Solution of the Kirsch problem for a binary mixture in the case of approximation \(N=1\) of Vekua’s theory. (English) Zbl 1425.74128

Janjgava, Roman

Math. Mech. Solids 24, No. 7, 2017-2029 (2019).

Summary: We consider a boundary value problem for an infinite plate with a circular hole. The plate is the mixture of two isotropic elastic materials. The hole is free from stresses, while unilateral tensile stresses act at infinity. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic binary mixture (Green-Naghdi-Steel model) by Vekua’s reduction method. The problem is solved analytically by the method of the theory of functions of a complex variable.

MSC:

74E30	Composite and mixture properties
74B05	Classical linear elasticity
74S70	Complex-variable methods applied to problems in solid mechanics

Keywords:

binary mixture; infinite plate with a circular hole; I Vekua’s theory of plates; Kirsch problem; analytical solution