Buckling and free vibration of laminated beams with arbitrary boundary conditions using a refined HSDT

Canales, F.G.; Mantari, J.L.

doi:10.1016/j.compositesb.2016.06.024

Cited by 37 publications

(14 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Chebyshev polynomials as expansion functions were employed by Filippi et al [26] to obtain a new class of refined beam models for static and free vibration analysis of laminated beams. On the basis of Ritz method, Mantari and Canales [27,28] presented the analytical solutions for free vibration and buckling analysis of laminated beams. Kahya [29] developed a finite element model based on FSDT, for buckling analysis of composite beams.…”

Section: Introductionmentioning

confidence: 99%

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

Karkon

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

In this paper, a new three-node element with three degrees of freedom per node is proposed for bending, free vibration and buckling analysis of laminated beams. The element's formulation is based on the first-order shear deformation theory (FSDT). For this aim, transverse displacement and rotation field of the element are selected from fifth and fourth order, respectively. Moreover, the shear strain is varied as quadratic function throughout the element. It is worth noting that the quadratic function can be used for axial displacement field. By employing equilibrium equation, curvature and shear strain relations of laminated beam with FSDT theory, the exact and explicit shape functions of the displacement fields are obtained. By utilizing the obtained shape functions, the explicit form of the stiffness matrix is calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. It should be mentioned, the proposed element is free of shear locking. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, bending, free vibration and buckling analysis of laminated beams with different boundary conditions and aspect ratios are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.

show abstract

Section: Introductionmentioning

confidence: 99%

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

Karkon

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…According to the authors, the proposed formulation achieves a slightly better performance than the HSDT used for comparison purposes. The HSDT concept can also be employed in the buckling and free vibration analysis of laminated composite beams (see [11], among others).…”

Section: Introductionmentioning

confidence: 99%

A new 2D beam finite element for nonlinear elastic analysis including warping and shear effects

Pascon

2019

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

In this paper, a finite-element formulation based on positional description is proposed to predict the large deformation behavior of short beams including shear deformation and cross section warping. A higher-order shear deformation beam theory is originally employed by means of two generalized vectors. A linear strain rate is also included in order to enrich the approximation of strains along the transverse direction. The formulation accounts for finite displacements, finite strains and plane stress conditions in elastic regime. Homogeneous materials, as well as functionally graded composite beams with varying properties along the height, are considered. In all, four beam formulations are described, combining the level of transverse enrichment and the cross section kinematics. A short cantilever beam problem with rectangular cross section is analyzed in detail to illustrate the differences among the four element formulations regarding displacements, strains and stresses. The numerical results confirm that the inclusion of both linear strain rate and cross section warping are needed to correctly predict the mechanical behavior of the cantilever beam, reproducing variable shear deformation across the height.

show abstract

“…A exponential HSDT was used for the bending, buckling and free vibration analyses of multi-layered laminated composite beams by Karama et al [11], showing that the proposed model was more precise than the trigonometric HSDT model and FEM model studied early by Karama et al [12]. In addition, other HSDT models [13] have been developed by various authors for describing the deformation through the thickness.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for free vibration analysis of laminated, box and sandwich beams by refined layer-wise theory

Yan

Pagani²,

Carrera³

2017

Composite Structures

View full text Add to dashboard Cite

The present work addresses a closed-form solution for the free vibration analysis of simply supported composite laminated beams via a refined one-dimensional (1D) model, which employs the Carrera Unified Formulation (CUF). In the framework of CUF, the 3D displacement field can be expanded as any order of generic unknown variables over the cross section , in the case of beam theories. Particularly, Lagrange expansions of cross-sectional displacement variables in conjunction with layer-wise (LW) theory are adopted in this analysis, which makes it possible to refine the kinematic fields of complex cross section by arbitrary order and accuracy. As a consequence, the governing equations can be derived using the principle of virtual work in a unified form and can be solved by a Navier-type, closed-form solution. Numerical investigations are carried out to test the performance of this novel method, including composite and sandwich beams ranging from simple to complex configurations of the cross section. The results are compared with those available in the literature as well as the 3D finite element method (FEM) solutions computed by commercial codes. The present CUF model is proved to be able of achieving high accurate results with less computational costs. Besides, they may serve as benchmarks for future assessments in this field.

show abstract

Buckling and free vibration of laminated beams with arbitrary boundary conditions using a refined HSDT

Abstract: Buckling and free vibration of laminated beams with arbitrary boundary conditions using a refined HSDT (PDF Download Available)

Cited by 37 publications

References 49 publications

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

A new 2D beam finite element for nonlinear elastic analysis including warping and shear effects

Exact solutions for free vibration analysis of laminated, box and sandwich beams by refined layer-wise theory

Contact Info

Product

Resources

About