A Smoothed GFEM Based on Taylor Expansion and Constrained MLS for Analysis of Reissner–Mindlin Plate

2021 ◽  
pp. 2150048
Author(s):  
Tang Jinsong ◽  
Qian Linfang ◽  
Chen Guangsong
Keyword(s):  
Taylor Expansion ◽  
Temporal Stability ◽  
Displacement Function ◽  
Least Square ◽  
Mindlin Plate ◽  
Square Function ◽  
Mesh Distortion ◽  
Nodal Displacement ◽  
Moving Least Square ◽  
Element Shape

Based on the Taylor Expansion and constrained moving least square function, a smoothed GFEM (SGFEM) is proposed in this paper for static, free vibration and buckling analysis of Reissner–Mindlin plate. The displacement function based on SGFEM is composed of classical linear finite element shape function and nodal displacement function, which are obtained by introducing the gradient smoothed meshfree approximation in Taylor expansion of nodal displacement function. A constrained moving least square function is proposed for constituting meshfree nodal displacement function. The merits of the proposed SGFEM, including high accuracy, rapid error convergence, insensitive to mesh distortion, free of shear-locking problem, no extra DOFs and temporal stability, etc., are demonstrated by several typical examples and comparisons with other numerical methods.

The Study of Meshless Method Simulation of Plate Bending Problem

2012 ◽  
Vol 446-449 ◽  
pp. 3633-3638
Author(s):  
Yu Ling Jiao ◽  
Guang Wei Meng ◽  
Xu Xi Qin
Keyword(s):  
Weight Function ◽  
Elastic Plate ◽  
Basis Function ◽  
Meshless Method ◽  
Least Square ◽  
Mindlin Plate ◽  
Plate Bending ◽  
Field Function ◽  
Moving Least Square ◽  
Plate Bending Problem

moving least square meshless method is a numerical approximation based on points that do not generate the grid of cells, as long as the node information. Basis function and weight function meshless method for the calculation of accuracy have a significant impact. In order to compare the order of the base functions and powers of the radius of influence domain function meshless method for computational accuracy and efficiency , this paper selected first, second and third basis function and spline-type weight function in a different influence domain radius, respectively construct the field function. Mindlin plate element is derived based on the format of the plate bending problem meshless discrete equations. Programming examples are calculated with elastic plate bending problems non-grid solutions, and analysis and comparison of their accuracy and efficiency, results show that the meshless method using elastic plate bending problem is feasible and effective.

A GFEM With Local Gradient Smoothed Approximation for 2D Solid Mechanics Problems

2020 ◽  
Author(s):  
Jinsong Tang ◽  
Linfang Qian ◽  
Guangsong Chen
Keyword(s):  
Finite Element ◽  
Basis Function ◽  
Taylor Expansion ◽  
Solid Mechanics ◽  
Shape Function ◽  
Displacement Function ◽  
Field Function ◽  
Integration Schemes ◽  
Local Gradient ◽  
Element Shape

Abstract In this paper, a generalized finite element method (GFEM) with local gradient smoothed approximation (LGS-GFEM) using triangular meshes is proposed. The displacement field function of LGS-GFEM consists of the finite element shape function and the node displacement function. In order to obtain the nodal displacement function, the second order Taylor expansion is considered. The derivative term in Taylor expansion is obtained by using gradient smoothed technique in a smoothed domain. The displacement in smoothed operation is interpolated by polynomial basis function and radial basis function. Two kinds of integration schemes are considered, i.e. LGS-GFEM-I and LGS-GFEM-II respectively. The smoothed composite shape function of LGS-GFEM retains the ideal Kronecker property of the finite element shape function. Besides, the proposed LGS-GFEM has some other important properties such as no extra DOFs, linear independent, etc. The superiority of LGS-GFEM including high accuracy, rapid error convergence and temporal stability, is demonstrated by two representative numerical examples of static and free vibration, and compared with the classical finite element of triangular (FEM-T3) and quadrilateral (FEM-Q4) elements.

scholarly journals Complex Variable Meshless Manifold Method for Elastic Dynamic Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Analytical Solution ◽  
Complex Variable ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Least Square ◽  
Dynamic Problems ◽  
Finite Covering ◽  
Moving Least Square ◽  
Elastic Dynamics ◽  
Good Agreement

Combining the finite covering technical and complex variable moving least square, the complex variable meshless manifold method can handle the discontinuous problem effectively. In this paper, the complex variable meshless method is applied to solve the problem of elastic dynamics, the complex variable meshless manifold method for dynamics is established, and the corresponding formula is derived. The numerical example shows that the numerical solutions are in good agreement with the analytical solution. The CVMMM for elastic dynamics and the discrete forms are correct and feasible. Compared with the traditional meshless manifold method, the CVMMM has higher accuracy in the same distribution of nodes.

An Efficient Meshfree Method for Fracture Analysis of Cracks in Bi-Materials

2006 ◽  
Author(s):  
B. Nandulal ◽  
B. N. Rao ◽  
C. Lakshmana Rao
Keyword(s):  
Computational Efficiency ◽  
Basis Function ◽  
Meshfree Method ◽  
Fracture Analysis ◽  
Least Square ◽  
Moving Least Square ◽  
Linear Elastic ◽  
Moving Least Square Approximation ◽  
Material Fracture ◽  
Element Free

This paper presents an enriched meshless method based on an improved moving least-square approximation (IMLS) method for fracture analysis of cracks in homogeneous, isotropic, linear-elastic, two-dimensional bimaterial solids, subject to mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with IMLS and a new enriched basis functions to capture the singularity field in linear-elastic bi-material fracture mechanics. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill-conditioned system of equations. The proposed enriched basis function can be viewed as a generalized enriched basis function, which degenerates to a linear-elastic basis function when the bimaterial constant is zero. Numerical examples are presented to illustrate the computational efficiency and accuracy of the proposed method.

Two Implicit Meshless Finite Point Schemes for the Two-Dimensional Distributed-Order Fractional Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 813-831
Author(s):  
Rezvan Salehi
Keyword(s):  
Reproducing Kernel ◽  
Point Method ◽  
Least Square ◽  
Computationally Efficient ◽  
Finite Point ◽  
Moving Least Square ◽  
Point Collocation ◽  
Finite Point Method ◽  
Distributed Order ◽  
Fractional Equation

AbstractIn this paper, the distributed-order time fractional sub-diffusion equation on the bounded domains is studied by using the finite-point-type meshless method. The finite point method is a point collocation based method which is truly meshless and computationally efficient. To construct the shape functions of the finite point method, the moving least square reproducing kernel approximation is employed. Two implicit discretisation of order{O(\tau)}and{O(\tau^{1+\frac{1}{2}\sigma})}are derived, respectively. Stability and{L^{2}}norm convergence of the obtained difference schemes are proved. Numerical examples are provided to confirm the theoretical results.

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