Singularities in elasticity and their treatment with Fourier series

Abstract

AbstractThis paper analyses the regularity of the weak solution of the linear elasticity system in three‐dimensional axisymmetric domains with reentrant edges under prescribed traction on the boundary by means of Fourier series. Using partial Fourier analysis with respect to one space direction (rotational angle), the three‐dimensional boundary value problem (BVP) is decomposed into a sequence of decoupled two‐dimensional boundary value problems on the meridian of the axisymmetric domain. The splitting of the 2D solutions near corners of the meridian domain into regular and singular parts provides coefficients from which the 3D edge singularity functions (generalized stress intensity factors) are derived. Two types of singularity functions are presented, namely, a tensorial type, which needs more smoothness assumption on the right hand side and a non‐tensorial type, which does not demand any further smoothness assumptions.