A new nonlinear 5-parameter beam model accounting for the Poisson effect

In this paper, a new kinematic beam model based on a five-parameter displacement field is proposed in a geometric nonlinear framework. The proposed displacement field enriches the classical Timoshenko beam displacement field with two additional parameters, accounting for the Poisson effect. The equilibrium equations have been derived through a variational approach, and the linearized equations are solved analytically. The adoption of the linear solution as approximation functions for the nonlinear case allows prediction of nonlinear response of problems involving complex geometries with a relatively small computational effort. Several numerical examples of benchmark problems are analyzed, highlighting the characteristic features of the proposed five-parameter model and comparing the results with those obtained using the classical Bernoulli beam model and 3D finite element model. Numerical results show that, although for thin beams the differences in generalized displacement are generally negligible, the proposed model predicts a comparable stress field only when the Poisson ratio is equal to zero. Conversely, the stress field is meaningfully enriched by the new parameters, with significant differences where the Poisson effect is more pronounced.