عنوان المقالة:Euler-Bernoulli Beam Theory in the Presence of Fiber Bending Stiffness Euler-Bernoulli Beam Theory in the Presence of Fiber Bending Stiffness
In the conventional one-dimensional mathematical modelling of fibre-reinforced thin-walled structures it is assumed that fibres have negligible thickness and they are perfectly flexible. Consequently, the constitutive equation forfinite deformations of fibre-reinforced elastic solids involves no natural length. Based on incorporatingfibre bending stiffness into a continuum theory, asymmetric linearised elasticity theory that takes into consideration the effects of fibres bending stiffness, has been produced in[1]. Relatively, an accurate 2d thin-walled structures modeling has been presented in [2]. Based on the aforementioned 2d-theory and, as a particular case, this study presents one-dimensional mathematical modeling that takes into consideration the fibres bending stiffness, with the use of the displacement approximation of the bernoulli-euler beam model. Unlike its conventional one-dimensionalmodelingthe solution is obtained that contains an intrinsic material length parameter which may, for instance, be considered representative of thefibre diameter. Numerical results on the basis of the obtained solution are presented and discussed in this article for different boundary conditions of homogeneous fibre-reinforced rectangular beams.
تاريخ النشر
06/05/2017
الناشر
IOSR Journal of Mathematics (IOSR-JM)
رقم المجلد
13
رقم العدد
3
الصفحات
10-17
الكلمات المفتاحية
fiber bending stiffness, beam deflection, couple-stress, asymmetric elasticity, intrinsic material area or length parameter.