This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.
THE SOLUTION OF A VARIABLE BOUNDARY PROBLEM
Copyright 2007
August 16 2007
NOTE:
This worksheet demonstrates Maple's capabilities in researching the numerical and graphical solution of the variable boundary problem of a thick-walled cylinder of material enclosed in a thin metallic shell .
All rights reserved. Copying or transmitting of this material without the permission of the authors is not allowed .
Abstract :
The relations between stress and strain in linear viscoelastic theory are discussed from the viewpoint of application to problems of stress analysis. This consideration includes some important differences from the estimation of linear viscoelastic laws for the representation of material properties , and the integral operators expressing the creep function or relaxation function can be applied . By using of the differential operator for the relation between stress and strain it is usually most convenient to solve some problems which have the variable boundary .
REFERENCES
[1] ю.н. РАБОТНОВ , Пoлзyчесть элементов конструкций , издательство “наука” , MOCKBA 1966
[2] Lee E .H ., Radok J.R.M., Woodward W.B., Stress Analysis for Linear Viscoelastic Materials , Trans. Soc. Rheol., 3, 41-59 (1959)
Disclaimer: While every effort has been made to validate the solutions in this worksheet, the author is not responsible for any errors contained and are not liable for any damages resulting from the use of this material.
Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities.
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.
-------------------------------------------------------------------------------------------
Toán học thuần túy, theo cách của riêng nó, là thi ca của tư duy logic.
Pure mathematics is, in its way, the poetry of logical ideas.
Albert Einstein .
[0] Two topics that we will be in discussion are - Finding the steady state solution of this equation by averaging method .- Estimating the stability of solution obtained . 1 .Define the model of problem : We examine the effect of non-linear system under external force caused by the AC generator ( see fig 1. )
( fig 1. ) The differential equation of this model is given in the form 
+ 
[1] After simplifying we obtain : 
[2] 
