Analytical solution for a 5-parameter beam displacement model

In this paper, a new beam model based on a 5-parameter displacement field, accounting for an enhanced kinematics and able to reproduce the Poisson effect, is proposed. The displacement field enriches the classical three-parameter Timoshenko beam with two new parameters capable to simulate the shortening effect over the thickness. The related differential equations, derived from a variational formulation, are analytically solved and implemented in a deformation method approach, capable of solving structural problems of beams with general geometry, boundary and load conditions. Several numerical applications are developed, highlighting the characteristic of the proposed 5-parameters model and comparing the results with those obtained using the classical Bernoulli, Timoshenko and Reddy beam models. Numerical results show that, although for homogeneous beam the differences in terms of generalized stress and displacement are generally very small, the proposed model returns local stress enriched by the new parameters, with more significant differences where the Poisson effect is more pronounced.