Abstract
In this paper, the bicubic splines in product form are used to construct the multifield functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.
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References
H. Antes, Bicubic fundamental splines in plate bending.Int. J. Numer Meth. Engng.,8 (1974), 503–511.
Shih Chungtze, On spline finite element method,Math. Numer. Sinica,1 (1979), 50–72. (in Chinese)
T. Mizusawa, T. Kajita and M. Naruoka, Vibration of skew plates by using B-spline functions,J. Soumd Vibr.,62, 2 (1979), 301–308.
Y. K. Cheung, et al,The Spline Finite Strip Method in Structural Analysis, Guangzhou Press of Science and Technology (1985). (in Chinese)
R. Qin, Spline finite point method,Numerical Calculations and Computer Applications,2 (1980).
Shen Pengcheng, Huang Dade and Wang Zongmon, Static, vibration and stability analysis of stiffened plates using spline functions,Int. J. Computers & Structures,27, 1 (1987), 73–78.
Shen Pengcheng and Wang Jianguo, A semianalytical method for static analysis of shallow shells,Int. J. Computers & Structures,31, 5 (1989), 825–831.
Shen Pengcheng and Huang Dade, Dynamic analysis of stiffened plates and shells using spline Gauss collocation method.Int. J. Computers & Structures,36, 4 (1990), 623–629.
Shen Pengcheng and Huang Dade. Analysis of stiffened structures on foundation using spline Gauss collocation method,Second World Congress on Computational Meshanics. Stuttgart, Gemany, Aug. 27–31. 1990.Proc. Vol.2 (1990), 451–454.
Shen Pengcheng and H. B. Kan. The multivariable spline element analysis for plate bending problems,Int. J. Computers and Structures,40 (1992), 1343–1349.
Shen Pengcheng, Analysis of plates and beams on foundation by using spline finite element method.Int. Conf. on Computational Engineering Science, Aug. 12–16, 1991, Melbourne, Australia (1991).
Shen Pengcheng,The Spline Finite Element Method in Structural Analysis, Press of Hydraulic and Power Engineering, Beijing (1992). (in Chinese)
Shen Pengcheng and He Peixiang, Vibration analysis for plates using multivariable spline element method,Int. J. Solids & Structures,29, 24 (1992), 3289–3295.
Kyuichiro Washizu,Variational Method in Elasticity and Plasticity, second edition, Pergamon Press (1975).
F. Fujii and Hoshino, Discrete and non-discrete mixed methods applied to eigenvalue problems of plates,J. Sound and Vibration,87, 4 (1983), 525–534.
R. M. Prenter,Splines and Variational Methods, John Wiley and Sons, Inc. (1975).
Chien Weizang,Variational Method and Finite Elements, Science Press, Beijing (1980). (in Chinese)
Hu Haichang,Variational Principles in Elasticity and Applications, Science Press, Beijing (1981). (in Chinese)
S. Timoshenko and S. Woinowsky-Krieger,Theory of Plates and Shells, McGraw-Hill, New York (1959).
R. D. Blevins,Formulas for Natural Frequency and Mode Shape, Van Nostrand, Reinhold Co. (1979).
S. Timoshenko and J. N. Gere,Theory of Elastic Stability, McGraw-Hill (1961).
S. Watkin Divid, On the construction of conforming rectangular plate elements,Int. J. Numer. Meth. Engng.,10 (1976), 925–933.
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Communicated by Tang Limin
Project supported by the National Natural Science Foundation of China
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Pengcheng, S., Peixiang, H. Analysis of bending, vibration and stability for thin plate on elastic foundation by the multivariable spline element method. Appl Math Mech 18, 779–787 (1997). https://doi.org/10.1007/BF00763130
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DOI: https://doi.org/10.1007/BF00763130