The cross-section properties of a beam is characterized by a six by six stiffness matrix, relating the six generalized strains to the conjugate section forces. The problem is formulated as a single-layer finite element model of a slice of the beam, on which the six deformation modes are imposed via Lagrange multipliers. The Lagrange multipliers represent the constraining forces, and thus combine to form the cross-section stiffness matrix. The theory is illustrated by a simple isotropic cross-section.
Proceedings of the 26th Nordic Seminar on Computational Mechanics, 2013