The flexure of simply curved composite shapes

Kedward, Keith T.; Wilson, R; McLean, S.K.

doi:10.1016/0010-4361(89)90880-x

Cited by 17 publications

(12 citation statements)

References 4 publications

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“…The stresses calculated with the current elliptic model display excellent correlation with both the elasticity solution of Timoshenko [2] and the strength of materials solution of Kedward [3]. An illustration of this is presented in Fig.…”

Section: Comparison To Circular Solutionsmentioning

confidence: 52%

“…The above stress distributions are validated by initially comparing the results to previously published elasticity [2] and strength of materials [3] solutions for circular beams, followed by a comparison to detailed finite element model solutions.…”

Section: Solution Validationmentioning

confidence: 99%

“…With this singularity in mind, we can compare the results of our elliptical solution to two circular solutions. The first is a mechanics of materials approach by Kedward [3] that relates the maximum normal stress to the applied moment by:…”

Section: Comparison To Circular Solutionsmentioning

confidence: 99%

“…Currently, there are numerous works [2][3][4][5][6][7] detailing different procedures to calculate the stresses in curved beams. For example, Timoshenko [2] used an elasticity approach to calculate the internal stresses in a circular arc, while Kedward [3] used a mechanics of materials approach to approximate maximal normal stress.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Timoshenko [2] used an elasticity approach to calculate the internal stresses in a circular arc, while Kedward [3] used a mechanics of materials approach to approximate maximal normal stress. A curved beam geometry, such as an ellipse, differs from a circular section with the added complexity of a variable radius of curvature, a factor that is a driving parameter for the distribution of stresses.…”

Section: Introductionmentioning

confidence: 99%

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Stresses in Half-Elliptic Curved Beams Subjected to Transverse Tip Forces

Velazquez¹,

Kosmatka

2012

Journal of Applied Mechanics

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Stresses in Half-Elliptic Curved Beams Subjected to Transverse Tip ForcesIn-plane bending of curved beams produces substantial through-thickness normal and shear stresses that can result in structural failures. A half-elliptic curved beam, having a known prescribed variable radius of curvature, is studied as an extension of the previously published circular arc beam. The equations for the normal, tangential, and shear stresses are developed for a curved beam outlined by two conf ocal half ellipses loaded by a pair of concentrated perpendicular forces on its ends. Closed-form analytical solutions for the stresses are found using an elasticity approach, where the solution is found by using selected terms of the biharmonic equation in elliptic coordinates. For the case of an elliptic beam with an aspect ratio of very close to unity, the solution closely agrees with published circular beam solutions. For other elliptic beam aspect ratios, the calculated stresses display good correlation to detailed finite element model solutions for thickness to semi-axis ratios <0.1. A parametric study revealed that the maximum normal stress is located at the midplane for high-aspect ratio (alb > 1) half-elliptic beams, but shifts toward the load tip for low aspect ratio (alb

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Section: Comparison To Circular Solutionsmentioning

confidence: 52%

Section: Solution Validationmentioning

confidence: 99%

Section: Comparison To Circular Solutionsmentioning

confidence: 99%