scholarly journals Elastic property prediction of long fiber composites using a uniform mesh finite element method

2008 ◽  
Author(s):  
Joseph Ervin Middleton
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Property ◽  
Fiber Composites ◽  
Uniform Mesh ◽  
Property Prediction ◽  
Element Method

A Lagrangian Uniform-Mesh Finite Element Method Applied to Problems Governed by Poisson’s Equation

2007 ◽  
Author(s):  
Linxia Gu ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Lagrangian Formulation ◽  
Uniform Mesh ◽  
Interpolation Function ◽  
Step Functions ◽  
Surface Integration ◽  
Interpolation Functions ◽  
Element Method

A method is presented for the solution of Poisson’s Equations using a Lagrangian formulation. The interpolation functions are the Lagrangian operation of those used in the classical finite element method, which automatically satisfy boundary conditions exactly even though there are no nodes on the boundaries of the domain. The integration is introduced in an implicit way by using approximated step functions. Classical surface integration terms used in the weak form are unnecessary due to the interpolation function in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplified the connection between the mesh and the solid structures, thus providing a very easy way to solve the problems without a conforming mesh.

PARAMETER-UNIFORM FINITE ELEMENT METHOD FOR TWO-PARAMETER SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION PROBLEMS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250047 ◽  
Author(s):  
M. K. KADALBAJOO ◽  
ARJUN SINGH YADAW
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reaction Diffusion ◽  
Rectangular Domain ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Spatial Direction ◽  
Small Parameters ◽  
Diffusion Problems ◽  
Element Method

In this paper, parameter-uniform numerical methods for a class of singularly perturbed one-dimensional parabolic reaction-diffusion problems with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and finite element method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(N-2( ln N)2 + Δt). Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.

scholarly journals The Elastic Property of Bulk Silicon Nanomaterials through an Atomic Simulation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jixiao Tao ◽  
Yuzhou Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Property ◽  
Young’S Modulus ◽  
Silicon Nanowires ◽  
Young's Modulus ◽  
Poisson Ratio ◽  
Bulk Silicon ◽  
Atomic Simulation ◽  
Element Method

This paper reports a systematic study on the elastic property of bulk silicon nanomaterials using the atomic finite element method. The Tersoff-Brenner potential is used to describe the interaction between silicon atoms, and the atomic finite element method is constructed in a computational scheme similar to the continuum finite element method. Young’s modulus and Poisson ratio are calculated for[100],[110], and[111] silicon nanowires that are treated as three-dimensional structures. It is found that the nanowire possesses the lowest Young’s modulus along the[100] direction, while the[110] nanowire has the highest value with the same radius. The bending deformation of[100] silicon nanowire is also modeled, and the bending stiffness is calculated.

scholarly journals Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Na An
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Initial Time ◽  
Uniform Mesh ◽  
Time Space ◽  
Conforming Finite Element ◽  
Conforming Finite Element Method ◽  
Element Method

Abstract In this work, a time-fractional diffusion problem with a time-space dependent diffusivity is considered. The solution of such a problem has a weak singularity at the initial time $t=0$ t = 0 . Based on the L1 scheme in time on a graded mesh and the conforming finite element method in space on a uniform mesh, the fully discrete L1 conforming finite element method (L1 FEM) of a time-fractional diffusion problem is investigated. The error analysis is based on a nonstandard discrete Gronwall inequality. The final superconvergence result shows that an optimal grading of the temporal mesh should be selected as $r\geq (2-\alpha )/\alpha $ r ≥ ( 2 − α ) / α . Numerical results confirm that our analysis is sharp.

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