非均匀弹性地基圆薄板大挠度问题的一般解*
General Solution for Large Deflection Problems of Nonhomogeneous Circular Plates on Elastic Foundation
-
摘要: 本文在文[1]的基础上提出了一个新的方法可用于求解任意变系数非线性常微分方程组.文中导出了任意轴对称载荷和不同边界条件下的非均匀弹性地基圆薄板大变形的一般解,并给出了收敛于精确解的证明.问题最后可归结为求解一个仅含有三个未知量的非线性代数方程组.该方法和其它方法比较,具有收敛范围大,计算简便迅速等特点.文末给出算例表明内力和位移均可得到满意的结果,验证了本文理论的正确性.Abstract: In this paper,a new method is presented based on [1].It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients.By this method,the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived.The convergence of the solution is proved.Finally,it is only necessary to solve a set of nonlinear algebraic equations with three unknowns.The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resultants and displacements can be obtained by the present method.The correctness of the theory in this paper is confirmed.
-
Key words:
- nonhomogeneous circular plate /
- elastic foundation /
- large deformation
-
[1] 纪振义、叶开沅,任意变系数微分方程的精确解祈法,应用数悦和力学,10(10)(1989),747-757. [2] Von Kármán,Th.,Festigkeitsproblem im maschinenbau,Encycl.der Math.Wiss,4(1910),348-351. [3] Chien Wei-zang,Large deflection of a circular clamped plate,under uniform pressure,Chinese J.Phys.,7(1942),102-113. [4] 黄黔,复合载荷下圆荷板大挠度问题,应用数学和力学,4(5)(1983),771-720. [5] 陈山林、光积昌,圆薄板大挠度问题的摄动参数,应用数学和力学,2(1)(1981),731-144. [6] Keller,H.B.and E.L.Reiss,Iterative solutions for the nonlinear bending of circular plates.Comm.Pure Appl.Math.,Ⅺ(1985),273-293. [7] Way,S.,Bending of circular plate with large deflection,ASME Trans,J.Appl.Mech.,56(1934),627-636. [8] 叶开沅、郑晓静、王新志,On some properties and calculation of the exact solution to Kálrmáns equations of circular plate under a concentrated load,Proc.ICNM,Science Press,Shanghai(1985),379-385. [9] 叶开沅、郑晓静、周又和,and Zhou You-he,An analytical formula of exact solution to Kármán's equation of circular plate under a concentrated load,Proc.ICNM,Science Press,Shanghai(1985),386-391. [10] 郑晓静、周又和,复合载荷下圆薄阪大挠度问题的精确解,中国科学,A辑(10)(7986),7045-1056. [11] Nath,Y.,Large amplitude response of circular plates foundations,Int.J.Nonlinear Mech.,17,4(1982),285-296. [12] Bdton,R.,Stress in circular plate on elastic foundation,J.Eng.Mech.Div.Proc.ASCE,98,EM3(1972),629-640. [13] 郑晓静、周又和,集合载荷作用下弹性地基圆荷板大挠度问题的精确解,力学学报,20(2)(1988),161-172. [14] 陈至达.板壳有限变形分析,力学进展.13(2)(1983). [15] Ji Zhen-yi and Ych Kal-yuan,General solution on nonlinear buckling of nonhomogeneous axial symmetric ring-and stringer-stiffened cylindrical shell,Computer & structure,34,4(1990),585-591. [16] Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plate and Shell,McGraw-Hill Book Company,Second Edition(1959). [17] 郑晓静,《圆薄板大挠度理论及应用》.百林科学出版社(1990).
点击查看大图
计量
- 文章访问数: 1669
- HTML全文浏览量: 63
- PDF下载量: 556
- 被引次数: 0