General beam cross-section analysis using a 3D finite element slice

A formulation for analysis of general cross-section properties has been developed. This formulation is based on the stress-strain states in the classic six equilibrium modes of a beam by considering a finite thickness slice modelled by a single layer of 3D finite elements. The displacement variation in the lengthwise direction is in the form of a cubic polynomial, which is here represented by Hermitian interpolation, whereby the degrees of freedom are concentrated on the front and back faces of the slice.

The theory is illustrated by application to a simple cross-section for which an analytical solution is available. The paper also shows an application to wind turbine blade cross-sections and discusses the effect of the finite element discretization on the cross-section properties such as stiffness parameters and the location of the elastic and shear centers.