Three-Dimensional Analysis of Axisymmetric Transient Waves in Hollow Elastic Cylinders

1984 ◽  
Vol 51 (4) ◽  
pp. 792-797 ◽  
Author(s):  
P.-A. Sva¨rdh
Keyword(s):  
Integral Transform ◽  
Three Dimensional ◽  
Step Function ◽  
Necessary Condition ◽  
Asymptotic Result ◽  
Axially Symmetric ◽  
Transient Waves ◽  
Linear Elastic ◽  
Elastic Cylinders ◽  
Integral Transform Technique

The axially symmetric problem of a semi-infinite, hollow, linear-elastic circular cylinder with traction-free lateral surfaces initially at rest and subjected to transient end loadings is solved using three-dimensional theory. Two cases are treated: an axial pressure applied to a radially clamped end and a prescribed axial velocity applied to an end that is free from shear stress. A double integral transform technique is used, and asymptotic solutions valid at large distances from the end are given for two types of time variation of the end loadings: step function and finite rise time function. A necessary condition for the validity of the asymptotic result is given.

Thermal Math Modeling and Analysis of an Electronic Assembly

2000 ◽  
Vol 123 (4) ◽  
pp. 372-378 ◽  
Author(s):  
K. N. Shukla
Keyword(s):  
Temperature Distribution ◽  
Integral Transform ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Circuit Board ◽  
Heat Sources ◽  
The Finite Element Method ◽  
Modeling And Analysis ◽  
Discrete Surface ◽  
Integral Transform Technique

This paper presents a mathematical model for a three-dimensional thermal analysis of a circuit board with multiple heat dissipating sources. The model considers the three-dimensional flat plate with discrete surface heat sources and integral transform technique is employed to determine the temperature distribution. The calculation procedure for the thermal characteristics of a circuit board, with surface mounted components, is presented and the solution is compared with those obtained from the finite element method. Also, the temperature distribution of a two-layered circuit board is presented in terms of Green’s function.

scholarly journals FIRST PRINCIPLES DERIVATION OF A STRESS FUNCTION FOR AXIALLY SYMMETRIC ELASTICITY PROBLEMS, AND APPLICATION TO BOUSSINESQ PROBLEM

2017 ◽  
Vol 36 (3) ◽  
pp. 767-772
Author(s):  
CC Ike
Keyword(s):  
First Principles ◽  
Stress Function ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Solution Process ◽  
Point Load ◽  
Axially Symmetric ◽  
Boussinesq Problem ◽  
Linear Elastic ◽  
Elasticity Problems

In this work, a stress function is derived from first principles to describe the behaviour of three dimensional axially symmetric elasticity problems involving linear elastic, isotropic homogeneous materials. In the process, the fifteen governing partial differential equations of linear isotropic elasticity were reduced to the solution of the biharmonic problem involving the stress function. thus simplifying the solution process. The stress function derived was found to be identical with the Love stress function. The stress function was then applied to solve the axially symmetric problem of finding the stress fields, strain fields and displacement fields in the semi-infinite linear elastic, isotropic homogeneous medium subject to a point load P acting at the origin of coordinates also called the Boussinesq problem. The results obtained in this study for the stresses and displacements were exactly identical with those from literature, as obtained by Boussinesq.http://dx.doi.org/10.4314/njt.v36i3.15

Integral Transforms for Three-Dimensional Steady Turbulent Dispersion in Rivers and Channels

2005 ◽  
Author(s):  
Felipe P. J. de Barros ◽  
Renato M. Cotta
Keyword(s):  
Turbulent Flows ◽  
Integral Transform ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Computational Effort ◽  
Velocity Fields ◽  
Turbulent Dispersion ◽  
Test Case ◽  
Solution Convergence ◽  
Integral Transform Technique

A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flows. The model allows for variable velocity fields and non-uniform turbulent diffusivities. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical-analytical solution is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the double eigenfunction expansion. A test case is presented to illustrate the proposed approach.

Contact Stresses Between Elastic Cylinders: A Comprehensive Theoretical and Experimental Approach

1981 ◽  
Vol 103 (1) ◽  
pp. 40-45 ◽  
Author(s):  
M. J. Hartnett ◽  
J. W. Kannel
Keyword(s):  
Experimental Approach ◽  
Three Dimensional ◽  
Contact Stresses ◽  
Linear Elastic ◽  
Theoretical Predictions ◽  
Elastic Cylinders ◽  
Force Displacement ◽  
Contact Pressures ◽  
Two Bodies ◽  
Theory And Experiments

The purpose of the paper has been to present a comparison of theoretical predictions and experimental data for contact stresses between two bodies lubricated in contact. The theoretical analysis is based on a three-dimensional linear elastic solution to the problem and combines Boussinesq force-displacement relationships for a half-space with a modified flexibility method. The experimental approach involves the direct measurement of contact pressures between profiled rollers using a thin-film pressure transducer. Pressure measurements and predictions were made for three roller designs under various conditions of loads and misalignments. The agreement between theory and experiments is very good.

scholarly journals Three-Dimensional Unsteady State Temperature Distribution of Thin Rectangular Plate with Moving Point Heat Source

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yogita M. Ahire ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Heat Source ◽  
Rectangular Plate ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Three Dimensional ◽  
Unsteady State ◽  
Point Heat Source ◽  
Thin Rectangular Plate ◽  
Special Case ◽  
Integral Transform Technique

This paper deals with the study of thermal stresses in thin rectangular plate subjected to point heat source which changes its place along x-axis. Governing heat conduction equation has been solved by using integral transform technique. Results are obtained in the form of infinite series. As a special case, aluminum plate has been considered and results for thermal stresses have been computed numerically and graphically.

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