New mathematical identities with applications to flexure and torsion

Obaid, Samih; Rung, D. C.

doi:10.1007/bf00945312

Cited by 2 publications

(2 citation statements)

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“…Many mathematicians have solved the torsion problem with different uniform, simply connected, cross sections of the cylinder bounded by closed curves such as a circle, ellipse, equilateral triangle, and cardioid. However, many others such as Bassali [1], [2], Bassali & Obaid [4], Sokolnikoff [13], Stevenson [14], Obaid and Rung [11], and Abassi [1] have developed different methods to solve a torsion problem.…”

Section: Introductionmentioning

confidence: 99%

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Applications to boundary value problems

2018

CRM Monograph Series

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In this thesis, we solved the Saint-Venant's torsion problem for beams with different cross sections bounded by simple closed curves using various methods. In addition, we solved the flexure problem of beams with certain curvilinear cross sections. The first method was derived by Bassali and Obaid. We focused on cross sections bounded by hyperbolas, circular groves, lemniscate of Booth, and sectorial cross sections. The second method used Tchebycheff polynomials to solve the torsion problem corresponding to the circle and ellipse. The third method used conformal mapping to derive the solution of different cross sections bounded by curvilinear edges. The flexure problem has been reduced to six boundary value problems; three are Dirichlet and three are Neumann problems. We derived the flexure functions

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Section: Introductionmentioning

confidence: 99%

“…Rung and Obaid have proven the above identities in two different ways. Refer to [11] and [12] for the proof of the identities and the complete solution of these flexure problems.…”

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confidence: 99%