Beam section stiffness properties using a single layer of 3D solid elements

• Determination of full six-by-six beam cross-section stiffness matrix.
• 3D finite element model using finite thickness slice of the beam.
• Procedure described in terms of vector–matrix operations.
• Valid for both solid and thin-walled beams and general anisotropic materials.

A method is presented for analysis of the properties of general cross-sections with arbitrary geometry and material distribution. The full six by six cross-section stiffness matrix is evaluated from a single element thickness slice represented by 3D solid elements with lengthwise Hermitian interpolation with six independent imposed deformation modes corresponding to extension, torsion, bending and shear. The flexibility matrix of the slice is obtained from complementary elastic energy, and the stiffness matrix is obtained by extracting and inverting the cross-section flexibility. Three examples illustrate the accuracy of the method for solid and thin-walled sections with isotropic and general anisotropic materials.