MLPG Method Research Articles

The basis of meshless domain discretization: the meshless local Petrov?Galerkin (MLPG) method

The MLPG method is the general basis for several variations of meshless methods presented in recent literature. The interrelation of the various meshless approaches is presented in this paper. Several variations of the meshless interpolation schemes are reviewed also. Recent developments and applications of the MLPG methods are surveyed.

Stress analysis in anisotropic functionally graded materials by the MLPG method

A meshless method based on the local Petrov–Galerkin approach is proposed for stress analysis in two-dimensional (2D), anisotropic and linear elastic/viscoelastic solids with continuously varying material properties. The correspondence principle is applied for non-homogeneous, anisotropic and linear viscoelastic solids where the relaxation moduli are separable in space and time. The inertial dynamic term in the governing equations is considered too. A unit step function is used as the test functions in the local weak-form. It leads to local boundary integral equations (LBIEs). The analyzed domain is divided into small subdomains with a circular shape. The moving least squares (MLS) method is adopted for approximating the physical quantities in the LBIEs. For time-dependent problems, the Laplace-transform technique is utilized. Several numerical examples are given to verify the accuracy and the efficiency of the proposed method.

Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions

A subdomain variational inequality and its meshless linear complementary formulation are developed in the present paper for solving two-dimensional contact problems. The subdomain variational inequality will be defined in detail. The meshless method is based on a local weighted residual method with the Heaviside step function as the weighting function over a local subdomain and radial basis functions as trial functions for interpolation. Three different radial basis functions (RBFs), i.e. Multiquadrics (MQ), Gaussian (EXP) and Thin Plate Splines (TPS) are examined and the selection of their shape parameters is studied based on 2D solid stress problems with closed-form solutions. The developed meshless/linear complementary method is applied to solve two frictionless contact problems. For the RBFs, it has been found that the TPS shape parameter is not sensitive to nodal distance and a value of 4 is found as a good choice for TPS from this research.

Numerical Analysis of 2-d. Crack Problems Using MLPG Method

Numerical Analysis of 2-d. Crack Problems Using MLPG Method

Free and Forced Vibrations of Thick Rectangular Plates using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Petrov-Galerkin (MLPG) Method

We use a meshless local Petrov-Galerkin Liu (2001) have used the MLPG method to find natu- (MLPG) method to analyze three-dimensional infinitesi- ral frequencies and forced plane ,strain deformations.of mal elastodynamic deformations of a homogeneous rect- a cantilever beam. Batra and Chmg .(2002~ have de!m- angular plate subjected to different edge conditions. We eated the time evolution of the stress-mtenslty factor m a employ a higher-order plate theory in which both trans- double edge-cracked plate. verse shear and transverse normal deformations are con- Atluri and Shen (2002a,b) have compared the perfor- sidered. Natural frequencies and the transient response manceof six' variants of the MLPG method for solving to external loads have been computed for isotropic Poisson's equation. Qian et al. (2002) used two of these and orthotropic plates. Computed results are found to formulations to study elastostatic deformations of a thick agree with those obtained from the analysis of the 3- rectangular plate with a compatible higher-order shear dimensional problem either analytically or by the finite and normal deformable plate theory (HOSNDPT) pro- element method.

Meshless analysis of the obstacle problem for beams by the MLPG method and subdomain variational formulations

In this paper, subdomain variational formulations are presented to describe the bending problem of thin beams, which is then analysed by using the MLPG meshless method. Particular attention is paid to the solution of the obstacle problem for beams by means of subdomain variational inequalities and the MLPG method. The local point interpolation method is employed to construct both trial and test functions. The present method is a truly meshless method based only on a number of randomly located nodes. No global background integration mesh is needed, no element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. Problems of thin beams under various loading, and boundary conditions, as well as the obstacle problem for beams are analysed by the proposed method and the numerical results are compared with analytical solutions. Some parameters which affect the performance of the present method are also investigated.

A Study on Support Radiuses and Weight Functions in a MLPG Method and Static and Dynamic Analyses of Bars

A Study on Support Radiuses and Weight Functions in a MLPG Method and Static and Dynamic Analyses of Bars

Dynamic Analysis on a Beam Supported with Nonlinear Distributed Spring by MLPG Method.

The purpose of this study is to develop a procedure for performing a dynamic analysis on a beam supported with nonlinear distributed spring by the MLPG method. Equations of motion on a beam supported with nonlinear distributed spring have been derived using the MLPG method. The computational programs for statics, eigen-value analysis and time history responses were developed using the derived equations. Appropriate values on the order of a basis vector used in an approximate displacement, the number of nodal points and the sizes of local domains were found under carrying out static analyses. Then the validity of the formulations and the computational programs were verified by comparing the numerical solutions obtained using the developed computational programs with the analytical solutions and the numerical ones by the finite-element analysis.

407 MLPG 法による非線形分布ばねで支持されたはりの動力学解析

407 MLPG 法による非線形分布ばねで支持されたはりの動力学解析

415 MLPG 法による棒の力学解析を行う場合のサポート半径と重み関数について

415 MLPG 法による棒の力学解析を行う場合のサポート半径と重み関数について

414 MLPG (Meshless Local Petrov-Galerkin) 法による二次元弾性問題の数値解析と精度の検討

414 MLPG (Meshless Local Petrov-Galerkin) 法による二次元弾性問題の数値解析と精度の検討

371 MLPG(Meshless Local Petrov-Galerkin)法による二次元弾性問題の数値解と精度の検討(OS24-4 ノードレス法・応用)(OS24 メッシュレス/粒子法)

371 MLPG(Meshless Local Petrov-Galerkin)法による二次元弾性問題の数値解と精度の検討(OS24-4 ノードレス法・応用)(OS24 メッシュレス/粒子法)