Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method

The present study is concerned with the bending, buckling and vibration analyzes of nonlocal Euler beams. Weak form of the governing equation of nonlocal Euler beams is outlined in this paper. Ritz method is selected in order to analyze the nonlocal beams with arbitrary boundary conditions along them. Analytical formulations are developed to find the stiffness matrix, buckling stiffness matrix and mass matrix. The results of the presented formulation for bending, vibration and buckling of nonlocal Euler beams with four classical boundary conditions are computed and compared, wherever possible. Finally, two types of beams with general boundary conditions are selected and new results are obtained which demonstrate the capability of the Ritz method to model such nonlocal beams.