Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T16:56:31.441Z Has data issue: false hasContentIssue false
  • English
  • Français

Bending Analysis of Thin Plates with Variable Thickness Resting on Elastic Foundation by Element Free Galerkin Method

Published online by Cambridge University Press:  09 August 2012

Ahmad Rahbar-Ranji  and
E. Bahmyari
Ahmad Rahbar-Ranji*
Affiliation:
Department of Ocean Engineering, Amirkabir University of Technology, Iran
E. Bahmyari
Affiliation:
Department of Ocean Engineering, Amirkabir University of Technology, Iran
*
*Corresponding author (rahbar@aut.ac.ir)
Get access

Abstract

Element Free Galerkin method was used to analyze bending of thin plates with variable thickness resting on one parameter elastic foundation. Thickness of plate is considered as linearly varying in one direction. Formulation could be applied to plates of any shape with general boundary conditions and loadings. Convergence of solution was examined for different number of nodes, thickness variation and foundation parameters. It was found that for deflection good results were achieved even with small number of nodes regardless of boundary condition, thickness variation and foundation parameters. Accuracy of method is checked against available results and good agreements were found. Applicability of method is demonstrated by solving numerical examples with different boundary conditions, thickness and foundation parameters, and loadings.

Keywords

Element free galerkin methodThin plateVariable thicknessElastic foundation
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 479 - 488
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Svec, O. J., “Thick Plates on Elastic Foundation by Finite Elements,” Journal of Engineering Mechanics, 102, pp. 461–477 (1976).Google Scholar
2. Ng, S. F. and Chan, M. Y., “Solution of Some Boundary Value Problems in Applied Mechanics by Collocation Least Square Method,” Computer Methods in Applied Mechanics and Engineering, 11, pp. 137–150 (1977).CrossRefGoogle Scholar
3. Ng, S. F. and Das, B., “Finite Deflection of Skew Sandwich Plates on Elastic Foundation by the Galerkin Method,” Journal of Structures Mechanics, 14, pp. 355–77 (1986).CrossRefGoogle Scholar
4. Kobayashi, H. and Sonoda, K., “Rectangular Mindlin Plates on Elastic Foundation,” International Journal of Mechanics Science, 31, pp. 679–692 (1989).CrossRefGoogle Scholar
5. Qin, Q. H., “Hybrid—Treffiz Finite Element Approach for Plate Bending on an Elastic Foundation,” Applied Mathematical Modelling, 18, pp. 334–339 (1994).CrossRefGoogle Scholar
6. Qin, Q. H., “Hybrid—Treffiz Finite Element Method for Reissner Plates on an Elastic Foundation,” Computer Methods in Applied Mechanics and Engineering, 122, pp. 379–92 (1995).CrossRefGoogle Scholar
7. Han, J. B. and Liew, K. M., “Numerical Differential Quadrature Method for Reissner/ Mindlin Plates on Two-Parameter Foundations,” International Journal of Mechanics Science, pp. 977–989 (1997).CrossRefGoogle Scholar
8. Costa, J. A. and Brebbia, C. A., “The Boundary Element Method Applied to Plates on Elastic Foundations,” Engineerging Analysis, 2, pp. 174–183 (1985).CrossRefGoogle Scholar
9. Katsikadelis, J. T. and Kallivokas, L. F., “Clamped Plates on Pasternak-Type Elastic Foundation by the Boundary Element Method,” Journal of Applied Mechanics, 53, pp. 909–917 (1986).CrossRefGoogle Scholar
10. Benzine, G., “A New Boundary Element Method for Bending of Plates on Elastic Foundations,” International Journal of Solids and Structures, 24, pp. 557–565 (1988).CrossRefGoogle Scholar
11. El-Zafrany, A., Fadhil, S. and Al-Hosani, K., “A New Fundamental Solution for Boundary Element Analysis of Thin Plates on Winkler Foundation,” International Journal for Numerical Methods in Engineering, 38, pp. 887–903 (1995).CrossRefGoogle Scholar
12. Chucheepsakul, S. and Chinnaboon, B., “An Alternative Domain/ Boundary Element Technique for Analyzing Plates on Two-Parameter Elastic Foundations,” Engineering Analysis with Boundary Elements, 26, pp. 547–555 (2002).CrossRefGoogle Scholar
13. Chucheepsakul, S. and Chinnaboon, B., “A Boundary Element Technique for Analyzing Plates on Two-Parameter Elastic Foundations with Nonlinear Boundary Conditions,” Computers & Structures, 81, pp. 2739–2748 (2003).CrossRefGoogle Scholar
14. Monaghan, J. J., “An Introduction to SPH,” Computational Physics Communications, 48, pp. 89–96 (1988).CrossRefGoogle Scholar
15. Atluri, S. N. and Zhu, T., “A New Meshless Local Petrov—Galerkin (MLPG) Approach in Computational Mechanics,” Computational Mechanics, 22, pp. 117–127 (1998).CrossRefGoogle Scholar
