Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Filippi, Matteo; Pagani, Alfonso; Petrolo, Marco; Colonna, Giovanni; Carrera, Erasmo

doi:10.1016/j.compstruct.2015.07.014

Cited by 64 publications

(28 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Due to the excellent properties in mechanical and thermal behaviours, a wide range of application for functionally graded (FG) structures can be found in different fields, leading to the intensive study in many types of FG structures in the last three decades. Chebyshev collocation method, finite element method and differential quadrature method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For analytical approaches, a Navier solution has been widely used to study various mechanical behaviours of simply supported beams [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

View full text Add to dashboard Cite

An analytical method for vibration and buckling behaviours of Functionally Graded (FG) beams with various boundary conditions under mechanical and thermal loads is presented. Based on linear straindisplacement relations, equations of motion and essential boundary conditions are derived from Hamilton's principle. In order to account for thermal effects, three cases of the temperature rise through the thickness, which are uniform, linear and nonlinear, are considered. The exact solutions are derived using the state space approach. Numerical results are presented to investigate the effects of boundary conditions, temperature distributions, material parameters and slenderness ratios on the critical temperatures, critical buckling loads, and natural frequencies as well as load-frequencies curves, temperature-frequencies curves of FG beams under thermal/mechanical loads. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

show abstract

Section: Introductionmentioning

confidence: 99%

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

View full text Add to dashboard Cite

show abstract

“…The accuracy of the method was verified by comparing the solutions with available results in the literature. Chebyshev polynomials are used extensively in the solution of engineering problems due to their fast convergence and accuracy as compared to other orthogonal functions as noted in Sari and Butcher (2010), Filippi et al (2015). Moreover they are easy to programme in symbolic form and the required accuracy can be attained by the number of polynomials (Sari and Butcher, 2010).…”

Section: Discussionmentioning

confidence: 99%

Buckling of nonuniform carbon nanotubes under concentrated and distributed axial loads

Robinson

Adali

2017

Mech. Sci.

View full text Add to dashboard Cite

Abstract. Buckling of nonuniform carbon nanotubes are studied with the axial load taken as a combination of concentrated and axially distributed loads. Constitutive modelling of the nanotubes is implemented via nonlocal continuum mechanics. Problem solutions are obtained by employing a weak formulation of the problem and the Rayleigh-Ritz method which is implemented by using orthogonal Chebyshev polynomials. The accuracy of the method of solution is verified against available results. Solutions are obtained for the cases of uniformly distributed and triangularly distributed axial loads. Contour plots are given to assess the effect of nonuniform crosssections and the small-scale parameter on the buckling load for a combination of simply supported, clamped and free boundary conditions.

show abstract

“…The aforementioned works have been performed by means of Taylor-like Expansion (TE). On the other hand, in [47] the displacement field across the section was modeled by means of Lagrange Expansion (LE) polynomials, whereas a beam theory based on Chebyshev Expansion (CE) polynomials has been introduced in [48]. The LE models have the great advantage of considering only pure displacement variables, enabling the use of the Component-Wise (CW) approach.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of aerospace structures by means of refined beam theories

Pagani

Petrolo

Colonna

et al. 2015

Aerospace Science and Technology

Self Cite

View full text Add to dashboard Cite

Please cite this article in press as: A. Pagani et al., Dynamic response of aerospace structures by means of refined beam theories, Aerosp. Sci. Technol. (2015), http://dx. AbstractThe present paper is devoted to the investigation of the dynamic response of typical aerospace structures subjected to different time-dependent loads. These analyses have been performed using the mode superposition method combined with refined one-dimensional models, which have been developed in the framework of the Carrera Unified Formulation (CUF). The Finite Element Method (FEM) and the principle of virtual displacements are used to compute the stiffness and mass matrices of these models. Using CUF, one has the great advantage to obtain these matrices in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. In this paper, Taylor-like expan- sions (TE), Chebyshev expansion (CE) and Lagrange expansion (LE) have been employed inthe framework of CUF. In particular, the latter class of polynomials has been used to develop pure translational displacementbased refined beam models, which are referred to as Component Wise (CW). This approach allows to model each structural component as a 1D element. The dynamic response analysis has been carried out for several aerospace structures, including thin-walled, open section and reinforced thin-shells. The capabilities of the proposed models are demonstrated, since this formulation allows to detect shell-like behaviour with enhanced performances in terms of computational efforts.

show abstract

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

Cited by 64 publications

References 67 publications

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Buckling of nonuniform carbon nanotubes under concentrated and distributed axial loads

Dynamic response of aerospace structures by means of refined beam theories

Contact Info

Product

Resources

About