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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 30

Analysis of Laminates using the Element-Free Galerkin Method

J. Belinha+ and L.M.J.S. Dinis*

+Idmec, Institute of Mechanical Engineering, Porto Portugal
*Faculty of Engineering of the University of Oporto, FEUP, Porto, Portugal

Full Bibliographic Reference for this paper
J. Belinha, L.M.J.S. Dinis, "Analysis of Laminates using the Element-Free Galerkin Method", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 30, 2004. doi:10.4203/ccp.79.30
Keywords: meshless methods, element-free Galerkin method, laminates, first-order shear deformation theory, bending, shear-locking, plates, direct nodal integration.

Summary
A meshless method based in a Galerkin formulation, the Element-Free Galerkin Method (EFGM) [1] has been extended for the use in the analysis of anisotropic laminates. A Reissner-Mindlin laminate theory, which is a first-order shear deformation theory (FSDT) is considered in order to define the displacement field and the strain field.

The basic equations of the Reissner-Mindlin laminates theory are presented and a description of the approximation functions to be used in the variational form of the equilibrium equations is made. The approximation functions are calculated considering a moving least squares (MLS) approach which is consistent provided the basis is complete in the polynomials up to a desired order. The EFGM is briefly described together with an alternative integration method that avoids the consideration of background cells for integration purposes. Shear locking in plate bending is avoided considering the appropriate polynomials for the displacements and rotations which insure continuity. The new form of integration for the variational form presented improves the behaviour of the laminated plates in what concerns shear locking, this is relevant for thin laminates.

The main contributions of this communication are the new method to integrate the variational forms of the equilibrium equations and the fact that some of the polynomial approximations have not been considered before to simulate the behaviour of composite laminates.

Several problems of bending of laminates are solved considering various types of polynomials approximations and the obtained solutions are compared with available exact solutions and finite element solutions which show that the meshless approach considered is a good alternative to the finite element method for the solution of laminates bending problems.

References
1
Belytschko T., Lu Y.Y., Gu L., "Element Free Galerkin methods", Int. J. Num. Meth. Eng., 37:229-256, 1994. doi:10.1002/nme.1620370205

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