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首页> 外文期刊>International journal of non-linear mechanics >Non-linear analysis of functionally graded microbeams using Eringen's non-local differential model
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Non-linear analysis of functionally graded microbeams using Eringen's non-local differential model

机译：使用Eringen的非局部微分模型对功能梯度微束进行非线性分析

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The primary objective of this paper is two-fold: (1) to formulate the governing equations of the Euler-Bernoulli and Timoshenko beams that account for (a) two-constituent material variation through beam thickness, (b) small strains but moderate displacements and rotations, and (c) material length scales based on Eringen's non-local differential model; and (2) develop the non-linear finite element models of beam theories with aforementioned features and obtain numerical results for static bending. The principle of virtual displacements is used to derive the non-linear equations governing functionally graded beams with Eringen's non-local constitutive models for both the Euler-Bernoulli and Timoshenko beam theories. A power-law model is used for the variation of the material properties of the two constituent materials. Finite element models of the resulting equations are developed and numerical results are presented for pinned-pinned and clamped-clamped boundary conditions, showing the effect of the non-local parameter and the power-law index on deflections and stresses.
机译：本文的主要目的是双重的：（1）制定Euler-Bernoulli和Timoshenko梁的控制方程，这些方程解释了（a）通过梁厚度产生的两成分材料变化，（b）小应变但位移适中和旋转，以及（c）基于Eringen的非局部微分模型的材料长度尺度； （2）建立具有上述特征的梁理论的非线性有限元模型，并获得静态弯曲的数值结果。虚拟位移原理用于根据Euer-Bernoulli和Timoshenko梁理论的Eringen的非局部本构模型推导控制功能梯度梁的非线性方程。幂律模型用于两种组成材料的材料特性的变化。建立了所得方程的有限元模型，并给出了销钉和钉扎边界条件的数值结果，显示了非局部参数和幂律指数对挠度和应力的影响。

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