Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series

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  •   Abdarrhim Mohammed Ahmed

  •   Saleh Y. Barony

Abstract

As Classical and Spline finite strip method based on stiffness and mixed variational formulation principle become important tool for continuum structural analysis , especially in the field of plate bending problems , a lot of researches has been focused on interpolation functions in order to improve the efficiency and increase the reliability of the method. The main objective of this paper is to introduce and propose a new spline interpolation function in the light of combination techniques of basic splines through introduction and brief review of previous studies in this field. This work which uses abbreviated form of augmented matrix proposed by authors published in past time , reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems.


Keywords: Combined Splines, Finite Strip Method, Mixed Formulation, Plate Bending, Spline Interpolation

References

Tham LG, Li WY, Cheung YK. Bending of skew plates by spline finite strip method. Computers and Structures 1986;22(1):31–38.

Li WY, Cheung YK, Tham LG. Spline finite strip analysis of general plates. J Engng Mech. Division ASCE 1986;112:43–54.

Shen P-C, Kan H-B. Multivariable spline element analysis for plate bending problems. Computers and Structures 1991;40:1343–1349.

Fan SC, Cheung YK. Flexural free vibrations of rectangular plates with complex support conditions. J Sound and Vibrations 1984;93(1):81–94.

Mizusana T, Kajita T, Naruoka M. Vibration of skew plates by B-spline functions. J Sound and Vibration 1979;155:301–308.

Mizusana T, Kajita T, Naruoka M. Buckling of skew plate structures using B-spline functions. Int J Num Meth Engng 1980;15:87–96.

Mizusana T, Leonard JW. Vibration and buckling of plates with mixed boundary conditions. Engng Struct 1990;12:285.

Ahmed, A. and Barony, S. 2019. Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending. European Journal of Engineering Research and Science. 4, 8 (Aug. 2019), 99-106. DOI:https://doi.org/10.24018/ejers.2019.4.8.1421.

Rudolph Szilard, Theories and Applications of Plate Analysis, Classical, Numerical and Engineering Methods, John Wiley & sons inc. 2004.

J. N. Reddy, Energy Principles & Variational Methods in Applied Mechanics, 2nd edition, John Wiley & sons inc. 2002.

L. R. Herrmann, Finite Element bending analysis for plates, Proc of ASCE,93,EM,Okt. 1967, pp. 13-26

Erwin Kreyszig, advanced engineering mathematics, 10th edition, 2011, ISBN 978-0-470-45836-5, John Wiley & Sons, Inc.

Y. K. Cheung, L. G. Tham, Finite Strip Method, CRC Press,1997

J.Schoenberg, contributions to the problem of approximation of equidistant by analytic functions,J. Q. appl. Math.,4. 45-99 and 112-114,1946.

De Boor, C.,”on calculating with B-splines”, J. approx. theory, vol. 6,1972, p.p. 50-62.

Dongxu Q. On the multiple-knot cardinal spline interpolation (I). J of Jilin University, China, in Chinese, Vol. 3, 1975.

Dongxu Q. On the multiple-knot cardinal spline interpolation (II). J of Jilin University, China, in Chinese, Vol. 6, 1975.

G. Sun, M. Kleeberger . The mixed strip method using combination splines for plate bending, Advances in Engineering Software, 1999, Elsevier

Stephen P. Timoshenko & S. Woinowsky-Krieger,Theory of Plates and Shell, 2nd edition, McGraw-Hill Inc.,1959.

J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, 2nd edition, CRC Press, Taylor & Francis Group. 2006.

Abdarrahim. M. Ahmed, " Numerical techniques for structural analysis with finite strip method”, Proc of 5th National conference for construction materials and structural engineering, Academy of graduate studies,Tripoli - Libya, 6-7/12/2010.(in Arabic).

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How to Cite
[1]
Ahmed, A. and Barony, S. 2019. Plate Bending Spline Finite Strip Models Using Mixed Formulation and Combined Spline Series. European Journal of Engineering Research and Science. 4, 10 (Oct. 2019), 42-51. DOI:https://doi.org/10.24018/ejers.2019.4.10.1489.