Finite Element Solution for the Rarefied Gas Lubrication Problem

1988 ◽  
Vol 110 (2) ◽  
pp. 335-341 ◽  
Author(s):  
Masahiro Kubo ◽  
Y. Ohtsubo ◽  
N. Kawashima ◽  
H. Marumo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Finite Width ◽  
Pressure Equation ◽  
Linearized Boltzmann Equation ◽  
The Boltzmann Equation ◽  
Element Method

This paper is useful in analyzing the performance of finite-width-air bearings in the rarefied gas region, using a newly developed finite element method. The linearized Boltzmann equation was solved by numerical iteration and a pressure equation was obtained, coupled with a continuous equation. The finite element method was developed for solving the pressure equation. The results were compared with a two moment approximate solution for the Boltzmann equation, which corresponds to the conventional slip flow analysis developed by Burgdorfer. An analysis of tapered flat slider flying characteristics in the rarefied gas regime, e.g., when the inverse Knudsen number in the trailing edge = 1, showed that the present exact solution for the Boltzmann equation was different from the two moment approximate solution by more than 10 percent in load capacity value, when the dimensionless load was not so large as when it is used for actual slider design.

A finite element solution technique for the Boltzmann equation

1970 ◽  
Vol 42 (1) ◽  
pp. 177-191 ◽  
Author(s):  
T. Taz Bramlette ◽  
Robert H. Mallett
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boltzmann Equation ◽  
Finite Elements ◽  
Solution Technique ◽  
Algebraic Models ◽  
Numerical Predictions ◽  
The Boltzmann Equation ◽  
Viscous Shear ◽  
Element Method

A new method is presented for solution of the Boltzmann equation governing the dynamic behaviour of gases. The essence of the method is idealization of the problem domain into subdomains called finite elements. Then, the Galerkin assumed-mode technique is employed as the basis for discretization of the individual finite elements and also for the assembly of the resulting algebraic models for these finite elements to form an algebraic model for the complete problem. The procedure is cast in a systematic matrix notation that makes evident the broad application potential of the analysis method. An illustrative application is presented for the problem of one-dimensional, linearized Couette flow. Numerical predictions of macroscopic flow velocity and viscous shear stress based upon the subject finite element method are compared with alternative analytical and numerical results. Special attributes of the finite element method are discussed in the context of this example problem. Applications to practical problems governed by generalized forms of the Boltzmann equation are projected on the basis of concepts established herein.

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

An Extrapolation Method to Compute Far-Field Pressures From Near-Field Pressures Obtained by Finite Element Method

1995 ◽  
Author(s):  
Jamal Assaad ◽  
Christian Bruneel ◽  
Jean-Michel Rouvaen ◽  
Régis Bossut
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Near Field ◽  
Radiation Condition ◽  
Directivity Pattern ◽  
Extrapolation Method ◽  
External Boundary ◽  
Finite Width ◽  
Far Field ◽  
Element Method

Abstract The finite element method is widely used for the modeling of piezoelectric transducers. With respect to the radiation loading, the fluid is meshed and terminated by an external nonreflecting surface. This reflecting surface can be made up with dipolar damping elements that absorb approximately the outgoing acoustic wave. In fact, with dipolar dampers the fluid mesh can be quite limited. This method can provides a direct computation of the near-field pressure inside the selected external boundary. This paper describes an original extrapolation method to compute far-field pressures from near-field pressures in the two-dimensional (2-D) case. In fact, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition, the far-field directivity pattern can be expressed in terms of the near-field directivity pattern. These developments are valid for any radiation problem in 2D. One test example is described which consists of a finite width planar source mounted in a rigid or a soft baffle. Experimental results concerning the far-field directivity pattern of lithium niobate bars (Y-cut) are also presented.

Rayleigh-Ritz Based Substructure Synthesis for Multiply Supported Structures

1998 ◽  
Vol 122 (1) ◽  
pp. 2-6 ◽  
Author(s):  
C. Morales
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Synthesis Method ◽  
The Finite Element Method ◽  
Compatibility Conditions ◽  
Substructure Synthesis ◽  
Stiffness Matrices ◽  
Element Method

This paper is concerned with the convergence characteristics and application of the Rayleigh-Ritz based substructure synthesis method to structures for which the use of a kinematical procedure taking into account all the compatibility conditions, is not possible. It is demonstrated that the synthesis in this case is characterized by the fact that the mass and stiffness matrices have the embedding property. Consequently, the estimated eigenvalues comply with the inclusion principle, which in turn can be utilized to prove convergence of the approximate solution. The method is applied to a frame and is compared with the finite element method. [S0739-3717(00)00201-4]

Two-Scale Algorithm for Computing the Approximation of the Displacement in Periodic Perforated Structure of Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1226-1229
Author(s):  
Ming Xiang Deng ◽  
Yong Ping Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Higher Order ◽  
New Method ◽  
Approximation Solution ◽  
Scale Method ◽  
Small Periodic ◽  
Element Method

By means of two-scale method, the approximation solution of the displacement for structure of composites with small periodic perforated configuration is built, and the algorithm corresponding to two-scale finite element method is presented. One new method of higher order for computing approximate solution of the displacement in periodic perforated composites is given.

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