Finite strip with a central crack under tension

In this study, a symmetrical finite strip with a length of 2L and a width of 2h, containing a transverse symmetrical crack of width 2a at the midplane is considered. Two rigid plates are bonded to the ends of the strip through which uniformly distributed axial tensile load of magnitude 2hp₀ is applied. The material of the strip is assumed to be linearly elastic and isotropic. Both edges of the strip are free of stresses. Solution for this finite strip problem is obtained by means of an infinite strip of width 2h which contains a crack of width 2a at y = 0 and two rigid inclusions of width 2c at y = ±L and which is subjected to uniformly distributed axial tensile load of magnitude 2hp₀ at y = ±∞. When the width of the rigid inclusions approach the width of the strip, i.e., when c → h, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. Fourier transform technique is used to solve the governing equations which are reduced to a system of three singular integral equations. By using the Gauss–Jacobi and the Gauss–Lobatto integration formulas, these integral equations are converted to a system of linear algebraic equations which is solved numerically. Normal and shearing stress distributions and the stress intensity factors at the edges of the crack and at the corners of the finite strip are calculated. Results are presented in graphical and tabular forms.