This paper presents a family of beam higher-orders finite elements based on a hierarchical one-dimensional unified formulation for a free vibration analysis of three-dimensional sandwich structures. The element stiffness and mass matrices are derived in a nucleal form that corresponds to a generic term in the displacement field approximation over the cross-section. This fundamental nucleus does not depend upon the approximation order nor the number of nodes per element that are free parameters of the formulation. Higher-order beam theories are, then, obtained straightforwardly. Timoshenko's classical beam theory is obtained as a special case. Short and slender beams are investigated. Simply supported, cantilevered and clamped-clamped boundary conditions are considered. Several natural frequencies as well as the corresponding modes are investigated. Results are validated in terms of accuracy and computational costs towards three-dimensional finite element solutions. The proposed hierarchical models, upon an appropriate choice of approximation order, yield accurate results with a reduced computational cost.

A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements / Hui, Yanchuan; G., Giunta; S., Belouettar; Q., Huang; H., Hu; Carrera, Erasmo. - In: COMPOSITES. PART B, ENGINEERING. - ISSN 1359-8368. - ELETTRONICO. - 110:(2017), pp. 7-19. [10.1016/j.compositesb.2016.10.065]

A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements

HUI, YANCHUAN;CARRERA, Erasmo
2017

Abstract

This paper presents a family of beam higher-orders finite elements based on a hierarchical one-dimensional unified formulation for a free vibration analysis of three-dimensional sandwich structures. The element stiffness and mass matrices are derived in a nucleal form that corresponds to a generic term in the displacement field approximation over the cross-section. This fundamental nucleus does not depend upon the approximation order nor the number of nodes per element that are free parameters of the formulation. Higher-order beam theories are, then, obtained straightforwardly. Timoshenko's classical beam theory is obtained as a special case. Short and slender beams are investigated. Simply supported, cantilevered and clamped-clamped boundary conditions are considered. Several natural frequencies as well as the corresponding modes are investigated. Results are validated in terms of accuracy and computational costs towards three-dimensional finite element solutions. The proposed hierarchical models, upon an appropriate choice of approximation order, yield accurate results with a reduced computational cost.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2686824
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