Static, vibration and stability analysis of non-uniform beams

An approximate finite element displacement method is introduced to analyze the problem of non-uniform beams. Using the displacement functions of a constant cross-section beam, an approximate stiffness and consistent mass matrices are derived. The moment of inertia and cross-sectional area of the beam can be prescribed by any power series of the axial coordinate. Using these matrices the results for static loading, vibration frequencies, and buckling load are found. The solution is compared with those obtained using other approximation techniques. The proposed method converges much faster, with fewer elements, and saves computer and data preparation time.