A higher-order nonlinear beam element for planar structures by using a new finite element approach

In the present research, a new finite element approach is presented for large deflection modeling of planar Euler–Bernoulli beams. In this approach, in addition to the position and rotation (kinematic variables), internal force and moment (kinetic variables) are considered as the nodal coordinates. For this purpose, each of the kinematic and kinetic variables are individually interpolated. Thereby, the primary governing equations of the elements (such as constitutive, equilibrium and geometric equations) are not combined with each other. On the other hand, the nonlinear governing equations are not simplified to linear equations. Finally, using the weighted residual method for each of the governing equations, several nonlinear equations are obtained due to the nodal coordinates. The Gauss–Legendre nodes are used for discretization of the finite element. Using the presented approach, a new higher-order nonlinear element is obtained which is simple, more efficient and more accurate than similar beam elements. The accuracy and efficiency of the presented higher-order element are investigated by comparing the results with recent works using the finite element method.