A Generalized Form Of Integral-Finite Element Formulations For Diffusion Equation

1984 ◽  
pp. 1-6
Author(s):  
Wan Mokhtar Nawang
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Variational Principle ◽  
Heat Flow ◽  
Three Dimensional ◽  
Integral Form ◽  
Physical Problem ◽  
Integral Formulation ◽  
Governing Differential Equation ◽  
Finite Element Formulations

A physical problem such as diffusion can be described mathematically in two ways, i.e. by Differential Equation Formulation or Integral Formulation. An integral form is derived from its governing differential equation using the method of Variational Principle for a three-dimensional heat flow equation.The equivalent Integral Formulation will be a very useful and an inevitable tool in the formulation of finite element equatipn.

The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion

1998 ◽  
Vol 65 (3) ◽  
pp. 614-618 ◽  
Author(s):  
Wensen Liu ◽  
X. Markenscoff ◽  
M. Paukshto
Keyword(s):  
Variational Principle ◽  
Heat Flow ◽  
Displacement Field ◽  
Elastic Energy ◽  
Rigid Inclusion ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Practical Method ◽  
Cosserat Spectrum ◽  
Thermoelastic Displacement

We apply the Cosserat Spectrum theory to boundary value problems in thermoelasticity and show the advantages of this method. The thermoelastic displacement field caused by a general heat flow around a spherical rigid inclusion is calculatedand the results show that the discrete Cosserat eigenfunctions converge fast and thus provide a practical method for solving three-dimensional problems in thermoelasticity. In the case of uniform heat flow, the solution is obtained analytically in closed form and a variational principle within the frame of the Cosserat Spectrum theory shows that the solution maximizes the elastic energy.

SIMULATION OF TURBULENT FLOW IN A COMPLEX PASSAGE WITH A VIBRATING STRUCTURE BY FINITE ELEMENT FORMULATIONS

2009 ◽  
Vol 23 (03) ◽  
pp. 257-260 ◽  
Author(s):  
L. X. ZHANG ◽  
Y. GUO
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Turbulent Flow ◽  
Numerical Computation ◽  
Fluid Structure Interaction ◽  
Coupling Method ◽  
Generalized Variational Principle ◽  
Structure Interaction ◽  
Computing Effort ◽  
Finite Element Formulations

A modeling of the turbulent flow in a complex passage with dynamical fluid-structure interaction (FSI) is established on the generalized variational principle. A monolithic coupling method on the finite element formulations (FEM) is used to realize numerical computation of the flow with dynamical FSI. The comparisons with LES show that the results on the FEM formulations suggested in this paper are favorable, and the computing effort is economical.

scholarly journals Three-Dimensional Inviscid Flow Computations in a Spatial Turbopump Inducer Using a Distributed Loss Model

1992 ◽  
Author(s):  
E. M. El Ghazzani ◽  
G. Bois ◽  
P. Geai ◽  
F. Leboeuf
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Euler Equations ◽  
Flow Model ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Rotational Part ◽  
Inviscid Flow Model

A Clebsch formulation, completely equivalent to the Euler equations is implemented from an Eulerian type variational principle. It leads to the decomposition of the velocity field into a potential and a rotational part and, thus, provides a unified solution scheme for potential and Euler equations. Although based on an inviscid flow model, this formulation includes a loss scheme. The numerical method uses a finite element discretization. Particular treatment of convection terms allows a low numerical diffusion. A pseudo time evolution enables a better stability behaviour. Numerical calculations have been performed on an industrial configuration of spatial turbopump. Different comparisons ere showed between measurements, calculations without and with distributed losses.

Unloading Process in Elastic-Plastic Contact of a Rough Surface With a Flat

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Finite Element ◽  
Rough Surface ◽  
Contact Force ◽  
Contact Area ◽  
Three Dimensional ◽  
Integral Form ◽  
Real Contact Area ◽  
Elastic Plastic ◽  
Real Contact ◽  
Approximate Equations

Three dimensional elastic-plastic contact of a nominally flat rough surface and a flat is considered. The asperity level Finite Element based constitutive equations relating contact force and real contact area to the interference is used. The statistical summation of asperity interaction during unloading phase is derived in integral form. Approximate equations are found that describe in closed form contact load as a function of mean plane separation during unloading. The approximate equations provide accuracy to within 6 percent for the unload phase of the contact force.

Coupling of finite element method and integral formulation for vector Helmholtz equation

2018 ◽  
Vol 37 (4) ◽  
pp. 1405-1417
Author(s):  
Sebastian Grabmaier ◽  
Matthias Jüttner ◽  
Wolfgang Rucker
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Formulation ◽  
The Finite Element Method ◽  
Content Type ◽  
Wide Range ◽  
Element Method

Purpose Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering. Design/methodology/approach The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation. Findings Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model. Research limitations/implications This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately. Practical implications This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications. Originality/value The novelty of the paper is the proposed formulation for the coupling of both methods.

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