Lekhnitskii’s Formalism for Stress Concentrations Around Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary Conditions

Abstract

Considering analytical methods in anisotropic elasticity, the complex potentials method (as extensively formulated by Lekhnitskii) may be regarded as a powerful tool. Among the various solutions generated by this approach, the analysis of thin anisotropic plates containing a geometrically simple irregularity is the most classical one as it reflects on an extensive collection of structures: from pinloaded holes to cutouts in aircraft fuselages. In this chapter we outline the complete solution for this particular geometry where the boundary conditions on the edge of the irregularity (forces or displacements) are formulated in Fourier series. The analytical solutions provided here can directly be evaluated as a function of the external boundary loads and the coefficients in the Fourier series, which represent the boundary conditions at the edge of the irregularity. Therefore, the analytical solutions provided here are able to cover a large variety of structural problems. Although Lekhnitskii’s formalism may be regarded as a well-established solution procedure, the availability of engineering-oriented, directly implementable solutions is rather limited. In this chapter we attempt to fill this gap.