LARGE DEFORMATION SOLUTION OF STIFFENED PLATES BY A MIXED FINITE ELEMENT METHOD

Abstract

Abstract: In the present paper, a finite element mixed variational functional and the iterative equations of the eccentric orthogonal stiffened plates are developed in accordance with nonlinear elasticity. By using an important technique the coupling coefficients of the two-dimensional coupling matrix are resolved into the known input data in the programming which is a three-dimensional coefficient matrix. The nonlinear equations are transformed into the instantaneous linear equations; and by using the conjugate gradient method the linear equations are solved. As a result, therefore, the calculation is enormously simplified, the precision manifested, and a satisfactory result obtained.

Key words: m-accretive operator, Ishikawa iterative sequence, uniformly smooth Banach space

Chen Yen-hang. LARGE DEFORMATION SOLUTION OF STIFFENED PLATES BY A MIXED FINITE ELEMENT METHOD. Applied Mathematics and Mechanics (English Edition), 1984, 5(1): 1121-1135 .

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References

(1) Murray, D. W., and E. L. Wilson, Finite element large deflection analysis of plates, J. Struct. Div. ASCE, 95 (1969).
(2) Walter, E. Haisler, Development and evaluation of solution procedures for geometrically nonlinear structural by the direct stiffness method, AIAA. J.4(1971),1-13.
(3) Fox, R. L., Development in structural analysis by direct energy minimzation,AIAA. J. Vol. 6, No. 6(1968).
(4) Liu Zhing-xing, FengTai-hua and Li Ding-xia, Solution of geometrical nonlinear problem of a stiffened plate and Shell by the finite element method, Journal of Nanjing Aeronautical Institute of China, No. 5, (1979). (in Chinese).
(5) Chang Fu-zong, Liu Ye-lang et al., Finite Element Analysis of Large Deformation and Post-buckling for Stiffened Plate, Science and Technology Material, No. 1,(1980). (Complied by No. 605 Research Institute, The Third Ministry of Machine-Building, People's Republic of China) (in Chinese).
(6) Novozhilov, V. V., Foundations of the Nonlinear Theory of Elasticity, (English version by F. Bagernihi, H. Komm, and W. Seidel). Rochester, New York: Graylock Press.(1953).
(7) Gass, N. and B. Tabarrod, Large Deformation analysis of plates and cylindrical shells by a mixed finite element method, Int. J. Num. Mesh, Eng. Vol.10, 711-746.
(8) Chen Yen-hang, A Quickly Convergent Rectangular Quasi-Conforming Plate Bending Element, Postgraduate Thesis of University of Science and Technology of China in 1981. (in Chinese).
(9) Feng Kang, Numerical Confuting Method, National Defence Industry Press of China,12 (1978). (in Chinese).
(10) Washizu, K., Variational Methods in Elasticity and Plasticity, Pergamon Press, (1968), 164.
(11) Oulemill, A. C., Pliable and Tough Plate and Shell, (Chinese version, tr. from Russian by Lu Yen-da et al.) Science Press, (1963).
(12) Timoshenko, S., and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1st ed. (1940), 2nd ed. (1959).

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