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Application of Spline Collocation Method in Analysis of Beam and Continuous Beam

Published online by Cambridge University Press:  05 May 2011

Lai-Yun Wu  and
Yang-Tzung Chen
Lai-Yun Wu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Yang-Tzung Chen*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Associate Professor
** Graduate Student
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Abstract

In this paper, spline collocation method (SCM) is successfully extended to solve the generalized problems of beam structures. The spline functions in SCM are re-formulated by finite difference method in a systematical way that is easily understood by engineers. The manipulation of SCM is further simplified by the introduction of quintic table so that the matrix-vector governing equation can be easily formulated to solve the weighting coefficients. SCM is first examined by the problems of a generalized single-span beam undergoing various types of loadings and boundary conditions, and it is then extended to the problems of continuous beam with multiple spans. By comparing with available analytical results, differential quadrature method (DQM), if any, excellent accuracy in deflection is achieved.

Keywords

Spline collocation methodSpline functionsFinite difference methodQuintic tableContinuous beamDifferential quadratic method
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 2 , June 2003 , pp. 319 - 326
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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References

REFERENCES

1Bellman, R., Kashef, B. and Casti, J., “Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equations,” J. Computational Phys., 10, pp. 40–52 (1972).CrossRefGoogle Scholar
2Jang, S. K., Bert, C. W. and Striz, A. G., “Application of Differential Quadrature to Static Analysis of Structural Components,” Int. J. Numerical Methods in Engrg., 28, pp. 561–577 (1989).CrossRefGoogle Scholar
3Chen, C. N., “Vibration of Prismatic Beam on an Elastic Foundation by the Differential Quadrature Element Method,” Computers and Structures, 77, pp. 1–9 (2000).CrossRefGoogle Scholar
4Wang, X. and Bert, C. W., “A New Approach in Applying Differential Quadrature to Static and Free Vibrational Analysis of Beams and Plates,” J. Sound and Vibration, 162(3), pp. 566–572 (1993).CrossRefGoogle Scholar
5Bert, Charles W. and Sheu, Youngkwang, “Static Analyses of Beams and Plates by Spline Collocation Method,” Journal of Engineering Mechanics, 122(4), pp. 375–378 (1996).CrossRefGoogle Scholar
6Prenter, P. M., “Splines and Variational Methods,” John Wiley & Sons, Inc., New York, N. Y. (1975).Google Scholar
7Chen, Y. T., “Study of Structural Analysis by Using SCM,” Master Thesis, Department of Civil Engineering, National Taiwan University, Taiwan (2001).Google Scholar