Logarithmic stress singularities at clamped-free corners of cantilever orthotropic beam under flexure

The rectangular orthotropic beam under flexure is studied by decomposing the problem into an interior problem and a boundary problem. The interior problem is required to satisfy field equations and boundary conditions at the lateral faces, whereas the boundary conditions at the beam ends are imposed in the average sense. The boundary problem, which reestablishes the pointwise boundary conditions at the beam ends, is solved via eigenfunction expansion under the assumption of transverse inextensibility. It is shown that logarithmic stress singularities are present at the corners of the clamped end section and the corresponding stress-intensity factor is computed.