Approximate method of solving boundary-value problems of elasticity theory for figures near ellipsoids of revolution

1970 ◽  
Vol 6 (9) ◽  
pp. 939-944 ◽  
Author(s):  
Yu. N. Podil'chuk
Keyword(s):  
Boundary Value Problems ◽  
Approximate Method ◽  
Elasticity Theory ◽  
Boundary Value

Some Mixed Boundary-Value Problems of the Semi-Infinite Strip

1957 ◽  
Vol 24 (2) ◽  
pp. 261-268
Author(s):  
G. Horvay ◽  
J. S. Born
Keyword(s):  
Shear Stress ◽  
Boundary Value Problems ◽  
Approximate Method ◽  
Normal Stress ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Normal Displacement ◽  
Infinite Strip ◽  
Elastic Strip ◽  
Variational Solutions

Abstract Rigorous and approximate (variational) solutions are given for the semi-infinite elastic strip, traction-free along the long edges, when the short edge is subjected (a) to a quadratic shear displacement, zero normal stress, (b) to a cubic normal displacement, zero shear stress. The approximate method of self-equilibrating functions is extended.

IX.—The Propagation of Thermal Stresses in Thin Metallic Rods

1959 ◽  
Vol 65 (2) ◽  
pp. 121-142 ◽  
Author(s):  
I. N. Sneddon
Keyword(s):  
Boundary Value Problems ◽  
Approximate Method ◽  
Finite Length ◽  
Thermal Stresses ◽  
Boundary Value ◽  
Elastic Rod ◽  
Time Dynamic ◽  
Simple Waves ◽  
Set Up

SynopsisIf the temperature in an elastic rod is not uniform and if it varies with time, dynamic thermal stresses are set up in the rod. This paper is concerned with the calculation of the distribution of temperature and stress in an elastic rod when its ends are subjected to mechanical or thermal disturbances. Simple waves in an infinite rod are first discussed and then boundary value problems for semi-infinite rods and rods of finite length. The paper concludes with an account of an approximate method of solving the equations of thermoelasticity.

scholarly journals Boundary value problems for the Lamé-Navier system in fractal domains

2021 ◽  
Vol 6 (10) ◽  
pp. 10449-10465
Author(s):  
Ricardo Abreu Blaya ◽  
◽  
J. A. Mendez-Bermudez ◽  
Arsenio Moreno García ◽  
José M. Sigarreta ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Representation Formula ◽  
Linear Elasticity Theory ◽  
Fractal Domains

<abstract><p>The aim of this paper is to establish a representation formula for the solutions of the Lamé-Navier system in linear elasticity theory. We also study boundary value problems for such a system in a bounded domain $ \Omega\subset {\mathbb R}^3 $, allowing a very general geometric behavior of its boundary. Our method exploits the connections between this system and some classes of second order partial differential equations arising in Clifford analysis.</p></abstract>

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