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

## TL;DR

This paper develops an enhanced Timoshenko beam model that accurately captures the complex effects of material anisotropy on structural behavior, including stress distribution and displacements, validated against finite element solutions.

## Contribution

It introduces a stress recovery method and consistent constitutive relations for anisotropic beams, extending analytical capabilities beyond homogeneous cases.

## Key findings

- Axial stress depends significantly on transversal internal force.
- Anisotropy affects displacements more than shear deformation.
- Model achieves errors less than 5% compared to finite element solutions.

## 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%.