Closed‐form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti‐plane shear

A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading. For four frequently encountered constraint edges, i.e. free‐free, clamped‐clamped, free‐clamped, or clamped‐free edges, the Fourier series method is used to reduce triple series equations, and then to a mixed boundary value problem associated with a mode‐III crack for each case to a singular integral equation. Closed‐form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading. Numerical results of the stress intensity factors for an eccentric, central, and edge crack are shown graphically for the case of uniform loading at the crack faces. Obtained formulae for determining stress intensity factors can be taken as a benchmark of numerical evaluations. The derived results are also applicable to an isotropic elastic strip with an anti‐plane shear crack normal to the edges.