Problems of cuts in a composite elastic wedge

✍ Scribed by V.M. Aleksandrov; D.A. Pozharskii

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 304 KB
• Volume: 73
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2009.03.003

✦ Synopsis

Problems of strip and elliptical cuts (tensile cracks) in the middle of a three-layer elastic wedge are investigated in a three-dimensional formulation. Free or rigid clamping conditions or the stress-free condition are stipulated on the outer surfaces of the composite wedge. The problems are assumed to be symmetrical about the plane of the cut. The wedge-shaped layer containing the cut is incompressible and hinged along both faces with two other layers. The integral equations of the problems with respect to the opening of the cut are derived. Inverse operators are obtained for the operators occurring in the kernels of these equations. The relation between problems on cuts and the corresponding contact problems for a composite wedge of half the aperture angle is used. The method of paired integral equations is used for the case of a strip cut emerging from the edge of the wedge. The problems are reduced to Fredholm integral equations of the second kind in certain auxiliary functions, in terms of the values of which the normal stress intensity factors are expressed. A regular asymptotic solution is constructed for the case of an elliptic cut.