Partial Interaction Analysis of Composite Beams by Means of the Finite Difference Method, the Finite Element Method, the Direct Stiffness Method and the Analytical Solution: A Comparative Study

2009 ◽  
Author(s):  
G. Ranzi ◽  
M.A. Bradford ◽  
F. Gar ◽  
G. Leon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Interaction Analysis ◽  
Composite Beams ◽  
The Finite Element Method ◽  
Stiffness Method ◽  
Partial Interaction ◽  
Direct Stiffness ◽  
The Finite Difference Method

Application of Finite Element Methods to Lubrication: An Engineering Approach

1972 ◽  
Vol 94 (4) ◽  
pp. 313-323 ◽  
Author(s):  
J. F. Booker ◽  
K. H. Huebner
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Finite Element Methods ◽  
Lubricant Film ◽  
The Finite Element Method ◽  
Engineering Approach ◽  
Stiffness Method ◽  
Direct Stiffness ◽  
System Properties

The finite element method of lubrication analysis is presented for the novice from a viewpoint closely analogous to that of the familiar direct stiffness method of structural analysis. The lubricant film is seen as a system of component elements interconnected at nodal points where flows are summed and pressures (but not necessarily thicknesses, viscosities, or densities) are equated. System properties are deduced from component properties and connections. Detailed equations needed for solution of practical problems are given in Appendices and their use is illustrated in Examples.

A Discussion on natural strain and geological structure - The finite element method and the solution of some geophysical problems

1976 ◽  
Vol 283 (1312) ◽  
pp. 139-151 ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Geological Structure ◽  
The Finite Element Method ◽  
Recent Developments ◽  
Limited Application ◽  
Discrete Problems ◽  
The Finite Difference Method ◽  
Made In ◽  
Element Method

The finite element method has become established as a powerful tool for the solution of many problems of continuum mechanics where its physical interpretation, by analogy with discrete problems of structural analysis permits the user to exercise a considerable degree of insight and judgement in its use. Further it is now a recognized mathematical procedure of approximation which embraces many older methodologies (such as the finite difference method) as a subclass. In the field of geological studies its impact is fairly recent and only a limited application has been made to date. The techniques used here have been limited to those established over a decade ago in the parallel fields and recent developments and possibilities barely touched upon. In this paper the author therefore attempts to ( a ) outline some of the general mathematical and practical aspects of the method with illustrations from various fields which are relevant to geological problems, ( b ) survey accomplishments already made in geology and geotechnical fields, and ( c ) suggest some possible new extensions of application.

scholarly journals Features of compressed rods calculations with account of initial imperfections and creep effects

2020 ◽  
Vol 164 ◽  
pp. 02003
Author(s):  
Viacheslav Chepurnenko ◽  
Batyr Yazyev ◽  
Ludmila Dubovitskaya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Software Package ◽  
Physical Nonlinearity ◽  
The Finite Element Method ◽  
Ansys Software ◽  
Modular Theory ◽  
Initial Imperfections ◽  
Creep Models ◽  
The Finite Difference Method

The article presents solutions to the problem of rod buckling, taking into account creep effects. Trigonometric series, the finite difference method in combination with the programming language MATLAB, as well as the finite element method in the ANSYS software package were used in the solutions. The behavior of the rods is researched for two types of relations between strain and stress during creep, with strains in an explicit and implicit form. When solving, the criterion of initial imperfections with their different values is used, as well as the tangential-modular theory. The results obtained for the two creep models are compared. The conclusion is made about the accuracy of the results of calculations in ANSYS with the presence of a combination of geometric and physical nonlinearity for various creep models.

scholarly journals The Finite Element Method Applied to the Magnetostatic and Magnetodynamic Problems

2020 ◽  
Author(s):  
Dang Quoc Vuong ◽  
Bui Minh Dinh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electric Fields ◽  
Complex Geometry ◽  
Analytic Method ◽  
The Finite Element Method ◽  
Electromagnetic Problems ◽  
Common Technique ◽  
The Finite Difference Method ◽  
Element Method

Modelling of realistic electromagnetic problems is presented by partial differential equations (FDEs) that link the magnetic and electric fields and their sources. Thus, the direct application of the analytic method to realistic electromagnetic problems is challenging, especially when modeling structures with complex geometry and/or magnetic parts. In order to overcome this drawback, there are a lot of numerical techniques available (e.g. the finite element method or the finite difference method) for the resolution of these PDEs. Amongst these methods, the finite element method has become the most common technique for magnetostatic and magnetodynamic problems.

