Session: 02-01-01: Dynamic Loads, Response, Vibration and Alleviation of Aerospace Structures - I

Paper Number: 107271

107271 - Are There Cases in Which Classical Beam Theories Fail to Compute the Fundamental Frequency? 

Beam structures are widely used in many engineering applications. Well-known examples are aircraft wings and helicopter rotor blades in aerospace engineering, and concrete made beams in civil constructions. When dealing with these kind of slender structures, one dimensional (1D) models are always the choice of engineers to analyse them. These models are based on the Euler–Bernoulli and Timoshenko theories. The former does not account for transverse shear effects on cross-section deformations. The latter provides a model which, at best, foresees a constant shear-deformation distribution on the cross-sections. As a result, they both consider the cross-section of the structure as rigid. This strong approximation has basically no effect when dealing with compact cross-sections. But when the cross-section is described by a more complicated geometry and show thin-walled portions, the approximation has a strong influence on the modelling capability of classical theories.

In this work, those aspects are underlined with practical examples. Computationally heavier two-dimensional (2D) and three-dimensional (3D) models are used to model the same structures to build reference results, and they are compared with those obtained with classical 1D models. The attention is given on the modal characteristics and, in particular, on the first frequency. The capability of the classical models to catch the first frequency is here related to geometrical properties of the cross-section.

Finally, a refined 1D model based on CUF [1,2] is built. This formulation allows to generate 1D models with classical formulations as well as refined theories, which make use of higher-order polynomial expansion of the nodal unknowns, in a hierarchical sense. It is demonstrated how this 1D model can efficiently evaluate the first frequency and, more in general, the modal behavior.

 

REFERENCES

[1]      E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino. Finite element analysis of structures through unified formulation. John Wiley & Sons, Hoboken, New Jersey, USA, 2014.

[2]      E. Carrera, G. Giunta, and M. Petrolo, Beam structures: classical and advanced theories. John Wiley & Sons, Hoboken, New Jersey, USA, 2011.

Presenting Author: Erasmo Carrera Politecnico di Torino

Presenting Author Biography: After earning two degrees (Aeronautics, 1986, and Aerospace Engineering, 1988) at the Politecnico di Torino, Erasmo Carrera received his PhD degree in Aerospace Engineering jointly at the Politecnico di Milano, Politecnico di Torino, and Università di Pisa in 1991. He became Associate Professor of Aerospace Structures and Computational Aeroelasticity in 2000, and Full Professor at the Politecnico di Torino in 2011. His main research topics are: composite materials, finite elements, plates and shells, postbuckling and stability, smart structures, thermal stress, aeroelasticity, multibody dynamics, and the design and analysis of non-classical lifting systems.
He serves as referee for international journals and as a contributing editor for Mechanics of Advanced Materials and Structures, Composite Structures, Journal of Thermal Stress, Computer and Structures and International Journal of Aeronautical and Space Sciences. He is the president of the Italian Association of Aeronautics and Astronautics (AIDAA).

Authors:

Erasmo Carrera Politecnico di Torino
Riccardo Augello Politecnico di Torino
Marco Petrolo Politecnico di Torino