Analytical beam theory for the in-plane deformation of a composite strip with in-plane curvature

Rajagopal, Anurag; Hodges, Dewey H.

doi:10.1016/j.compstruct.2012.06.010

Cited by 9 publications

(6 citation statements)

References 11 publications

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“…tT F , nT F , and bT W which appears in the last equation of (26), should be obtained by solving the equation system given by (25).…”

Section: Free Vibration Problemmentioning

confidence: 99%

“…To reduce complexity, second order terms appearing in Eq. (25) can be neglected with an assumption of small deflections. By this assumption, the differential equation system becomes linear and the exact solution can be obtained.…”

Section: Solution Of Static Problemmentioning

confidence: 99%

“…Some of the works concerning VABS can be seen in Refs. [25][26][27][28]. Geometrically Exact Beam Theory (GEBT) is an another approach which is coupled with VABS [29].…”

Section: Introductionmentioning

confidence: 99%

“…Without any a priori assumptions, original 3-D problem is reduced to 1-D beam problem using the small parameters regarding the geometry [24]. Variational Asymptotic Beams Section (VABS), which is a cross sectional analysis tool for composite beams, is constructed on the principles of the VAM [25]. Some of the works concerning VABS can be seen in Refs.…”

Section: Introductionmentioning

confidence: 99%

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In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

Eroğlu

2015

Composite Structures

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“…tT F , nT F , and bT W which appears in the last equation of (26), should be obtained by solving the equation system given by (25).…”

Section: Free Vibration Problemmentioning

confidence: 99%

Section: Solution Of Static Problemmentioning

confidence: 99%

“…Some of the works concerning VABS can be seen in Refs. [25][26][27][28]. Geometrically Exact Beam Theory (GEBT) is an another approach which is coupled with VABS [29].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

Eroğlu

2015

Composite Structures

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“…Such studies have been undertaken by the authors to study the effects of span-wise non-uniformity 14 and initial curvature. 4,15 These serve as validation tools for VABS in the same sense that elasticity validates FEM. • The presence of elasticity solutions for several loading cases, 16, 17 which shall be described in detail.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

Rajagopal

Hodges

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Structural and aeroelastic analyses using beam theories by default choose a cross section that is perpendicular to the reference line. In several cases, such as swept wings with high A, a beam theory that allows for the choice of a cross section that is oblique to the reference line may be more convenient. This work uses the Variational Asymptotic Method to develop such a beam theory. The problems addressed are the planar deformation of a strip and the full 3D deformation of a solid prismatic circular cylinder, both made of homogenous, isotropic material. The motivation for choosing these problems is primarily the existence of 3D elasticity solutions, which comprise a complete validation set for all possible deformations and which are shown to be accurately captured by the current analysis. A secondary motivation was that the development and final results of the beam theory, i.e., the cross-sectional stiffness matrix and stress-strain-displacement recovery relations, are obtainable as closed-form analytical expressions. This, coupled with the VAM-based beam analysis being devoid of ad hoc assumptions, is of significant aid when formulating a general oblique cross-sectional analysis for beams with anisotropic material and initial curvature/twist, the treatment of which is alluded to at the end.

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Introduction

Ghorashi¹

2016

Statics and Rotational Dynamics of Composite Beams

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Analytical beam theory for the in-plane deformation of a composite strip with in-plane curvature

Cited by 9 publications

References 11 publications

In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

Asymptotic Approach to Oblique Cross-Sectional Analysis of Beams

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