Spatial stability and free vibration of shear flexible thin-walled elastic beams. II: Numerical approach

In a companion paper,1 equations of motion and closed-form solutions for spatial stability and free vibration analysis of shear flexible thin-walled elastic beams were analytically derived from the linearized Hellinger–Reissner principle. In this paper, elastic and geometric stiffness matrices and consistent mass matrix for finite element analysis are evaluated by using isoparametric and Hermitian interpolation polynomials. Isoparametric interpolation functions with 2, 3 and 4 nodes per element are utilized in isoparametric beam elements, and in Hermitian beam elements, the third- and fifth-order Hermitian polynomials including shear deformation effects are newly derived and applied for the calculation of element matrices. In order to verify the validity of the finite element formulation, both analytic and numerical solutions for spatial buckling and free vibration problems including shear effects are presented and compared.

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