Basic solution of a plane rectangular crack in a 3-D infinite orthotropic elastic material

• A plane rectangular crack in a 3-D orthotropic material is firstly analyzed by using the generalized Almansi's theorem and the Schmidt method.
• The material properties and the constitutive equations are different from other literatures.
• The effects of the geometric shape of the rectangular crack on the stress intensity factors are concluded.

The solution of a plane rectangular crack in a 3-D infinite orthotropic elastic material is investigated by means of the generalized Almansi's theorem and the Schmidt method in the present paper. By using the 2-D Fourier transform and defining the jumps of displacement components across the crack surfaces as the unknown variables, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are directly expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack on the stress intensity factors in an orthotropic elastic material.