Stiffness analysis of beams using a higher-order theory

Petrolito, J.

doi:10.1016/0045-7949(94)00505-w

Cited by 30 publications

(18 citation statements)

References 5 publications

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“…For instance, [13] developed a new spectral element matrix for the laminated composite beams on the basis of hyperbolic shear deformation theory; Petrolito [19] derived the shape functions for the beam from the solution of the differential equations and then proceeded as in the finite element method; [20]also presented static analysis of functionally graded beams using higherorder beam theory in which the finite element formulation followed the conventional displacement-based approach to derive the stiffness matrices.…”

Section: Introductionmentioning

confidence: 99%

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

et al. 2015

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Since the accuracy of results obtained through displacement-based finite element method (FEM) considerably depends on the accuracy of shape functions used to interpolate the displacement field within an element, this paper aims at presenting a new efficient element for static and free vibration analysis of higher-order shear deformable beams using FEM with introducing basic displacement functions (BDFs). First, BDFs are introduced and computed. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions, static and free vibration behavior of the higher-order shear deformable beam is studied using FEM. The accuracy and economy of the method are demonstrated through several numerical examples.Keywords Higher-order beam theory (HOBT) · Finite element method (FEM) · Basic displacement functions (BDFs) · Free vibration B Rahmat Kazemi Firouzjaei

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Section: Introductionmentioning

confidence: 99%

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

et al. 2015

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“…where primes denote the total derivatives with respect to the space variable ζ , T can be interpreted as a generalized shear force, M 1 and M 2 are generalized moments and [4] …”

Section: Downloaded By [York University Libraries] At 09:44 17 Novembmentioning

confidence: 99%

“…Bickford [3] corrected the variational inconsistency of the Levinson theory by moving from the Hamilton's principle. There are some finite element solutions for Bickford's theory [4], with some references to the buckling problem [5].…”

Section: Introductionmentioning

confidence: 99%

Buckling of a Higher-Order Beam: Exact and Numerical Results

Tomasiello

2008

International Journal for Computational Methods in Engineering

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“…The theory accurately accounted for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the crosssectional plane. Petrolito [14] presented a finiteelement solution of uniformly loaded thick beams using Bickford's theory. Wang et al [15] extensively discussed the topic of the shear deformations in beams extensively and presented the derivation and comparison of Bernoulli-Euler, Timoshenko, and Reddy-Bickford beam theories.…”

Section: Introductionmentioning

confidence: 99%

The effects of shear deformation on the free vibration of elastic beams with general boundary conditions

2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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Free vibration characteristics of shear deformable elastic beams subjected to different sets of boundary conditions are investigated. The analysis is based on a unified one-dimensional shear deformation beam theory. The governing equations of the elastic beams are obtained by means of Hamilton's principle. Four different boundary conditions are considered. The natural frequencies and mode shapes are obtained by applying the dynamic stiffness method, where the elements of the exact dynamic stiffness matrix are derived by using the analytical solutions of the governing equations of the beam in free vibration. The numerical results for the particular beams with different slenderness ratios are presented and compared with those available in the literature.

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Stiffness analysis of beams using a higher-order theory

Cited by 30 publications

References 5 publications

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

Buckling of a Higher-Order Beam: Exact and Numerical Results

The effects of shear deformation on the free vibration of elastic beams with general boundary conditions

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