A two-dimensional consistent approach for static and dynamic analyses of uniform beams

A unified technique based on the scaled boundary finite element method is presented in this paper to analyze the bending, free vibration and forced vibration of thin to moderately thick beams with constant material properties and rectangular cross sections. The structure model is treated as a plane stress problem and the principle of virtual work involving the inertial force is applied to derive the scaled boundary finite element equation. Higher order spectral elements are used to discretize the longitudinal dimension and the solution through the thickness is expressed analytically as a Padé expansion. A variable transformation technique facilitates the development of the dynamic stiffness matrix, which leads to the static stiffness and mass matrices naturally. Rayleigh damping and Newmark-β method are employed to perform the forced vibration analysis. Numerical examples covering static and dynamic analyses validate the excellent performance and capability of this approach.