A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements. (1st February 2017)

• Record Type: Journal Article
• Authors: Hui, Y.; Giunta, G.; Belouettar, S.; Huang, Q.; Hu, H.; Carrera, E.
• Is Part Of: Composites. Number 110(2017)
• Page Start: 7
• Page End: 19
• Publication Date: 2017-02-01
• Subjects: Free vibration analysis -- Sandwich beam structures -- Unified formulation -- Finite element method; Composite materials -- Periodicals; Materials science -- Periodicals; Composite materials; Periodicals; Electronic journals; 620.118
• DOI: 10.1016/j.compositesb.2016.10.065
• Languages: English
• ISSNs: 1359-8368

Abstract

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.