienko, S, and S.Woinowsky-Krieger, Theory of Plates and Shells (second edition) (1959).(中译本.《板壳理论》,《板壳理论》翻译组译(1977)). [5] 张福范,《弹性薄板》,科学出版社(1963). [6] 诺瓦茨基,W.,《弹性薄板及薄壳的研究》,科学出版社(1956). [7] Воломир А.С.,Гuбкuе Пласmuнкu u Оболочекu,Гостехиздат москва(1956).(中译本,《柔韧板与柔韧壳》,卢文达等译(1959)). [8] 何广乾、陈伏,确定矩形底四边简支或滑动固支扁壳在任意法向荷载作用下应力函数边界值φr的计算公式,力学学报,5. 3 (1962). [9] 尹思明,正交各向异性变截而双曲扁壳非线性理论的弹性平衡问题,内部资料(1965.3). [10] Ониашбили О.Д.,Некоmорые Дuнамuческuе Забчu Теорuu Оболочек,Изд.АНСССР(1957).

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