Computational Technology Resources - CCP

Keywords: meshless method, EFG, equilibrium model.

Summary

The equilibrium approach with using the element free Galerkin method [1] is presented in this paper. Together, a scaling parameter study

is carried out so as to better understand the effects of the interpolation domain size on the quality of the results.

We used the Lagrange multipliers to impose the essential boundary conditions and used the moving least squares method to approximate the stress fields from an Airy stress function. These comparison show that the accuracy and agreement of the two models. Nevertheless, our aim was not to replace the classical displacement model with the equilibrium model but rather to obtain a global error estimator based upon the combination of both models.

Furthermore, in the equilibrium model, for most of the values of took from 2.5 to 4.0 gave good results. The size of the support should be sufficiently large so that the moment matrix is regular and well conditioned and that the spatial distribution of neighbours is fairly even. On the other hand, selecting domains of influence that are too large leads to a great deal of computational expense in forming the approximations as well as assembling the stiffness matrix. Support sizes that are too large also detract from the local character of the approximation, for problems involving sharp gradients; some loss of accuracy is typically noted as the effect of the gradient is smeared. This model seems to need more nodes inside the support domain than the displacement model. However, as in Duflot et al. [2], the advantage is that there is only one degree of freedom associated with each node while in the traditional method; the number of degree of freedom for each node is equal to the number of space dimensions.

The method was illustrated in two-dimensional elasticity but it can be extended to other complex problems, to see Duflot et al. [2,3] in details. As the first step we will apply for three-dimension problem, thin plate problems and fracture mechanics problems, where the meshless method has proved to be particularly efficient.

References

1: T. Belytschko, Y.Y. Lu and L. Gu. "Element-free Galerkin method", International Journal for Numerical Methods in Engineering; 37:229-256, 1994. doi:10.1002/nme.1620370205
2: M. Duflot and N.D. Hung. "Dual analysis by a meshless method", International Journal for Numerical Methods in Engineering, 2002.
3: M. Duflot and N.D. Hung. "Global error estimation with displacement and equilibrium meshless method", Computational mechanics WCCM VI in conjunction with APCOM'04, Sept. 5-10, Beijing, China, 2004.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)

	Computational & Technology Resources an online resource for computational, engineering & technology publications
	not logged in - login
Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 83 PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro Paper 177 An Equilibrium Model in the Element Free Galerkin Method B.Q. Tinh¹ and H. Nguyen-Dang² ¹Department of Computational Mechanics, University of Natural Science, Ho Chi Minh City, Vietnam ²LTAS, Department of Fracture Mechanics, Institute of Mechanics and Civil Engineering, Liège, Belgium doi:10.4203/ccp.83.177 purchase the full-text of this paper Full Bibliographic Reference for this paper B.Q. Tinh, H. Nguyen-Dang, "An Equilibrium Model in the Element Free Galerkin Method", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 177, 2006. doi:10.4203/ccp.83.177 Keywords: meshless method, EFG, equilibrium model. Summary The equilibrium approach with using the element free Galerkin method [1] is presented in this paper. Together, a scaling parameter study is carried out so as to better understand the effects of the interpolation domain size on the quality of the results. We used the Lagrange multipliers to impose the essential boundary conditions and used the moving least squares method to approximate the stress fields from an Airy stress function. These comparison show that the accuracy and agreement of the two models. Nevertheless, our aim was not to replace the classical displacement model with the equilibrium model but rather to obtain a global error estimator based upon the combination of both models. Furthermore, in the equilibrium model, for most of the values of took from 2.5 to 4.0 gave good results. The size of the support should be sufficiently large so that the moment matrix is regular and well conditioned and that the spatial distribution of neighbours is fairly even. On the other hand, selecting domains of influence that are too large leads to a great deal of computational expense in forming the approximations as well as assembling the stiffness matrix. Support sizes that are too large also detract from the local character of the approximation, for problems involving sharp gradients; some loss of accuracy is typically noted as the effect of the gradient is smeared. This model seems to need more nodes inside the support domain than the displacement model. However, as in Duflot et al. [2], the advantage is that there is only one degree of freedom associated with each node while in the traditional method; the number of degree of freedom for each node is equal to the number of space dimensions. The method was illustrated in two-dimensional elasticity but it can be extended to other complex problems, to see Duflot et al. [2,3] in details. As the first step we will apply for three-dimension problem, thin plate problems and fracture mechanics problems, where the meshless method has proved to be particularly efficient. References 1 T. Belytschko, Y.Y. Lu and L. Gu. "Element-free Galerkin method", International Journal for Numerical Methods in Engineering; 37:229-256, 1994. doi:10.1002/nme.1620370205 2 M. Duflot and N.D. Hung. "Dual analysis by a meshless method", International Journal for Numerical Methods in Engineering, 2002. 3 M. Duflot and N.D. Hung. "Global error estimation with displacement and equilibrium meshless method", Computational mechanics WCCM VI in conjunction with APCOM'04, Sept. 5-10, Beijing, China, 2004. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £140 +P&P)
Back to top	©Civil-Comp Limited 2023 - terms & conditions