• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.22 no.4
• /
• pp.335-341
• /
• 2009

In this paper, review of developed MLS-based finite elements and a proposal for their applications are described. The shape functions and their derivatives of MLS-based finite elements are constructed using Moving-Least Square approximation. In MLS-based finite element, using the adequate influence domain of weight function used in MLS approximation, kronecker delta condition could be satisfied at the element boundary. Moreover, because of the characteristics of MLS approximation, we could easily add extra nodes at an arbitrary position in MLS-based finite elements. For these reasons, until now, several variable-node elements(2D variable element for linear case and quadratic case and 3D variable-node elements) and finite crack elements are developed using MLS-based finite elements concept. MLS-based finite elements could be extended to 2D variable-node triangle element, 2D finite crack triangle element, variable-node shell element, finite crack shell element, and 3D polyhedron element. In this paper, we showed the feasibility of 3D polyhedron element at the case of femur meshing.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.416-418
• /
• 2004

Tracking of evolving solid-fluid interfaces is treated using level set method and MLS-based finite element with variable nodes. Several applications will be illustrated to demonstrate the effectiveness of the present scheme

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.567-574
• /
• 2006

We present applications of MLS-based finite elements, which enable us to easily treat highly complex nonmatching finite element meshes and discontinuities. The shape functions of MLS-based finite element can be easily generated with the aid of Moving Least Square approximation on the parental domain. The major advantage includes that the position of element nodes as well as the number of the element nodes can be conveniently adjusted according to the nature of the problems under consideration, so that finite-element mesh is straightforwardly adapted to evolving discontinuities and. interfaces. Furthermore, we show that the present MLS-based finite elements are efficiently applied for elastic-plastic deformations, wherein the implicit constraint of incompressibility should be properly handled.

• Structural Engineering and Mechanics
• /
• v.25 no.1
• /
• pp.91-106
• /
• 2007

A new class of finite elements is described for dealing with mesh gradation. The approach employs the moving least square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with polynomial shape functions for which the $C^1$ continuity breaks down across the boundaries between the subdomains comprising one element. Among those, (4 + n)-noded MLS based finite elements possess the generality to be connected with an arbitrary number of linear elements at a side of a given element. It enables us to connect one finite element with a few finite elements without complex remeshing. The effectiveness of the new elements is demonstrated via appropriate numerical examples.

• Proceedings of the KSME Conference
• /
• 2008.11a
• /
• pp.1633-1637
• /
• 2008

In this study, we developed 3D MLS-based variable-node elements for easy meshing. These elements should be derived from 2D MLS-based variable-node elements and would be utilized as key elements of easy meshing technique we proposed. Using developed 3D MLS-based variable-node elements, we demonstrated several examples having complex configuration compared with conventional meshing technique. Moreover, we compared with the stress results of our model and conventional one.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.405-410
• /
• 2007

We present a new global/local analysis with the aid of MLS(Moving Least Square)-based finite elements which can handle an arbitrary number of nodes on every element side. It give a great flexibility in constructing finite element meshes at the specified local regions without remeshing. Compared to other type global/local analysis, it does not require any superimposed mesh or need not solve the equilibrium equation twice as well as shows an excellent accuracy. To demonstrate the performance of proposed scheme, we will show several examples in relation to capturing highly local stress field.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.27 no.1
• /
• pp.17-26
• /
• 2014

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.12 s.255
• /
• pp.1626-1633
• /
• 2006

In the present paper, in the context of the meshless interpolation of a moving least squares (MLS) type, a novel method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The support domains for the shape functions in the MLS approximation are defined from the primary nodes, and the secondary nodes use the same support domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and moved without an additional mesh. Several numerical examples are presented to illustrate the effectiveness of the present method.

• 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.

• Structural Engineering and Mechanics
• /
• v.11 no.2
• /
• pp.123-132
• /
• 2001

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.