An efficient beam element for the analysis of laminated composite beams of thin-walled open and closed cross sections

Sheikh, Abdul Hamid; Thomsen, Ole Thybo

doi:10.1016/j.compscitech.2008.04.018

Cited by 46 publications

(29 citation statements)

References 28 publications

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“…K depends linearly and quadratically on the vector of generalized coordinates q, but also contains constant terms. The coefficients of the matrices are obtained from the integrations given in (12). They depend on the shape functions and cross sectional properties, i.e.…”

Section: Wwwzamm-journalorgmentioning

confidence: 99%

“…Attard [11] derived the expressions for the displacements of thin-walled open beams by imposing that the shear deformation is constrained to zero on the middle surface. Sheikh and Thomsen [12] investigated static deformations of thin-walled beams, the equilibrium equation was also derived by considering different analytical expressions for the warping function for the cases of open and closed cross sections. Saadé at al.…”

Section: Introductionmentioning

confidence: 99%

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An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Stoykov

Manoach

Margenov

2015

Z. Angew. Math. Mech.

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A 3D beam model, i.e. a beam that may deform in space and experience longitudinal and torsional deformations, is developed considering Timoshenko's theory for bending and assuming that the cross section rotates as a rigid body but may deform in longitudinal direction due to warping. The cross sectional properties are firstly calculated and then inserted at the equation of motion. The beam is assumed to be with an arbitrary cross section, with linearly varying thickness and width, and with an initial twist. The model is appropriate for open and closed thin-walled cross sections, and also for solid cross sections. The objective of the current research is to demonstrate that complex beam structures can be modeled accurately with reduced number of degrees of freedom.

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Section: Wwwzamm-journalorgmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Stoykov

Manoach

Margenov

2015

Z. Angew. Math. Mech.

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“…Thin-walled beams are structural members of great importance, and analyses of this structure is given in Refs. [19][20][21][22][23]. To model the stresses with a smoothness via FEM, Hermite-cubic polynomial was used to ensure C 1 continuous elements.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Finite element formulation of laminated beams with capability to model the thickness expansion

Mantari

Canales

2016

Composites Part B: Engineering

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This paper presents a static analysis of laminated beams by using a 6 degree-of-freedom hybrid type quasi-3D higher order shear deformation theory (HSDT). The governing equations are derived by employing the principle of virtual work and solved by means of Hermite-Lagrangian finite element method for laminated beams with several boundary conditions. A mixed interpolation, 1 C cubic Hermite and a 0 C linear Lagrange interpolation are used for the kinematic variables. Different types of shear strain shape functions were introduced a priori and in general manner to model the displacement field of the laminated beams. Convergence studies were performed in order to validate the HSDTs solved through finite element method and the results are compared with a Navier solution. Numerical results of the present generalized quasi-3D theory are also compared with FEM solutions predicted by other HSDT and with experimental results.

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“…The latter theory is important for beams with open cross-section and it leads to a 5x5 v C matrix (Lee and Lee, 2004;Vo and Lee, 2007). The former theory leads to a 6x6 v C matrix (Vo and Lee, 2010a matrix becomes 7x7 (Sheikh and Thomsen, 2008). In addition, it can be found in literature 8x8 (Vo and Lee, 2008;Vo and Lee, 2009a) and 9x9 (Salim and Davalos, 2005;Vo and Lee, 2011) v C matrices to assess box and open cross-section beams.…”

Section: Beam Theorymentioning

confidence: 99%

Geometrically nonlinear analysis of thin-walled laminated composite beams

Melo

Mororã

Parente

2015

Lat. Am. j. solids struct.

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The use of thin-walled composite beams in Engineering has attracted great interest in recent years. Composite beams and other structural elements tend to have thin walls due to the high strength of the material. Other important aspect is that, even without reaching large strains and without overcoming the elastic limit of the material, such as beams present geometric nonlinear behavior due to their high slenderness, leading to large displacements and rotations. In this paper, a three-dimensional frame finite element for geometric nonlinear analysis of thin-walled laminated composite beams is presented. The finite element uses the Total Lagrangian formulation in order to allow the treatment of large displacements, but with moderated rotations. The constitutive matrix of the laminated beams is evaluated through a suitable thin-walled beam theory. In this theory, the effects of the couplings for several layups are considered, but the effects of the warping and transverse shear are neglected. Comparisons with numerical experiments demonstrate the very good accuracy of the proposed finite element.

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An efficient beam element for the analysis of laminated composite beams of thin-walled open and closed cross sections

Cited by 46 publications

References 28 publications

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Finite element formulation of laminated beams with capability to model the thickness expansion

Geometrically nonlinear analysis of thin-walled laminated composite beams

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