scholarly journals A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Hongyin Yang ◽  
Hailin Lu ◽  
Xuyong Chen
Keyword(s):  
Parameter Space ◽  
Delta Function ◽  
Least Square ◽  
Shape Functions ◽  
Boundary Node ◽  
Boundary Integrals ◽  
Moving Least Square ◽  
Additional Information ◽  
Number Of Cells ◽  
Mls Method

The presented study proposed an improved interpolating boundary node method (IIBNM) for 2D potential problems. The improved interpolating moving least-square (IIMLS) method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS) method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.

A Comparison between Moving Least-Square Method and Natural Neighbour Interpolation

2013 ◽  
Vol 739 ◽  
pp. 653-656
Author(s):  
Zhi Feng Nie ◽  
Xing Long Li ◽  
Heng Heng Wu
Keyword(s):  
Computational Efficiency ◽  
Matrix Multiplication ◽  
Least Square Method ◽  
Matrix Inversion ◽  
Least Square ◽  
Shape Functions ◽  
Computational Accuracy ◽  
Computational Stability ◽  
Moving Least Square ◽  
Order Continuous

The construction procedures of shape functions in the moving least-square method (MLS) are complicated, in which many matrix multiplication and matrix inversion are included, so that the computational efficiency is low. Moreover, the choices of some parameters are influenced by the artificial factors, and the computational stability is poor. However, the construction procedures of shape functions in natural neighbour interpolation (NNI) are based on Voronoi diagram and its dual Delaunay triangulation, computational results are only related with the locations of the discretized nodes, and the computational stability is good. In order to study the differences in the computational accuracy, the computational efficiency, and the adaptability to the fitted objects between MLS-based shape functions andC1natural neighbour interpolant, the two higher-order continuous shape functions are introduced in surface fitting.

Analysis of Piezoelectric Fracture under Combined Mechanical and Electrical Loading based on Meshless Method

2004 ◽  
Vol 261-263 ◽  
pp. 543-548 ◽  
Author(s):  
Xiang Hua Guo ◽  
Dai Ning Fang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Hoop Stress ◽  
Least Square ◽  
Growth Path ◽  
Moving Least Square ◽  
Propagation Behavior ◽  
Meshless Approximation ◽  
Crack Propagation Behavior ◽  
Mls Method

In this paper, the moving least-square (MLS) method, one of the most promising meshless methods, is modified to construct whole field meshless approximation for coupled electromechanical problems. Based on this method, the crack propagation behavior and the elasto-electric fields near a crack tip in a PZT-5H piezoelectric ceramic under mechanical, electrical and mechanical-electrical mixed loads are investigated. The numerical results show that for a negative applied electric field, the hoop stress will be maximum at a certain angle other than 00 when the ratio of the electric field to tensile stress is relatively high, which makes the crack turn away from its original growth path.

A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow

2017 ◽  
Vol 22 (4) ◽  
pp. 913-934 ◽  
Author(s):  
Duc-Vinh Le ◽  
Boo-Cheong Khoo
Keyword(s):  
Immersed Boundary Method ◽  
Numerical Technique ◽  
Least Square ◽  
Immersed Boundary ◽  
Moving Least Square ◽  
Boundary Method ◽  
Direct Forcing ◽  
Delta Functions ◽  
Deformable Boundaries ◽  
Mls Method

AbstractWe present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, noslip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

FURTHER INVESTIGATION OF ELEMENT-FREE GALERKIN METHOD USING MOVING KRIGING INTERPOLATION

2004 ◽  
Vol 01 (02) ◽  
pp. 345-365 ◽  
Author(s):  
P. TONGSUK ◽  
W. KANOK-NUKULCHAI
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Least Square ◽  
Kriging Interpolation ◽  
Shape Functions ◽  
Element Free Galerkin Method ◽  
Basic Premise ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

