Analytical solutions of transient hygrothermal stresses in elastic bodies

1986 ◽  
pp. 47-88
Author(s):  
G. C. Sih ◽  
J. G. Michopoulos ◽  
S. C. Chou
Keyword(s):  
Analytical Solutions ◽  
Elastic Bodies

scholarly journals Stress fields around two pores in an elastic body: exact quadrature domain solutions

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150240
Author(s):  
Darren Crowdy
Keyword(s):  
Elastic Body ◽  
Analytical Solutions ◽  
Plane Elasticity ◽  
Stress Fields ◽  
Quadrature Domain ◽  
Mathematical Approach ◽  
Quadrature Domains ◽  
Planar Domains ◽  
Elastic Bodies ◽  
Prime Function

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

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