Papers by Keyword: Element Free Galerkin Method

Abstract: An improved element free Galerkin method coupled the precise time-step integration method in the time domain is proposed for solving transient heat conduction problem with spatially varying conductivity in the paper. Firstly the nodal influence domain of element free Galerkin methods is extended to arbitrary convex polygon rather than rectangle and circle. When the dimensionless size of the nodal influence domain is 1.01, the shape function almost possesses interpolation property, thus essential boundary conditions can be implemented without any difficulties for the meshless method. Secondly, the precise time-step integration method is selected for the time discretization in order to improve the computational efficiency. Lastly, one numerical example is given to illustrate the highly accurate and efficient algorithm.

Abstract: The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

Abstract: The element-free Galerkin method is proposed to solve the stability of the moving rectangular plates. Utilizing the extended Hamilton’s principle for the elastic dynamics system, the variational expression of the moving thin plate are established. The dimensionless equations of motion of the moving thin plate are obtained by the element-free Galerkin method, and the complex eigenvalue equation is presented. Via numerical calculation, the variation relationship between the first three complex frequencies of the system and the moving speed is obtained. The effects of dimensionless moving speed on the stability and critical load of the thin plates are analyzed.

Abstract: Partial interaction between two different materials of composite beam is consequent from longitudinal slip and transverse uplift effects at interfacial surface. The behaviour has yielded higher order differential equation as compared to beam that interacts fully. In this paper, a meshless approach for the analysis of composite beam with partial interaction by Element Free Galerkin (EFG) method is formulated and investigated. Discretized solely by nodes, the Moving Least Square (MLS) method is adopted for the EFG shape functions formulation and the variational approach is chosen in developing its Galerkin weak form. The weak form essential boundary conditions are enforced by Lagrange multiplier, where comparable results are obtained between developed EFG code and established analytical solutions. In addition, influence of various weight functions on shape function smoothness of EFG code is explored.

Abstract: Abstract:Seepage is an important issue in geotechnical engineering projects such as dams, levees, canals, reservoirs, etcetera, and has made researchers and specialists to pay special attention to this problem. Lots of destructions in buildings, towers, dams, tunnels, slopes, and etcetera have been reported in history which, have been caused by liquefaction, ground water movement or other related seepage problems. In this article, seepage in soil-water systems and their related problems are studied using Element Free Galerkin Method (EFGM). For time dependent problems, implied finite difference method is used. A program is also written for both stable and time dependent cases. With estimation of a function and comparing the results with the exact function, the quantity of the errors is calculated and the accuracy of the method is evaluated. Based on this method, various geotechnical engineering problems are solved and analyzed. The results showed that not only is the EFGM more exact and accurate in comparison with other conventional methods but the time and costs for network production is omitted. With variations in boundaries, the application of EFGM is easier than that of Finite Element Method (FEM). Also, the ability of solving seepage problems without any limitation is a preference of EFGM in comparison with other approximate methods.

Abstract: Mesh-less methods belong to a new class of numerical methods in computational mechanics and offer several advantages over the conventional mesh-based methods. They enable modelling of processes involving high deformation, severe discontinuities (e.g. fracture) and multiple physical processes. These types of situations are usually encountered in arc welding, rendering its modelling suitable via mesh-less methods. In this paper, a mesh-less Element Free Galerkin (EFG) method has been developed to model the heat transfer during welding. The results predicted by the EFG method are found to be in close agreement with those obtained by the finite element method and those observed in welding experiments. This demonstrates the effectiveness and utilities of the EFG method for modelling and understanding the heat transfer processes in arc welding.

Abstract: This paper introduces the simulation method of concrete temperature cracking propagation process by element-free Galerkin method (EFGM). Due to its no-remeshing property, EFGM is very suitable for cracking problem. The governing equation of EFGM is presented for concrete heat conduction problem. A numerical simulating program is developed and an example including an initial crack is computed to validate the program. Result shows good accuracy and reliability of this method and cracking process may be simulated effectively by EFGM.

Abstract: Combining element free Galerkin method with rigid/visco-plastic flow theory, the paper establishes the three-dimensional rigid/visco-plastic element free Galerkin method, and introduces it to analyze three-dimensional bulk metal forming processes. The velocity field is approximated by MLS method. Employing the incomplete generalized variation principle, stiffness matrix equation and solution formulas are derived. And STL format discrete triangular patches are used to describe the mould cavity. An analysis program for simulating three-dimensional bulk metal forming processes is developed. The program is capable of simulating three-dimensional unsteady bulk metal forming processes with severe deformation and arbitrarily shaped dies. A numerical example is analyzed. Numerical results such as material flow patterns and distributions of the effective stress are obtained. The effectiveness and validity of the proposed method and techniques are demonstrated by comparing with results obtained by using commercial finite element software.