GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION

Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (11): 995-1007.

GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION

纪振义¹, 叶开沅²

1. Anhui Architectural Industry College, Hefei;
2. Lanzhou University, Lanzhou

收稿日期:1991-05-21 出版日期:1992-11-18 发布日期:1992-11-18
基金资助:
Project Supported by the National Natural Science Foundation of China

GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION

Ji Zhen-yi¹, Yeh Kai-yuan²

1. Anhui Architectural Industry College, Hefei;
2. Lanzhou University, Lanzhou

Received:1991-05-21 Online:1992-11-18 Published:1992-11-18
Supported by:
Project Supported by the National Natural Science Foundation of China

摘要/Abstract

摘要： 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.

关键词: nonhomogeneous circular plate, elastic foundation, large deformation

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

纪振义;叶开沅. GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(11): 995-1007.

Ji Zhen-yi;Yeh Kai-yuan. GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(11): 995-1007.

参考文献

[1] Ji Zhen-yi and Yeh Kai-yuan, An exact analytic method for solving arbitrary variable coefficient differential equation, Applied Mathematics and Mechanics, 10, 10(1989), 885-896.
[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] Hwang Chien, Large Deflection of circular plate under compound load, Applied Mathematics and Mechanics, 4,5(1983), 711-720.
[5] Chen Shan-lin and Guang Ji-chang, The perturbation parameter in the problem of large deflection of clamped circular plates, Applied Mathematics and Mechanics, 4,5(1983),711-720.
[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] Yeh Kai-yuan, Zheng Xiao-jing and Wang Xin-zhi, 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] Yeh Kai-yuan, Zheng Xiao-jing 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] Zheng Xiao-jing and Zhou You-he, On the exact solution to large deflection problem of circular plate under compound load, Scientia sinca, Series A, 10(1986), 1045-1056.
[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] Zheng Xiao-jing and Zhou You-he. On the exact solution to large deflection problem of circular plate on elastic foundation under a concentrated load, Acta Mechanics Sinica, 20, 2(1988). 161-172.
[14] Chen Zhi-da, Nonlinear analysis of large deformation of plates and shells, Advances in Mechanics. 13, 2(1983), 119-124.(in Chinese).
[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] Zheng Xiao-jing, The Theory and Application for Large Deflection of Circular Plate, Jilin Science Technology Press,(1990).(in Chinese).

GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION

GENERAL SOLUTION FOR LARGE DEFLECTION PROBLEMS OF NONHOMOGENEOUS CIRCULAR PLATES ON ELASTIC FOUNDATION

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