• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2001.04a
• /
• pp.77-80
• /
• 2001

The element-free Galerkin (EFG) method is one of meshless methods, which is an efficient method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper discusses the theory of the EFG method and its applications to modeling of groundwater flow. In the EFG method, shape functions are constructed based on the moving least square (MLS) approximation, which requires only set of nodes. The EFG method can eliminate time-consuming mesh generation procedure with irregular shaped boundaries because it does not require any elements. The coupled EFG-FEM technique was introduced to treat Dirichlet boundary conditions. A computer code EFGG was developed and tested for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. The accuracy of solutions by the EFG method was similar to that by the FEM. The EFG method has the advantages in convenient node generation and flexible boundary condition implementation.

• Journal of Mechanical Science and Technology
• /
• v.20 no.11
• /
• pp.1881-1890
• /
• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2002.10a
• /
• pp.615-622
• /
• 2002

In this paper, the modification of double projection method for the adaptive analysis of Element-free Galerkin(EFG) method were proposed. As results of the double projection method, the smoothed error profile that is adequate for adaptive analysis was obtained by re-projection of error that means the differences of EFG stress and projected stress. However, it was found that the efficiency of double projection method is degraded as increase of the numerical integration order. Since, the iterative refinement to single step error estimation made the same effect as increasing of integration order, the application of the iterative refinement base on double projection method could be produced the inadequately refined analysis model. To overcome this defect, a modified scheme of double projection were proposed. In the numerical example, the results did not show degradation of double projection effect in iterative refinement and the efficiency of proposed scheme were proved.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.04a
• /
• pp.84-91
• /
• 2001

In this study, the adaptive analysis procedure of crack propagation based on the element-free Galerkin(EFG) method is presented. The adaptivity analysis in quasi-static crack propagation is achieved by adding and/or removing the node along the background integration cell that are refined or recovered according to the estimated error. These errors are obtained basically by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples. The results of these examples show the efficiency and accuracy of proposed scheme in crack propagation analysis.

• Structural Engineering and Mechanics
• /
• v.10 no.6
• /
• pp.635-650
• /
• 2000

In this paper, the adaptive nodal generation procedure based on the estimated local and global error in the element-free Galerkin (EFG) method is proposed. To investigate the possibility of h-type adaptivity of EFG method, a simple nodal refinement scheme is used. By adding new node along the background cell that is used in numerical integration, both of the local and global errors can be controlled adaptively. These errors are estimated by calculating the difference between the values of the projected stresses and original EFG stresses. The ultimate goal of this study is to develop the reliable nodal generator based on the local and global errors that is estimated posteriori. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated for several examples.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.04a
• /
• pp.76-83
• /
• 2001

In this study, a new method coupling of Element-Free Galerkin(EFG) method and Infinite Elements(IE) method is presented for extending application of the EFG method to engineering problems in unbounded domain. EFG method and IE method are briefly reviewed, and then the coupling procedure of the two methods is proposed. Numerical Algorithm by way of EFG-lE coupling technique is also developed. Numerical results illustrate the performance of the proposed technique. The accuracy of numerical solutions by the developed algorithm is guaranteed in comparing those of the other methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.1 no.1
• /
• pp.1-34
• /
• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• International Journal of CAD/CAM
• /
• v.8 no.1
• /
• pp.1-10
• /
• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.15 no.1
• /
• pp.85-94
• /
• 2002

In this study an adaptive node generation procedure in the Element-free Galerkin (EFG) method using bubble-meshing technique is Proposed. Since we construct the initial configuration of nodes by subdivision of background cell, abrupt changes of inter-nodal distance between higher and lower error regions are unavoidable. This unpreferable nodal spacing induces additional errors. To obtain the smooth nodal configuration the nodal configurations are regenerated by bubble-meshing technique. This bubble meshing technique was originally developed to generate a set of well-shaped triangles and tetrahedra. In odder to evaluate the effect of abrupt changes of nodal spacing, one-dimensional problems with various nodal configurations mere investigated. To demonstrate the performance of proposed scheme, the sequences of making optimal nodal configuration with bubble meshing technique are investigated for several problems.

• Structural Engineering and Mechanics
• /
• v.61 no.6
• /
• pp.765-773
• /
• 2017

The quadratic B-spline finite element method yields mass and stiffness matrices which are half the size of matrices obtained by the conventional finite element method. We solve the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method. Rayleigh beam theory includes the rotary inertia effects in addition to the Euler-Bernoulli theory assumptions and presents a good mathematical model for rotating beams. Galerkin's approach is used to obtain the weak form which yields a system of symmetric matrices. Results obtained for the natural frequencies at different rotating speeds show an accurate match with the published results. A comparison with Euler-Bernoulli beam is done to decipher the variations in higher modes of the Rayleigh beam due to the slenderness ratio. The results are obtained for different values of non-uniform parameter ($\bar{n}$).