Following its first introduction, this study further scrutinizes the new type of shape functions for Element-free Galerkin Method (EFGM) based on the Moving Kriging (MK) interpolation. Kriging is a geostatistical method of spatial interpolation. Its basic premise is that every unknown point can be interpolated from known scattered points in its specified neighborhood. This property is ideal for EFGM. Previously, a shortcoming of EFGM based on Moving Least Square (MLS) approximation is associated with its limitation to satisfy essential boundary conditions exactly. With MK interpolation functions, EFGM solution can satisfy essential boundary conditions automatically. Numerical tests on one and two-dimensional elasticity problems have confirmed the effectiveness of MK in addressing this specific shortcoming of EFGM. Furthermore, the study also finds the accuracy of EFGM to be greatly enhanced with the use of MK shape functions.

Constructing Continuous Strain and Stress Fields From Spatially Discrete Displacement Data in Soft Materials

2015 ◽  
Vol 83 (1) ◽  
Author(s):  
Wanru Liu ◽  
Rong Long
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Local Strain ◽  
Soft Materials ◽  
Element Model ◽  
Least Square ◽  
Stress Fields ◽  
Moving Least Square ◽  
Data Points ◽  
Mls Method

A recent study demonstrated that three-dimensional (3D) continuous displacement fields in transparent soft gels can be constructed from discrete displacement data obtained by optically tracking fluorescent particles embedded in the gels. Strain and stress fields were subsequently determined from gradients of the displacement field. This process was achieved through the moving least-square (MLS) interpolation method. The goal of this study is to evaluate the numerical accuracy of MLS in determining the displacement, strain, and stress fields in soft materials subjected to large deformation. Using an indentation model as the benchmark, we extract displacement at a set of randomly distributed data points from the results of a finite-element model, utilize these data points as the input for MLS, and compare resulting displacement, strain, and stress fields with the corresponding finite-element results. The calculation of strain and stress is based on finite strain kinematics and hyperelasticity theory. We also perform a parametric study in order to understand how parameters of the MLS method affect the accuracy of the interpolated displacement, strain, and stress fields. We further apply the MLS method to two additional cases with highly nonuniform deformation: a plate with a circular cavity subjected to large uniaxial stretch and a plane stress crack under large mode I loading. The results demonstrate the feasibility of using optical particle tracking together with MLS interpolation to map local strain and stress field in highly deformed soft materials.

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 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.

scholarly journals Can Job Satisfaction Mediate the Relationship between Emotional Intelligence and Spiritual Intelligence on Teacher Performance?

2021 ◽  
Vol 5 (1) ◽  
pp. 136
Author(s):  
Efendi Efendi ◽  
Sri Harini ◽  
Sudung Simatupang ◽  
Marto Silalahi ◽  
Acai Sudirman
Keyword(s):  
Job Satisfaction ◽  
Emotional Intelligence ◽  
Teacher Performance ◽  
Partial Least Square ◽  
Least Square ◽  
Spiritual Intelligence ◽  
Additional Information ◽  
Saturated Sample ◽  
The Relationship

This study aims to analyze the role of job satisfaction in mediating the relationship between emotional intelligence and intellectual intelligence on the performance of the high school teachers. This study uses a research design with an associative quantitative approach. Data was collected through documentation and online questionnaires. This study used a sample of 39 respondents with the determination of the sample size using the saturated sample formula. Partial least square is applied to examine the relationship between teacher performance, job satisfaction, emotional intelligence and intellectual intelligence. The results of this study indicate that of the seven hypotheses developed there are two accepted hypotheses, that is, for the effect of emotional intelligence on job satisfaction, it is obtained that the results of a significant effect and the influence of spiritual intelligence on teacher performance are also obtained significant results. Meanwhile, the other 5 hypotheses developed were not significant. Through the findings of this study, it is hoped that it can provide additional information for various parties, especially the school, to pay attention to the factors that affect teacher performance and job satisfaction, so that teachers gain comfort and confidence to continue to improve their performance in implementing learning in schools.

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