16. Liu, W. K., Jun, S. and Zhang, Y. F., “Reproducing Kernel Particle Methods,” International Journal of Numerical Methods in Engineering, 20, pp. 1081–1106 (1995).CrossRefGoogle Scholar
17. Belytschko, T., Lu, Y. Y. and Gu, L., “Element-Free Galerkin Methods,” International Journal of Numerical Methods in Engineering, 37, pp. 229–256 (1994).CrossRefGoogle Scholar
18. Chen, X. L., Liu, G. R. and Lim, S. P., “An Element Free Galerkin Method for the Free Vibration Analysis of Composite Laminates of Complicated Shape,” Composite Structures, 59, pp. 279–289 (2003).CrossRefGoogle Scholar
19. Dai, K. Y., Liu, G. R., Lim, K. M. and Chen, X. L., “A Mesh-Free Method for Static and Free Vibration Analysis of Shear Deformable Laminated Composite Plates,” Journal of Sound and Vibration, 269, pp. 633–652 (2004).CrossRefGoogle Scholar
20. Belinha, J. and Dinis, L. M. J. S., “A Mesh-Free Method for Static and Free Vibration Analysis of Shear Deformable Laminated Composite Plates,” Journal of Sound and Vibration, 269, pp. 633–652 (2004).Google Scholar
21. Liu, G. R. and Gu, Y. T., “A Local Radial Point Interpolation Method (LRPIM) for Free Vibration Analyses of 2-D Solids,” Journal of Sound and Vibration, 246, pp. 29–46 (2001).CrossRefGoogle Scholar
22. Liu, G. R. and Wang, J. G., “A Point Interpolation Meshless Method Based on Radial Basis Functions,” International Journal of Numerical Methods in Engineering, 54, pp. 1623–1648 (2002).Google Scholar
23. Chen, J. T., Chen, I. L., Chen, K. H., Yeh, Y. T. and Lee, Y. T., “A Meshless Method for Free Vibration of Arbitrarily Shaped Plates with Clamped Boundaries Using Radial Basis Function,” Engineering Analysis with Boundary Elements, 28, pp. 535–545 (2004).CrossRefGoogle Scholar
24. Chen, J. T., Lee, Y. T., Chen, I. L. and Chen, K. H., “Mathematical Analysis and Treatment for the True and Spurious Eigenequations of Circular Plates in the Meshless Method Using Radial Basis Function,” Journal of Chinese Institute of Engineers, 27, pp. 547–561 (2004).CrossRefGoogle Scholar
25. Sladek, J., Sladek, V. and Mang, H. A., “Meshless Local Boundary Integral Equation Method for Simply Supported and Clamped Plates Resting on Elastic Foundation,” Computer Methods in Applied Mechanics and Engineering, 191, pp. 5943–5959 (2002).CrossRefGoogle Scholar
26. Chinnaboon, B., Katsikadelis, J. T. and Chucheepsakul, S., “A BEM-Based Meshless Method for Plates on Biparametric Elastic Foundation with Internal Supports,” Computer Methods in Applied Mechanics and Engineering, 196, pp. 3165–3177 (2007).CrossRefGoogle Scholar
27. Zhuojiam, F., Wen, C. and Wei, Y., “Winkler Plate Bending Problems by a Truly Boundary Only Boundary Particle Method,” Computational Mechanics, 44, pp. 757–763 (2009).Google Scholar
28. Ferreira, A. J. M., Roque, C. M. C., Neves, A. M. A., Jorge, R. M. N. and Soares, C. M. M., “Analysis of Plates on Pasternak Foundations by Radial Basis Functions,” Computational Mechanics, 46, pp. 791–803 (2010).CrossRefGoogle Scholar
29. Katsikadelis, J. T. and Yiotis, A. J., “The BEM for Plates of Variable Thickness on Nonlinear Bi-parametric Elastic Foundation: An Analog Equation Solution,” Journal of Engineering Mathematics, 46, pp. 313–330 (2003).CrossRefGoogle Scholar
30. Dolbow, J. and Belytschko, T., “An Introduction to Programming the Meshless Element Free Galerkin Method,” Archives of Computational Methods in Engineering, 5, pp. 207–241 (1998).CrossRefGoogle Scholar
31. Liu, G. R. and Yang, K. Y., “A Penalty Method for Enforcing Essential Boundary Conditions in Element Free Galerkin Method,” The Proceeding of the 3rd HPC Asia′98 Singapore, pp. 715–721 (1998).Google Scholar
32. Hegen, D., “Element-Free Galerkin Methods in Combination with Finite Element Approaches,” Computer Methods in Applied Mechanics and Engineering, 135, pp. 143–166 (1996).CrossRefGoogle Scholar
33. Liu, G. R. and Gu, Y. T., “Coupling of Element Free Galerkin and Hybrid Boundary Element Methods Using Modified Variational Formulation,” Computational Mechanics, 26, pp. 166–173 (2000).CrossRefGoogle Scholar
34. Krysl, P. and Belytschko, T., “Analysis of Thin Plates by the Element-Free Galerkin Method,” Computational Mechanics, 17, pp. 26–35 (1995).CrossRefGoogle Scholar
35. Liu, G. R., Mesh Free Methods: Moving Beyond the Finite Element Method, New York: CRC Press, 2002.CrossRefGoogle Scholar
36. Petrian, P. and Conway, H. D., “Deflection and Moment Data for Rectangular Plates of Variable Thickness,” Journal of Applied Mechanics Series E, 39, pp. 814–815 (1972).CrossRefGoogle Scholar