Mixed finite-element method in V.I. Slivker’s semi-shear thin-walled bar theory

Mixed variational formulation of static and dynamic problems for thin-walled beams is presented. Stiffness and mass matrixes are derived from the Reissner-like functional. Shear deformation is taken into account by using Slivker’s semi-shear theory of thin-walled bars. Corresponding Euler equations are derived from the proposed mixed functional. Linear Hermite polynomials were considered as approximation for all the internal forces and displacements functions. The exact analytical solutions to some particular eigenfrequency and static problems for thin-walled beam are obtained from mixed formulation. The effect of “spurious” frequencies in thin-walled beam spectrum is discussed. Comparison of the numerical results from the mixed and classical finite element methods is presented.