Abstract
A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper. The method is completely general with respect to various boundary conditions, load cases and shapes of plates. This difference scheme is simple and the numerical results agree well with those obtained by other methods.
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References
Wu Chang-chun, A new method for numerical analysis of plates—the discrete operator method,Chinese Science,4 (1975).
Liszha, T. and J. Qrkisz, The FDM at arbitrary irregular grids and its applications in applied mechanics,Compt. Struct.,11, (1980).
Lau, P.C., Carvilinear FDM for biharmonic equations,Int. J. NME,14 (1979).
Buragohairr, D.N., and S.C. Patodi, Large deflection analysis of plates and shells by discrete energy method,Comput. Struct.,9 (1978).
Pavlin, V. and N. Perone, Finite difference energy techniques for arbitrary meshes applied to linear plate problems,Int. J. NME.,14, 5 (1979).
Atkatsh, R. S., and M. L. Baron, A finite difference variational method for bending of plates,Comput. Struct.,11, 6 (1980).
Barue, V. D. and S. S. Dey, Isoparametric difference energy method for plate bending problems,Comput. Struct.,17, 3 (1983).
Liu Xiao-ming, The FDM for irregular grids with its application in structural analysis, Ph. D. Thesis, Hehai University (1988). (in Chinese)
Yeh Kai-yuan et al., The general solution of elastic mechanics with variable thickness,J. of Lanzhou University, 1 (1979). (in Chinese)
Yeh Kai-yuan et al., Bending problem of rectangular plate with variable thickness under the action of arbitrary distributed loading,Applied Mathematics and Mechanics,7, 10 (1986).
Timoshenko, S.P.,Theory of Plates and Shells, McGraw-Hill (1959).
Fang Jia-ran, Rectangular plate with variable thickness,Shanghai Mechanics,3, 1 (1982). (in Chinese)
Yun Shi-ming, Navier solution of elastic equilibrium problem of Rectangular plate with variable thickness using linear and non-linear theory,Applied Mathematics and Mechanics,6, 6 (1985).
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Communicated by Xu Ci-da
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Guang-yao, L., Han-bin, Z. A finite difference method at arbitrary meshes for the bending of plates with variable thickness. Appl Math Mech 14, 299–304 (1993). https://doi.org/10.1007/BF02451414
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DOI: https://doi.org/10.1007/BF02451414