Stress intensity factors of a rhombic hole with symmetric cracks under uniform transverse thin plate bending

A thin plate bending problem (Kirchhoff thin plate) is solved analytically for an infinite plate with a rhombic hole with symmetric cracks at the both corners. The loading is a uniform transverse bending at infinity. The stress distribution and the stress intensity factors of the bending are obtained for a range of corner angles and crack lengths of the rhombic hole. Approximate expressions of the stress intensity factor are proposed for some corner angles and Poisson's ratios using the stress distribution expressed by the roots of the characteristic equation of the sharp notched plate before the crack initiation. The precision of the expressions are investigated. Characteristic factors for the approximate expressions are stated. A rational mapping function of a sum of fractional expressions and complex stress functions are used for the stress analysis.