On a plane problem of thermoelasticity for the composite rectangule with cracks

Р. Алексанян ; M. K. Saghatelian

Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1985), pp. 47-50

Résumé

The problem of plane strain thermoelasticity is considered for a rectangle containing a symmetrically located circular inclusion and having four cracks. Two of these cracks are located along the $x$ axis and are symmetrical with respect to the $y$ axis, and the other two are located along the $y$ axis and are symmetrical with respect to the $x$ axis. The cracks do not cross the circular inclusion and start from the edges of the rectangle. The materials of the rectangle and the inclusion have the same elastic characteristics, but different coefficients of linear thermal expansion. A rectangle with an inclusion is subjected to a uniform change in temperature. The hermoelastic problem reduces to solving an equivalent elastic mixed problem for a rectangle, which in turn reduces to solving quasi-completely regular infinite systems of linear algebraic equations. The paper also considers a particular problem when a rectangle has two cracks symmetrical about the $y$ axis and located along the $x$ axis.