Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

##plugins.themes.bootstrap3.article.main##

  •   Abdarrhim Mohammed Ahmed

  •   Saleh Y. Barony

Abstract

Although Spline finite strip method for the analysis of plate bending based on a mixed variational formulation principle , using a variety B-Spline series as interpolation function  was widely used in researches , the explicit form of the Augmented Matrix  nowhere  given. This leads to some difficulties concerning the verification and understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size through a detailed review of the mixed formulation for different spline finite strip models. The derived matrix will be helpful subject of research future work  as it is examined by the time, reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems as the reader can verified.


 


Keywords: B-Spline Interpolation, Finite Strip Method, Mixed Formulation, Plate Bending

References

Richards T. H., Energy methods in stress analysis, New York: John Wily & Sons, 1977.

J. N. Reddy, An Introduction to the Finite Element Method, 2nd edition, McGraw-Hill Inc. 1993.

J. N. Reddy and Chen-Shyh-Tsay, “Mixed Rectangular Finite Element for Plate Bending”, Proc. Okla. Acad. Sci. 57:144-148,1977

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

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

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

Riesenfeld, R., Application of B-spline approximation to geometric problems of computer-aided design, University of Utah computer Science Report UTEC-CSC-73-126.

James M. McKee, “B-Spline functions as solution to some knotty geometric modeling problems”, Proceedings of the symposium on: Applications of computer methods in engineering, sponsored by: school of engineering, university of southern California, vol. II,1977, CALIFORNIA.

Y. K. Cheung, L. G. Tham,Mixed formulation of finite strip method, J Engng Mech. Division ASCE 1982;108(EM2):452-456.

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

Lavy Y, Bar-Yoseph P, Rosenhouse G, “Mixed-hybrid finite strip method for folded plate structure”, Int. J. computers and structures,1992;42(3):433-446.

Z. M. Elias, “Mixed Finite Element Methods for axisymmetric shells”, Int. J. num. Meth. Engng, 4, 261-277(1972).

Saleh. Y. Barony & H. Tottenham, “The analysis of rotational shells using a curved ring element and mixed variational formulation”, Inter. Journal for Numerical methods in Engineering,Vol. 10. 861-872,1976.

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

Abdarrhim M. Ahmed, “Numerical analysis of Plate Bending Based on Stiffness & Mixed Formulation Using Trigonometric & Spline Functions”, MSc. Thesis, 2007, Supervised by Prof. Saleh Y. Barony, University of AL-Fateh, Libya

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

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

Abdarrhim M. Ahmed, Saleh Y. Barony, “Stiffness formulation of spline finite strip method for plate bending”, 13th Arab Structural Engineering Conference, University of Blida 1, December 13-15, 2015, ALGERIA

O. C. Zienkiewicz & R. L. Taylor, The Finite Element Method, Volume 2, 5th edition, Butterworth-Heinemann, 2000.

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

Y. K. Cheung, Fan and Wu, ”Spline finite strip in structural analysis”, Proceedings, The international conference on finite element method, Shanghai, 704-709. in 1982

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

Downloads

Download data is not yet available.

##plugins.themes.bootstrap3.article.details##

How to Cite
[1]
Ahmed, A. and Barony, S. 2019. Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending. European Journal of Engineering and Technology Research. 4, 8 (Aug. 2019), 99-106. DOI:https://doi.org/10.24018/ejers.2019.4.8.1421.