Nonlinear bending analysis of composite plates using mesh free method and Legendre basis functions

Document Type : Research Paper

Authors

Abstract

Nonlinear bending analysis of thin rectangular composite plates with arbitrary boundary conditions requires the use of numerical methods. One of the most common numerical methods in recent decades is meshfree collocation method with legendre basis functions. The meshfree method means that does not require the generation of meshes as in the finite element method, but only requires a scattered set of nodes to descretize the domain of interest. The nodes used in the present research are legendre-gauss-lobatto points. Classical laminated plate theory is used for developing equilibrium equations that it produces acceptable results for thin plates. In this paper, the equilibrium equations are solved directly by substituting the displacement fields with equivalent finite legendre polynomials. Equations system is obtained by discretizing the equilibrium equations and boundary conditions with finite legendre polynomials. Nonlinear terms are caused by the product of variables in the equilibrium equations and the nonlinear set of equations is solved by Newton-Raphson technique. Since the number of equations is always more than the number of unknown parameters, the least square technique is used to solve the system of equations. Some results for composite plates with different boundary conditions are computed and compared with those available in the literature, wherever possible.

Keywords

Main Subjects

References

[1] J. N. Reddy, Mechanics of Laminated Composite Plates and Shells Theory and Analysis, CRC Press, 2003.
[2] J. Pagano, Exact Solution for Rectangle Bidirectional Composites and Sandwich Plates, Journal of Composites Materials, Vol. 4, No. 1, pp. 20-34, 1970.
[3] S. Sirinivas, A. K. Rao, Bending, Vibration and Buckling of Simply Supported Thick Orthotropic Rectangular Plates and Laminates, International Journal of Solids and Structures, Vol. 6, No. 11, pp. 1463-1481, 1970.
[4] N. J. Pango, S. J Hatfield, Elastic Behaviour of Multilayerd Bidirectional Composites, AIAA Journal, Vol. 10, No. 7, pp. 931-933, 1972.
[5] K. K. Shukla, Y. Nath, Nonlinear Analysis of Moderately Thick Laminated Rectangular Plates, Journal of  Engineering Mechanics ASCE, Vol. 126, No. 8, pp. 831-839, 2000.
[6] J. s. Chang, Y. P. Huang, Geometrically Nonlinear and Transiently Dynamic Behaviour of Laminated Composite Plates Based on a Higher Order Displacement Field, Composite Structures, Vol. 18, No. 4, pp. 327-364, 1991.
[7] P. Yang, C. Noris, Y Stavsky, Elastic Wave Propagation in Heterogeneous Plates, International Journal of Solids and Structures, Vol. 2, No. 4, pp. 665-684, 1991.
[8] J. Whitney, N Pagano, Shear Deformation in Heterogeneous Anisotropic Plates, Journal of Applied Mechanics, Vol. 37, No. 4, pp. 1031-1036, 1970.
[9] E .J Kansa, Multiquarics Scattered Data Approximation with Applications to Computational Fluid Dynamics, Surface Approximations and Partial Derivative Estimates, Computers and Mathematics.with  Applications, Vol. 19, No. 8-9, pp. 127-145, 1990.
[10] K. M. Liew, Zhao, Xin, Ferrira, J. M. Antonio, A Review of Meshless Method for Laminated and Functionally Graded Plates and Shells, Composite Structures, Vol. 93, No. 8, pp. 2031-2041, 2011.
[11] J. N Reddy, An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, 2004.
[12] Jeoot Singh., K. K. Shukla, Nonlinear Flexural of Laminated Composite Plates Using RBF Based Meshless Method, Composite. Structures, Vol. 94, No. 5, pp. 1714-1720, 2012.

Files

Share

How to cite

Statistics