Analytical solution for a 5-parameter beam displacement model

An accurate and refined nonlinear beam model accounting for the Poisson effect

“…The analytical solution of the linear expressions of Eqs. (9-10), reported in [13] and [14] are finally adopted in a displacement-based approach to solve structures with general geometries.…”

“…Moreover, the assumption of constant transverse displacement in the beam thickness does not allow to evaluate the Poisson effects which, in some cases, can be of considerable interest [12]. In this paper, the nonlinear version of the enhanced beam model based on a 5-parameter displacement field, recently proposed in [13] and able to reproduce the Poisson effect in transverse direction is presented. This work summarizes the results recently published by the authors in [14] and stems from the 7-parameter displacement field, proposed in [15] for large deformation analysis of composite shell structures, simplified by the one-dimensional nature inherent in the beam model.…”

Theories and Analysis of Functionally Graded Beams

“…All modern developments are refinements to the above stated two theories, where the displacement fields are expanded in terms of powers of the thickness [3] and accounting for other non-classical continuum mechanics aspects (e.g., stress and strain gradient effects and material length scales). For example, a general higher-order theory is of the form u = u x êx + u y êy + u z êz (1) where…”