کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
784838 1465319 2015 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Surface and non-local effects for non-linear analysis of Timoshenko beams
ترجمه فارسی عنوان
اثرات سطحی و غیر محلی برای تحلیل غیر خطی پرتو تیموشنکو
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی


• A non-local non-linear finite element formulation for the Timoshenko beam theory surface stress effects.
• A beam element with three degrees of freedom has been developed.
• It has been shown that for a cantilever beam with concentrated load at free end, there is definitely a dependency on non-local parameter when Timoshenko beam theory is used. Also the effect of local and non-local boundary conditions for various loading conditions has been demonstrated in this example.

In this paper, we present a non-local non-linear finite element formulation for the Timoshenko beam theory. The proposed formulation also takes into consideration the surface stress effects. Eringen׳s non-local differential model has been used to rewrite the non-local stress resultants in terms of non-local displacements. Geometric non-linearities are taken into account by using the Green–Lagrange strain tensor. A C0 beam element with three degrees of freedom has been developed. Numerical solutions are obtained by performing a non-linear analysis for bending and free vibration cases. Simply supported and clamped boundary conditions have been considered in the numerical examples. A parametric study has been performed to understand the effect of non-local parameter and surface stresses on deflection and vibration characteristics of the beam. The solutions are compared with the analytical solutions available in the literature. It has been shown that non-local effect does not exist in the nano-cantilever beam (Euler–Bernoulli beam) subjected to concentrated load at the end. However, there is a significant effect of non-local parameter on deflections for other load cases such as uniformly distributed load and sinusoidally distributed load (Cheng et al. (2015) [10]). In this work it has been shown that for a cantilever beam with concentrated load at free end, there is definitely a dependency on non-local parameter when Timoshenko beam theory is used. Also the effect of local and non-local boundary conditions has been demonstrated in this example. The example has also been worked out for other loading cases such as uniformly distributed force and sinusoidally varying force. The effect of the local or non-local boundary conditions on the end deflection in all these cases has also been brought out.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Non-Linear Mechanics - Volume 76, November 2015, Pages 100–111
نویسندگان
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