Using a Fourier integral transform, the problem of a cracked plate, of an arbitrary thickness 2h and subjected to a uniform external load of mode I, is reduced to that of the solution of a two-dimensional singular integral equation. * This method was fully articulated by M.L. Williams [1] for classical planar elasticity in order to establish the singular behavior at re-entrant corners. ** That is the point where the crack front meets the free surface of the half space. 0376-9429/80/040335-14500.20/0 Int. Journ. of Fracture, 16 (1980) 335-348 * The reader should note that this result was actually obtained by 'marching out' the solution from the inner to the outer layers, and as a result such a hypothesis may not be totally unreasonable. See also comments on p. 5. ** See Discussion of paper by Benthem and Koiter [5] and author's Closure [6]. *** Mathematically, Kawai's method of construction of the solution is more systematic than that of Benthem's. **** This is not to be confused with the question of completeness of the solution to Navier's equations, i.e. Eqns. (52)-(54) Ref. [4]. The corrected result to (85) of [4] is given in Appendix I.
* The first few roots are tabulated in Appendix II. ** Notice that the derivative of ( 27) with respect to z leads to the integrand of ( 22).