A New Weighted Average Method and It's Applications in Finite Element Method

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter α is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper- and lower-bound solutions can always be obtained by adjusting α; (2) there exists a preferable α at which the H-SFEM can produce the ultrasonic accurate solution.

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A Variational Finite Element Method for Solving Unsteady Viscous-Flow Problems

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1978-0006 ◽

1978 ◽

Vol 5 (1) ◽

pp. 39-45

Author(s):

H.M. Badr ◽

T.E. Base

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Stream ◽

Weighted Average ◽

Leading Edge ◽

Flow Problems ◽

Poisson Equations ◽

Drag Forces ◽

Unsteady Viscous Flow ◽

Element Method

The effects of a two-dimensional ‘real’ vortex convected along by an incompressible free stream impinging on a flat plate of finite length, situated midway between two parallel sides of a channel and near to the entrance of the channel, were studied analytically using the variational approach. Of particular interest were the effects of the free stream vorticity on the behaviour of the viscous layer developed on the plate. In the solution, the vorticity (Helmholtz) and stream function (Poisson) equations were integrated in space, using the finite element method and a weighted-average marching scheme in the direction of time. Results have been compiled for the variation of the pressure and shear along the plate with time and also for the variation of lift, drag forces, and pitching moment about the leading edge of the plate.

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A Modified Smoothed Finite Element Method for Static and Free Vibration Analysis of Solid Mechanics

International Journal of Computational Methods ◽

10.1142/s0219876216500432 ◽

2016 ◽

Vol 13 (06) ◽

pp. 1650043 ◽

Cited By ~ 13

Author(s):

Xiang Yang Cui ◽

Xiao Bin Hu ◽

Guang Yao Li ◽

Gui Rong Liu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Convergence Rate ◽

Solid Mechanics ◽

Weighted Average ◽

Free Vibration Analysis ◽

Average Value ◽

Smoothed Finite Element Method ◽

Element Method

The smoothed finite element method (S-FEM) proposed recently is more accurate and has higher convergence rate compared with standard four-node isoparametric finite element method (FEM). In this work, a modified S-FEM using four-node quadrilateral elements is proposed, which greatly reduces further the computation cost while maintaining the high accuracy and convergence rate. The key idea of the proposed modification is that the strain of the element is a weighted average value of the smoothed strains in the smoothing cells (SCs), which means that only one integration point is required to construct the stiffness matrix, similar to the single cell S-FEM. A stabilization item is proposed using the differences of the smoothed strains obtained in four SCs, which installs the stability of algorithm and increases the accuracy. To verify the efficiency, accuracy and stability of the present formulation, a number of numerical examples of static and free vibration problems, are studied in comparison with different existing numerical methods.

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A New Crack Propagation Algorithm Combined with the Finite Element Method

Journal of Mechanics ◽

10.1017/jmech.2020.1 ◽

2020 ◽

Vol 36 (4) ◽

pp. 405-422

Author(s):

L.D.C. Ramalho ◽

J. Belinha ◽

R.D.S.G. Campilho

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Crack Propagation ◽

Domain Boundary ◽

Crack Opening ◽

Crack Tip ◽

Weighted Average ◽

Engineering Problem ◽

The Finite Element Method ◽

Element Method

ABSTRACTThe prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.

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Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽

10.1039/c9nr06508c ◽

2019 ◽

Vol 11 (43) ◽

pp. 20868-20875 ◽

Cited By ~ 1

Author(s):

Junxiong Guo ◽

Yu Liu ◽

Yuan Lin ◽

Yu Tian ◽

Jinxing Zhang ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Interfacial Effect ◽

Infrared Photodetector ◽

The Finite Element Method ◽

Ferroelectric Domains ◽

Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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