Sharpening of metal sheets during electrochemical polishing. Theory and experiments

1984 ◽  
Vol 49 (5) ◽  
pp. 1267-1276
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference Method ◽  
The Finite Element Method ◽  
Electrochemical Polishing ◽  
Electrochemical Parameters ◽  
Metal Sheets ◽  
The Finite Difference Method ◽  
Shape Changes ◽  
Theory And Experiments

The electrochemical polishing with simultaneous shape changes of anodes was studied. A theory was derived based on the knowledge of basic electrochemical parameters and the solution of the Laplace equation. To this purpose, the finite element method and the finite difference method with a double transformation of the inter-electrode region were employed. Only the former method proved well and can therefore be recommended for different geometries.

HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION

2001 ◽  
Vol 09 (02) ◽  
pp. 671-680 ◽  
Author(s):  
W. A. MULDER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Finite Elements ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
The Finite Element Method ◽  
Efficient Scheme ◽  
The Finite Difference Method

The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.

Comparation of Numerical Methods for Calculation of Thin Slabs

2014 ◽  
Vol 969 ◽  
pp. 73-77 ◽  
Author(s):  
Oldrich Sucharda ◽  
Jan Kubosek
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Concrete Slabs ◽  
The Finite Element Method ◽  
Thin Slab ◽  
Calculation Methods ◽  
Element Mesh ◽  
Internal Forces ◽  
The Finite Difference Method ◽  
Element Method

The purpose of this paper is to compare calculation of internal forces and deformations of slabs for two calculation methods: the finite element method and the finite difference method. Two concrete slabs have been analysed. In the case of the finite element method, different element mesh are used, providing, thus, solutions in different variants. The calculation and algorithms is based on a thin slab theory. Variants calculate in program Scia Engineer effects of shearing forces by means of the Midlins theory or thin slab theory. Algorithms for the calculation were developed in Matlab.

An Analytical Solution for Stress and Displacement in Casing-Cement Combined Cylinder under Non-Uniform Loading

2011 ◽  
Vol 291-294 ◽  
pp. 2133-2138 ◽  
Author(s):  
Mu Hui Fan ◽  
Yong Shu Jiao ◽  
Zong Xi Cai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Computer Program ◽  
Theory Of Elasticity ◽  
Composite Cylinder ◽  
The Finite Element Method ◽  
Uniform Loading ◽  
Cement Sheath ◽  
Good Agreement

Based on the theory of elasticity and taken the casing-cement sheath as a totally contacted composite cylinder subjected to arbitrarily distributed loading on inner and outer surfaces, an analytical solution in Fourier serial form was obtained for stresses and displacements. A computer program was developed to evaluate the stress and displacement in the combined cylinder. The results are in good agreement with those from the finite element method (FEM). With these solutions we can investigate the interaction between casing and the cement sheath. This is of importance in improving the design of casing.

scholarly journals The optimal dimensions of the domain for solving the single-band Schrödinger equation by the finite-difference and finite-element methods

2014 ◽  
Vol 11 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Dusan Topalovic ◽  
Stefan Pavlovic ◽  
Nemanja Cukaric ◽  
Milan Tadic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Element Methods ◽  
Ground State ◽  
Difference Method ◽  
Grid Size ◽  
The Finite Element Method ◽  
The Finite Difference Method

The finite-difference and finite-element methods are employed to solve the one-dimensional single-band Schr?dinger equation in the planar and cylindrical geometries. The analyzed geometries correspond to semiconductor quantum wells and cylindrical quantum wires. As a typical example, the GaAs/AlGaAs system is considered. The approximation of the lowest order is employed in the finite-difference method and linear shape functions are employed in the finite-element calculations. Deviations of the computed ground state electron energy in a rectangular quantum well of finite depth, and for the linear harmonic oscillator are determined as function of the grid size. For the planar geometry, the modified P?schl-Teller potential is also considered. Even for small grids, having more than 20 points, the finite-element method is found to offer better accuracy than the finite-difference method. Furthermore, the energy levels are found to converge faster towards the accurate value when the finite-element method is employed for calculation. The optimal dimensions of the domain employed for solving the Schr?dinger equation are determined as they vary with the grid size and the ground-state energy.

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