scholarly journals Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least-Square Method

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
H. M. Zhou ◽  
X. M. Zhang ◽  
Z. Y. Wang
Keyword(s):  
Meshless Method ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Linear Equations ◽  
Least Square Method ◽  
Field Variable ◽  
Least Square ◽  
Power Law Distribution ◽  
Weighted Least Square ◽  
Fgm Beam

The paper analyzed the thermal problem of the 2D FGM beam using meshless weighted least-square (MWLS) method. The MWLS as a meshless method is fully independent of mesh, and an approximate function was used to construct a series of linear equations to solve the unknown field variable, which avoided the troublesome task of numerical integration. The effectiveness and accuracy of the approach were illustrated by a clamped-clamped FGM beam which was subjected with interior heat source. The volume fraction of FGM beam was assumed to be given by a simple power law distribution. The effective material properties of the FGM beam were assumed to be temperature independent and calculated by Mori-Tanaka method. The results showed that a good agreement was achieved between the proposed meshless method and commercial COMSOL Multiphysics.

Numerical Analysis of Electromagnetic Levitation Employing Meshless Method Based on Weighted Least Square Method

2015 ◽  
Vol 15 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Shuhei Matsuzawa ◽  
Kenta Mitsufuji ◽  
Yurika Miyake ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Magnetic Field ◽  
Meshless Method ◽  
Fluid Motion ◽  
Electromagnetic Levitation ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square ◽  
Frequency Magnetic Field ◽  
Thermo Physical Properties ◽  
The Magnetic Field

AbstractElectromagnetic levitation is a kind of magnetohydrodynamic phenomena which is useful to measure the thermo-physical properties of pure metals under high temperature. However, this phenomenon is complicated and detailed mechanisms of this phenomenon have not been clarified yet. This study proposes the meshless method based on weighted least square method for the analysis of electromagnetic levitation. In this study, the fluid motion equation and the magnetic field equation are coupled by this method. The behavior of a molten metal under high-frequency magnetic field is calculated by this method.

Validation of Meshless Method Based on Weighted Least Square Method for Simulating Electromagnetic Levitation

2016 ◽  
Vol 52 (3) ◽  
pp. 1-4 ◽  
Author(s):  
Shuhei Matsuzawa ◽  
Kenta Mitsufuji ◽  
Yurika Miyake ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Meshless Method ◽  
Electromagnetic Levitation ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square

Meshless Method Based on Weighted Least Square Method for Electrohydrodynamic Problems

2015 ◽  
Vol 51 (3) ◽  
pp. 1-4 ◽  
Author(s):  
Gaku Yoshikawa ◽  
Shuhei Matsuzawa ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Meshless Method ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1993 ◽  
Vol 115 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J. C. Wang ◽  
R. F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

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