Papers by Keyword: Meshless

Abstract: In this paper, θ-EFG(theθfamily of methods –Element Free Galerkin) method is developed and adopted for the simulation of chloride diffusion in concrete. Diffusion of chloride ions is generally assumed to follow the Fick’s second law and its solving process usually adopts finite element and finite difference method. θ-EFG is a meshless method which uses a moving least square approximation in space domain, then uses the θ family of methods in time domain. Some discussions and One dimensional examples are carried out. The computational results compared with the analytical solution are shown that the relative error norm that time=20years, chloride content of different depth and depth =45 mm, chloride content are about 0.5% and 1% respectively.

Abstract: The novelty of this paper is the use of a meshless local collocation method based on the multiquadric radial basis functions for free vibration analysis of functionally graded plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. The natural frequencies computed by the present method are in good agreement with the element-free solutions of Zhao et al.

Abstract: In present paper, deflection and stress of laminated composite plates are analyzed by a meshless local collocation method based on inverse multiquadrics radial basis function. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. Transverse displacement, normal stresses, and shear stresses of the simply supported laminated composite plates under sinusoidal load are computed by the present method. The convergence characteristics are studied by several numerical examples. The present results are compared with available published results which demonstrate the accuracy and efficiency of present method.

Abstract: In this paper, a new meshless local B-spline basis functions-finite difference (FD) method is presented for two-dimensional heat conduction problem with spatially varying heat generation. In the method, governing equations are discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation. The key aspect of the method is that any derivative at a point or node is stated as neighbouring nodal values based on the B-spline interpolants. Compared with mesh-based method such as FEM the method is simple and efficient to program. In addition, as the method poses the Kronecker delta property, the imposition of boundary conditions is also easy and straightforward. Moreover, it poses no difficulties in dealing with arbitrary complex domains. Heat conduction problem in complex geometry is presented to demonstrate the accuracy and efficiency of the present method.

Abstract: The thermal bending response of laminated composite plates has been studied by the use of various higher order shear deformation theories of Levinson, Touratier, Karama and Aydogdu. The governing differential equations are discretized by a meshless method based on inverse multiquadric radial basis function. The center deflections of laminated composite plates subjected to sinusoidal temperature distribution are solved and compared with available published results to assess the performance of the present method.

Abstract: In the present paper, the higher order shear deformation theories of Touratier and Karama and meshless global collocation method based on the inverse multiquadric radial basis function are used to analyze the bending response of the exponentially graded plates. The material properties of the plates vary exponentially in the thickness direction. The present results are compared with three-dimensional elasticity solutions.

Abstract: Large Eddy Simulation (LES) based on the least square meshless method was proposed in the present paper to simulate the classical turbulent flow around a stationary 2D circular cylinder. The subgrid scale model of Smagorinsky-Lily was employed to close the Navier-Stokes equations filtered by Favre filter. The Reynolds number is 3900 which means that the flow is subcritical and the wake is fully turbulent but the cylinder boundary is still laminar. Results obtained in this paper were evaluated by comparison with published experimental results and other numerical results. The results obtained in the present work show better agreement with the experimental values than other two-dimensional LES results .

Abstract: Coupling method is developed in recent years to solve numerical problems a new method, meshless - the finite element of a direct coupling method is based on the definition of the generalized unit of coupling of the new method . The core of this method is the use of each unit in the shape function to the assumption that the brain that the whole sub-domain to be seeking to solve the unknown field function. Coupling with other compared with the method is simple to calculate the advantages of a short time.

Abstract: The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive remeshing is often the proposed solution in this case. But the remeshing raises the problems of precision and computing time. In this context and in order to avoid the remeshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.

Abstract: A meshless natural neighbour Petrov–Galerkin method (NNPG) is presented for solving the elasticity problems in this paper. In a certain domain, a discrete model consists of a set of distinct nodes, and a polygonal description of the boundary. The natural neighbour interpolation has Kronecker delta function property, and the construction of local sub-domain is simple both for internal nodes and boundary nodes. The whole interpolation is constructed with respect to the natural neighbour nodes and Voronoi tessellation of the given point. A local weak form over the local Delaunay triangular sub-domain is used to obtain the discretized system of equilibrium equations. The numerical results show the presented method is easy to implement and very accurate, especially for solving the problems of crack propagation or large deformations.