MLS based local approximation in numerical manifold method

2018 ◽  
Vol 35 (7) ◽  
pp. 2429-2458
Author(s):  
Yuanqiang Chen ◽  
H. Zheng ◽  
Wei Li ◽  
Shan Lin
Keyword(s):  
Interpolation Method ◽  
Partition Of Unity ◽  
Local Approximation ◽  
Least Square ◽  
Triangular Element ◽  
Numerical Manifold Method ◽  
Content Type ◽  
Moving Least Square ◽  
The Individual ◽  
Numerical Manifold

Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns. Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function. Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element. Originality/value The proposed element inherits the individual merits of the NMM and the MLS.

A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems

2020 ◽  
pp. 2041002
Author(s):  
Wei Li ◽  
Qifan Zhang ◽  
Qiang Gui ◽  
Yingbin Chai
Keyword(s):  
Acoustic Radiation ◽  
Interpolation Method ◽  
Partition Of Unity ◽  
Local Approximation ◽  
Triangular Element ◽  
Two Dimensional ◽  
Shape Functions ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

ARBITRARY DISCONTINUITIES IN THE NUMERICAL MANIFOLD METHOD

2011 ◽  
Vol 08 (02) ◽  
pp. 315-347 ◽  
Author(s):  
XINMEI AN ◽  
GUOWEI MA ◽  
YONGCHANG CAI ◽  
HEHUA ZHU
Keyword(s):  
Solid Mechanics ◽  
Shear Bands ◽  
Partition Of Unity ◽  
Physical Problem ◽  
Numerical Manifold Method ◽  
Problem Domain ◽  
Material Interfaces ◽  
Cover System ◽  
Local Approximations ◽  
Numerical Manifold

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.

Dispersion Error Reduction for Acoustic Problems Using the Finite Element-Least Square Point Interpolation Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
L. Y. Yao ◽  
J. W. Zhou ◽  
Z. Zhou ◽  
L. Li
Keyword(s):  
Finite Element ◽  
Interpolation Method ◽  
Local Approximation ◽  
Least Square ◽  
Numerical Dispersion ◽  
Benchmark Problems ◽  
Shape Functions ◽  
Dispersion Error ◽  
Point Interpolation Method ◽  
Point Interpolation

The shape function of the finite element-least square point interpolation method (FE-LSPIM) combines the quadrilateral element for partition of unity and the least square point interpolation method (LSPIM) for local approximation, and inherits the completeness properties of meshfree shape functions and the compatibility properties of FE shape functions, and greatly reduces the numerical dispersion error. This paper derives the formulas and performs the dispersion analysis for the FE-LSPIM. Numerical results for benchmark problems show that, the FE-LSPIM yields considerably better results than the finite element method (FEM) and element-free Galerkin method (EFGM).

Stress Intensity Factor for Interfacial Cracks in Bi-Materials Using Incompatible Numerical Manifold Method

2011 ◽  
Vol 327 ◽  
pp. 109-114
Author(s):  
Gao Feng Wei ◽  
Hong Fen Gao ◽  
Hai Hui Jiang
Keyword(s):  
Stress Intensity ◽  
Interfacial Crack ◽  
Partition Of Unity ◽  
Complex Stress ◽  
Element Approximation ◽  
Numerical Manifold Method ◽  
Displacement Fields ◽  
Interfacial Cracks ◽  
Crack Problems ◽  
Numerical Manifold

Incompatible numerical manifold method (INMM) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement. This paper describes the application of INMM to bi-material interfacial crack. The two dimensional near-tip asymptotic displacement functions are added to the trial function approximation. This enables the domain to be modeled by manifold elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The INMM facilitates the incorporation of the oscillatory nature of the singularity within a conforming manifold element approximation. The complex stress intensity factors for bi-material interfacial cracks are numerically evaluated. Good agreement between the numerical results and the analytical solutions for benchmark interfacial crack problems is realized.

