Elastic buckling analysis of folded plates using the moving-least square meshfree method

2011 ◽  
Author(s):  
Linxin Peng
Keyword(s):  
Meshfree Method ◽  
Buckling Analysis ◽  
Least Square ◽  
Elastic Buckling ◽  
Moving Least Square

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.

Perturbation-Based Stochastic Meshless Method for Buckling Analysis of Plates

2021 ◽  
pp. 2150044
Author(s):  
M. Aswathy ◽  
C. O. Arun
Keyword(s):  
Perturbation Method ◽  
Random Field ◽  
Random Fields ◽  
Buckling Analysis ◽  
Least Square ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Moving Least Square ◽  
Parametric Studies ◽  
Element Free

The current paper presents a perturbation-based stochastic eigenvalue buckling analysis of thin plates using element free Galerkin method. Spatial variation in Young’s modulus is modeled as a homogeneous random field and moving least square-based shape function method is employed for discretizing the random field. Perturbation method is used to evaluate the statistics of buckling loads. Numerical examples wherein rectangular plates with different boundary conditions are solved and the statistics obtained are compared with those calculated using Monte Carlo simulation. Different parametric studies are also conducted. The results obtained from perturbation method are found to be reasonably accurate for coefficient of variation (CV) values less than 20% for random fields with normal distribution. Further it is observed that for random fields with lognormal distribution, the proposed method produces reasonably accurate results up to a CV of 30%.

Numerical Analysis of a Semi-Infinite Solid with Temperature Dependent Thermal Conductivity using Truly Meshfree Method

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Rajul Garg ◽  
Harishchandra Thakur ◽  
Brajesh Tripathi
Keyword(s):  
Meshfree Method ◽  
Least Square ◽  
Penalty Function Method ◽  
Temperature Dependent ◽  
Essential Boundary Condition ◽  
Moving Least Square ◽  
Mlpg Method ◽  
Constant Coefficients ◽  
Temperature Dependent Properties ◽  
Predictor Corrector

This article presents Meshless Local Petrov-Galerkin (MLPG) method to obtain the numerical solution of linear and non-linear heat conduction in a semi-infinite solid object with specific heat flux. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th(x). These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary condition is imposed by the penalty function method. A predictor-corrector scheme based on direct substitution iteration has been applied to address the non-linearity and two-level  method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with the exact solutions. Once the accuracy of MLPG method is established, the method is further extended to investigate the effects of temperature-dependent properties.

Nonlinear analysis of convective-radiative longitudinal fin of various profiles

2019 ◽  
Vol 30 (6) ◽  
pp. 3065-3082
Author(s):  
Prashant Dineshbhai Vyas ◽  
Harish C. Thakur ◽  
Veera P. Darji
Keyword(s):  
Heat Transfer ◽  
Nonlinear Analysis ◽  
Convective Heat Transfer Coefficient ◽  
Radiation Condition ◽  
Meshfree Method ◽  
Accurate Solution ◽  
Least Square ◽  
Content Type ◽  
Moving Least Square ◽  
Predictor Corrector

Purpose This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles. Design/methodology/approach A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate. Findings A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity. Research limitations/implications Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces. Originality/value The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.

scholarly journals Coupling of Point Collocation Meshfree Method and FEM for EEG Forward Solver

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Chany Lee ◽  
Jong-Ho Choi ◽  
Ki-Young Jung ◽  
Hyun-Kyo Jung
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Current Source ◽  
Meshfree Method ◽  
Forward Problem ◽  
Least Square ◽  
Head Model ◽  
Source Modeling ◽  
Moving Least Square ◽  
Point Collocation

For solving electroencephalographic forward problem, coupled method of finite element method (FEM) and fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed using meshfree method. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM adopts point collocation scheme. Suggested method is tested using simple equation using 1-, 2-, and 3-dimensional models, and error tendency according to node distance is studied. In addition, electroencephalographic forward problem is solved using spherical head model. Proposed hybrid method can produce well-approximated solution.

Option pricing and Greeks via a moving least square meshfree method

2013 ◽  
Vol 14 (10) ◽  
pp. 1753-1764 ◽  
Author(s):  
Yongsik Kim ◽  
Hyeong-Ohk Bae ◽  
Hyeng Keun Koo
Keyword(s):  
Option Pricing ◽  
Meshfree Method ◽  
Least Square ◽  
Moving Least Square

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.

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