Modeling the non-trivial behavior of anisotropic beams: A simple Timoshenko beam with enhanced stress recovery and constitutive relations

Abstract

This paper analyzes the non-trivial influence of the material anisotropy on the structural behavior of an anisotropic multilayer planar beam. Indeed, analytical results available in literature are limited to homogeneous beams and several aspects has not been addressed yet, impeding an in-depth understanding of the mechanical response of anisotropic structural elements. This paper proposes an effective recovery of stress distribution and an energetically consistent evaluation of constitutive relations to be used within a planar Timoshenko beam model. The resulting structural-analysis tool highlights the following peculiarities of anisotropic beams: (i) the axial stress explicitly depends on transversal internal force, which can weigh up to 30% on the maximal magnitude of axial stress, and (ii) the anisotropy influences the beam displacements more than standard shear deformation and even for extremely slender beams. A rigorous comparison with analytical and accurate 2D Finite Element solutions confirms the accuracy of the proposed approach that leads to errors exceptionally greater than 5%.

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

“…In general, classical beam models generalize the external load through the entire crosssection. This hypothesis, although not best representing surface forces and partial cross-sectional loads, is widely accepted in beam modeling approaches (Masjedi et al 2019;Weaver 2020a, b, 2022;Masjedi et al 2021;Doeva et al 2020aDoeva et al , b, 2021Doeva et al , 2022Balduzzi et al 2019;Bertolini et al 2019;Bertolini and Taglialegne 2020;Chockalingam et al 2020Chockalingam et al , 2021Vilar et al 2021a). Another issue not addressed in analytical laminated beam formulations is for cases where the stiffness distribution is different from the transverse and axial load distributions, which gives rise to non-classical transverse stresses.…”

“…For example, the state of stress on beam surfaces is governed by Cauchy’s traction-stress relation, resulting in non-vanishing transverse stresses (Balduzzi et al. 2016 , 2017a , b , c , d , 2019 ; Mercuri et al. 2020 ; Hodges et al.…”

“…2020a , b , 2021 , 2022 ; Balduzzi et al. 2019 ; Bertolini et al. 2019 ; Bertolini and Taglialegne 2020 ; Chockalingam et al.…”

On a consistent rod theory for a linearized anisotropic elastic material II. Verification and parametric study

“…There is a vast amount of work in the literature [9–28] studying the static deformation or the vibration frequency of a rod/beam structure composed of linear anisotropic material with various shapes and boundary conditions. We focus on the static deformation of a rod structure in the current paper.…”

“…Compared with [25], in the current paper, more insightful information about the coupling effects are revealed in Section 4. Balduzzi et al [22] developed a recursive procedure for recovering stress based on Timoshenko’s beam theory. This model was applied to a multilayered planar rod composed of anisotropic material with four elastic moduli and the influence of material anisotropy on the structure behavior was investigated.…”