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 From Instagram overuse to instastress and emotional fatigue: the mediation of addiction

2019 ◽  
Vol 23 (2) ◽  
pp. 143-161 ◽  
Author(s):  
Silvia Sanz-Blas ◽  
Daniela Buzova ◽  
María José Miquel-Romero
Keyword(s):  
Social Networking Site ◽  
Partial Least Square ◽  
Least Square ◽  
Equation Modeling ◽  
Negative Feeling ◽  
Content Type ◽  
Mediating Role ◽  
Key Factor ◽  
The Individual ◽  
The Impact

Purpose Today’s society interest in mobile photography drives consumers’ and brands’ growing usage of Instagram. This paper aims to address the consequences of excessive use of Instagram on the negative feeling of losing information when not connected and the emotional fatigue resulting from an overcharge with new information. The mediating role of addiction between Instagram overuse and the two outcomes is also analyzed. Design/methodology/approach Data from 342 active Instagram users were used to test the proposed model, applying the partial least square equation modeling method (SmartPLS 3). Findings Addiction partially mediates the impact of overuse on emotional fatigue and instastress. Addiction to Instagram was mainly due to respondents’ lack of control over the time spent on it resulting in incapability to reduce its usage. Social implications Social networking site managers, educators, families and public institutions should promote an adequate use of Instagram, making users (especially the young) aware of the potential threats of its excessive usage. The control on the amount of time devoted to Instagram is a key factor for detaining overuse and addiction, as well as avoiding the negative outcomes analyzed in this research. Originality/value The findings contribute to the extant knowledge on the negative side of the digitization of the individual, as little is known about it to the best of the authors’ knowledge.

A GENERALIZED AND EFFICIENT METHOD FOR FINITE COVER GENERATION IN THE NUMERICAL MANIFOLD METHOD

2013 ◽  
Vol 10 (05) ◽  
pp. 1350028 ◽  
Author(s):  
YONGCHANG CAI ◽  
XIAOYING ZHUANG ◽  
HEHUA ZHU
Keyword(s):  
Complex Geometry ◽  
Partition Of Unity ◽  
Jointed Rock ◽  
Numerical Manifold Method ◽  
Finite Cover ◽  
Unified Framework ◽  
Structure Interaction ◽  
Block System ◽  
Finite Covers ◽  
Numerical Manifold

The numerical manifold method (NMM) based on the concept of finite covers and the partition of unity (PU) provides a unified framework to analyze continuum and discontinuum without changing predefined mesh in a discretized way. The NMM has been applied in the modeling of fluid structure interaction as well as in rock mechanics including the analysis of block system, jointed rock and fractured body, showing particular advantages over other PU based methods. Unlike other PU methods, the degrees of freedoms in the NMM are associated with the physical covers, rather than the nodes, which allow it to be naturally adapted to the changing geometries in analyzing complex discontinuum such as multiple intersecting cracks and branched cracks. Despite these recent advances, there is no publication available to date describing the physical cover generation of the NMM in a systematic way or giving a general principle of cover numbering, which has practically limited a wider application of the NMM. To address this issue, a generalized cover generation method is developed in the paper based on the concept of "detached physical cover" where manifold elements belonging to the same mathematical cover and having common mathematical edges are collected to form a new detached physical cover. The present method has a concise formulation for implementation, and is effective and generally applicable for dealing with interfaces, inclusions or discontinuities of complex geometry. A test example is performed showing the correctness, robustness and efficiency of the proposed method.

Effect of online political incivility on partisan attitude: role of issue involvement, moral identity and incivility accountability

2020 ◽  
Vol 44 (7) ◽  
pp. 1421-1441
Author(s):  
Isha Sharma ◽  
Kokil Jain ◽  
Gurinder Singh
Keyword(s):  
Social Media ◽  
Peer Review ◽  
Structural Equation ◽  
Moral Identity ◽  
Partial Least Square ◽  
Least Square ◽  
Equation Modeling ◽  
Content Type ◽  
Issue Involvement ◽  
The Individual

PurposeThe study investigates the effect of an uncivil comment made by a party representative on social media and tests whether it can lead to a change in observers' attitude toward the party.Design/methodology/approachData are collected from 196 respondents using a scenario-based survey. Proposed model is tested using partial least square structural equation modeling (PLS-SEM).FindingsIt is found that individual's moral identity and issue involvement influence perceived civility of the online post, which in turn affects attitude toward the party as well as the individual. It is observed that for high partisans, effect of perceived civility on attitude toward the party is stronger compared to low partisans. Party's lack of responsiveness to address the uncivil comment from its representative increases party's incivility accountability and lowers the partisan attitude toward the party.Originality/valueThe study presents a novel understanding of how political party representatives can influence the image of the party by engaging in an uncivil discourse on social media. Results support that strong partisan would react more unfavorably indicating that loyalty toward the party cannot be taken for granted.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/OIR-03-2020-0084

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