Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements

• Determination of full set of cross-section parameters for Vlasov beam theory.
• Efficient modeling by cubic-linear isoparametric element.
• Procedure described in terms of vector–matrix multiplications.
• Solution for warping functions and stress distributions.

In technical beam theory the six equilibrium states associated with homogeneous tension, bending, shear and torsion are treated as individual load cases. This enables the formulation of weak form equations governing the warping from shear and torsion. These weak form equations are solved numerically by introducing a cubic-linear two-dimensional isoparametric element. The cubic interpolation of this element accurately represents quadratic shear stress variations along cross-section walls, and thus moderately thin-walled cross-sections are effectively discretized by these elements. The ability of this element to represent curved geometries, and to accurately determine cross-section parameters and shear stress distributions is demonstrated.