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.

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.

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.

scholarly journals A Generalized Analytical Model for Joule Heating of Segmented Wires

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Vivekananthan Balakrishnan ◽  
Toan Dinh ◽  
Hoang-Phuong Phan ◽  
Dzung Viet Dao ◽  
Nam-Trung Nguyen
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Joule Heating ◽  
Numerical Solutions ◽  
Analytical Data ◽  
Experimental Studies ◽  
Governing Equations ◽  
Steady State Temperature ◽  
The One ◽  
Good Agreement

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

scholarly journals The Interpolating Boundary Element-Free Method for Unilateral Problems Arising in Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fen Li ◽  
Xiaolin Li
Keyword(s):  
Variational Inequalities ◽  
Boundary Element ◽  
Meshless Method ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Least Square ◽  
Moving Least Square ◽  
Unilateral Problems ◽  
Element Free Method ◽  
Element Free

The interpolating boundary element-free method (IBEFM) is developed in this paper for boundary-only analysis of unilateral problems which appear in variational inequalities. The IBEFM is a direct boundary only meshless method that combines an improved interpolating moving least-square scheme for constructing interpolation functions with boundary integral equations (BIEs) for representing governing equations. A projection operator is used to formulate the BIEs and then the formulae of the IBEFM are obtained for unilateral problems. The convergence of the developed meshless method is derived mathematically. The capability of the method is also illustrated and assessed through some numerical experiments.

A Finite Pointset Method for Extended Fisher–Kolmogorov Equation Based on Mixed Formulation

2020 ◽  
Vol 18 (01) ◽  
pp. 2050019
Author(s):  
L. Jones Tarcius Doss ◽  
N. Kousalya
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Coupled System ◽  
Least Square ◽  
Kolmogorov Equation ◽  
System Of Differential Equations ◽  
Good Efficiency ◽  
Splitting Technique

In this paper, numerical solutions of the extended Fisher–Kolmogorov equation are obtained using finite pointset method. Finite pointset method is a meshless method which is a local iterative method based on the weighted least square approximation. By employing splitting technique, the extended Fisher–Kolmogorov equation is split into a two coupled system of differential equations by introducing an intermediate function. The method is applied to the resulting coupled system of differential equation. The numerical results confirm the good efficiency of the finite pointset method.

The Element-Free Galerkin Method for the Unsteady Magnetohydrodynamic Flow in a Duct

2015 ◽  
Vol 723 ◽  
pp. 181-185
Author(s):  
Xing Hui Cai ◽  
Hong Fu Qiang ◽  
Jiang Ren Lu ◽  
Guo Liang Wang
Keyword(s):  
Galerkin Method ◽  
Numerical Solutions ◽  
Magnetohydrodynamic Flow ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Coupled Equations ◽  
Element Free Galerkin ◽  
Moving Least Square Approximation ◽  
Element Free

In this paper, a meshless global element-free Galerkin method is given to obtain the numerical solutions of the coupled equations in the velocity and magnetic field for the unsteady magnetohydrodynamic flow through a straight duct with arbitrary electrical conductivity, that is, from perfectly conducting to insulated duct walls. The moving least-square approximation scheme is employed to construct shape functions. A time stepping method is employed to deal with the time derivatives. Non-uniform background grids and nodes are applied for numerical simulations. Computations are performed for different Hartmann numbers and wall conductivities at different time.

scholarly journals AN ELASTO-PLASTIC ANALYSIS OF SOLIDS BY THE LOCAL MESHLESS METHOD BASED ON MLS

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5780-5786 ◽  
Author(s):  
Y.T. GU
Keyword(s):  
Meshless Method ◽  
Deformation Theory ◽  
Weak Form ◽  
Least Square ◽  
Shape Functions ◽  
Total Deformation ◽  
Moving Least Square ◽  
Numerical Studies ◽  
Plastic Analysis ◽  
Local Weak Form

A pseudo-elastic local meshless formulation is developed in this paper for elasto-plastic analysis of solids. The moving least square (MLS) is used to construct the meshless shape functions, and the weighted local weak-form is employed to derive the system of equations. Hencky's total deformation theory is applied to define the effective Young's modulus and Poisson's ratio in the nonlinear analysis, which are obtained in an iterative manner using the strain controlled projection method. Numerical studies are presented for the elasto-plastic analysis of solids by the newly developed meshless formulation. It has demonstrated that the present pseudo-elastic local meshless approach is very effective for the elasto-plastic analysis of solids.

scholarly journals Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

2020 ◽  
Vol 41 (12) ◽  
pp. 1897-1914
Author(s):  
Linchong Chen ◽  
Xiaolin Li
Keyword(s):  
Complex Variable ◽  
Solid Angle ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Least Square ◽  
Integral Formulation ◽  
Variable Boundary ◽  
Moving Least Square ◽  
Weakly Singular ◽  
Boundary Integral Formulation

AbstractThe Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as κ = 10 000.

Sign in / Sign up

Export Citation Format

Share Document