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.

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.

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.

Meshless Local Petrov-Galerkin (MLPG) Method for Incompressible Viscous Fluid Flows

2006 ◽  
Author(s):  
Mohammad Haji Mohammadi
Keyword(s):  
Stream Function ◽  
Meshless Method ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Least Square ◽  
Test Problems ◽  
Gauss Point ◽  
Driven Cavity ◽  
Moving Least Square ◽  
Mlpg Method

In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of unsteady incompressible flows, governed by the Navier–Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based only on a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction eq. (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Moving Least Square approximation (MLS) is employed in shape function construction for approximation of a gauss point. Due to dissatisfaction of kronecker delta property in MLS approximation, the penalty method is employed to enforce the essential boundary conditions. In order to overcome instability and numerical errors encountering in convection dominant flows, a new upwinding scheme is used to stabilize the convection operator in the streamline direction (as is done in SUPG). In this upwinding technic, instead of moving subdomains the weight function is shifted in the direction of flow. The efficiency, accuracy and robustness are demonstrated by some test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The comparison of computational results shows that the developed method is capable of accurate resolution of flow fields in complex geometries.

A BEM-BASED MESHLESS METHOD FOR ELASTIC BUCKLING ANALYSIS OF PLATES

2007 ◽  
Vol 07 (01) ◽  
pp. 81-99 ◽  
Author(s):  
BOONME CHINNABOON ◽  
SOMCHAI CHUCHEEPSAKUL ◽  
JOHN T. KATSIKADELIS
Keyword(s):  
Boundary Conditions ◽  
Meshless Method ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Buckling Analysis ◽  
Plate Bending ◽  
Elastic Plates ◽  
Actual Problem ◽  
Fictitious Load ◽  
Plate Bending Problem

In this paper, a BEM-based meshless method is developed for buckling analysis of elastic plates with various boundary conditions that include elastic supports and restraints. The proposed method is based on the concept of the Analog Equation Method (AEM) of Katsikadelis. According to this method, the original eigenvalue problem for a governing differential equation of buckling is replaced by an equivalent plate bending problem subjected to an appropriate fictitious load under the same boundary conditions. The fictitious load is established using a technique based on BEM and approximated by using the radial basis functions. The eigenmodes of the actual problem are obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. Thus, the kernels of the boundary integral equations are conveniently established and evaluated. The method has all the advantages of the pure BEM. To validate its effectiveness, accuracy as well as applicability of the proposed method, numerical results of various problems are presented.

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