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Boundary integral equations for an anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities

Sulym H., Pasternak I., Tomashivskyy M.

Acta Mechanica et Automatica

2016

Vol. 10, no. 1

66--74

This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant interfacial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

An Elastic Membrane With an Attached Non-Linear Thermoelastic Rod

Horn W., Sokołowski J.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no. 4

479-486

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain W is subset R2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence of a unique global weak solution to this problem using a fixed point argument.