An accurate and refined beam model fulfilling the shear and the normal stress traction condition

This paper presents an analytical refined beam model taking into account the axial, shear and transverse normal stress distributions. Based on equilibrium equations in local form iterative procedure for solution of bipotential equation, differential axial motion are derived. From a mathematical point view formal structure obtained is identical to Timoshenko but with increased accuracy. achieved by splitting ansatzfunctions displacement field three weight-averaged degrees freedom (for deflection rotation) residual deflections, so-called higher order terms which depend state stress. It shown that traction condition always fulfilled even may hold. Furthermore analogy given it correction coefficient depends Poisson’s ratio. Finally results theory compared several theories two-dimensional finite element statically determinate indeterminate configurations.