Analysis of Thin Isotropic and Orthotropic Plates with Element-Free Galerkin Method and Various Geometric Shapes
Authors
Abstract
Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG) is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.
Keywords
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19. Autar K. K., Mechanics of Composite Materials, 2rd ed., CRC Press, Taylor & Francis Group, 2006.
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26. Reddy, J. N., Mechanics of Laminated Composite Plates and shell theory and analysis, 2rd ed., CRC Press, 2003.
27. Sridhar, C., and Rao, K. P., “Large Deformation Finite Element Analysis of Laminated Circular Composite Plates”, Computers and Structures, Vol. 54, pp. 59-64, 1994.
2. Szafrana, Z., “Elastic Analysis of Thin Fiber-Reinforced Plates”, Civil and Environmental Engineering Reports, Vol. 1, 2005.
3. Colagrossi, A., and Landrini, M., “Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics”, Journal of Computational Physics, Vol. 191, No. 2, pp. 448-475, 2003.
4. Johnson, G. R, Stryk, R. A., and Beissel, S. R., “SPH for High Velocity Impact Computations”, Computer Methods in Applied Mechanics and Engineering, Vol. 139, No. 1-4, pp. 347-373, 1996.
5. Liu, W. K., Jun, S., Li. S., Adee, J., and Belytschko, T., “Reproducing Kernel Particle Method For Structural Dynamics”, International Jornal for Numerical Methods in Engineering, Vol. 38: pp. 1655-1679, 1995.
6. Liu, W. K., Jun, S., Zhang, Y. F., “Reproducing Kernel Particle Methods”, International Jornal for Numerical Methods in Fluids, Vol. 20: pp. 1081-1106, 1995.
7. Krysl, P., and Belytschko,T., “Analysis of Thin Plates by the Element-Free Galerkin Method”, Computational Mechanics, Vol. 17, pp. 25-36, 1996.
8. Ouatouati, A. E., and Johnson, D. A., “A New Approach for Numerical Modal Analysis Using the Elementfree Method”, International Jornal for Numerical Methods in Engineering, Vol. 46, pp. 1-27, 1999.
9. Liu, G. R., and Chen, X. L, “Bucking of Symmetrically Laminated Composite Plates Using the Element-Free Galerkin Method”, International Journal of Structural Stability and Dynamics, Vol. 2, No. 3, pp. 281-294, 2002.
10. 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, Vol. 59, No. 2, pp 279-289, 2003.
11. Memar Ardestani, M., Soltani, B., and Shams, Sh., “Analysis of Functionally Graded Stiffened Plates Based on FSDT utilizing Reproducing Kernel Particle Method”, Composite Structures, Vol. 112, pp. 231-240, 2014.
12. Sladek, J., Sladek, V., Stanak, P., Zhang, Ch., and Wünsche, M., “Analysis of the Bending of Circular Piezoelectric Plates with Functionally Graded Material Properties by a MLPG Method”, Engineering Structures, Vol. 47, pp. 81-89, 2013.
13. Liew, K. M., Zhao, X. and. Ferreira, A. J. M., “A Review Of Meshless Methods For Laminated And Functionally Graded Plates and Shells”, Composite Structures, Vol. 93, No. 8, pp. 2031-2041 .2011.
14. Ghasemi, M. R., and Behshad, A., “An Element-FreeGalerkin-Based Multi-Objective Optimization of Laminated Composite Plates”, Journal of Optimization Theory and Applications, Vol. 156, No. 2, pp. 330-344, 2012.
15. Jaberzadeh, E., Azhari. M, and Boroomand. B., “Inelastic Buckling of Skew and Rhombic Thin Thickness-Tapered Plates with and without Intermediate Supports Using the Element-Free Galerkin Method”, Applied Mathematical Modelling, Vol. 37, No. 10-11, pp. 6838-6854, 2013.
16. Jaberzadeh, E., Azhari, M., and Boroomand, B., “Thermal Buckling of Functionally Graded Skew and Trapezoidal Plates with Different Boundary Conditions Using the Element-Free Galerkin Method”, European Journal of Mechanics- A/Solids, Vol. 42, pp. 18-26, 2013.
17. Lancaster, P., and Salkauskas. K, “Surfaces Generated by Moving Least Squares Methods”, Mathematics of Computation, Vol. 37, pp. 141-158, 1981
18. Krysl, P., and Belytschko, T., “Analysis of Thin Plates by the Element-Free Galerkin Method”, Computational Mechanics, Vol. 17, pp. 26-35, 1996.
19. Autar K. K., Mechanics of Composite Materials, 2rd ed., CRC Press, Taylor & Francis Group, 2006.
20. Belytschko, T., Lu, Y Y., and Gu, L., “Element-Free Galerkin Method”, International Journal of Numerical Method in Engineering, Vol. 37, pp. 229-256, 1994.
21. Shu, C., Differential Quadrature and its Application in Engineering, Springer, 2000:
23. Liu, G. R., Meshfree Methods Moving Beyond the Finite Element Method, CRC Press, 2002.
24. Timoshenko, S., Theory of plates and shells, 2rd ed. McGRAW-HILL Book Company ,1959.
25. Zienkiewicz, O. C., and Taylor, R. L., The Finite Element Method, 4rd ed. Vol. 2. Taylor, 1989.
26. Reddy, J. N., Mechanics of Laminated Composite Plates and shell theory and analysis, 2rd ed., CRC Press, 2003.
27. Sridhar, C., and Rao, K. P., “Large Deformation Finite Element Analysis of Laminated Circular Composite Plates”, Computers and Structures, Vol. 54, pp. 59-64, 1994.
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