This paper discusses a method for solving three-dimensional mixed-boundary-value problems which arise in elastostatics. Specifically, the method is applied to a plate of finite thickness which contains a finite, through the thickness, line crack. The analysis shows that (a) in the interior of the plate only the stresses σx, σy, σz, τxy are singular of order 1/2; (b) in the vicinity of the corner point all the stresses are singular of order |(1/2) + 2ν|; (c) as the thickness h → ∞ the plane strain solution is recovered and; (d) as ν → 0 the plane stress solution is recovered. Finally, it is found that in the neighborhood of the corner points, even though the displacements are singular for certain values of the Poisson’s ratios, the derived stress field satisfies the condition of local finite energy.

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