Nonlinear large deflection problems of beams with gradient: A biparametric perturbation method
Nonlinear large deflection problems of beams with gradient: A biparametric perturbation method
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DOI：
10.1016/j.amc.2013.01.037
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发表时间：
2013-03-15
影响因子：
4
通讯作者：
Sun, Jun-Yi
中科院分区：
文献类型：
--
作者：
He, Xiao-Ting;Cao, Liang;Sun, Jun-Yi
对于梯度梁，由于荷载和梯度的共同影响，Euler-Bernoulli方程中的一阶导数项不可忽略，从而使问题的解成为非线性大挠度问题。本文用一种新的摄动法，在两种不同的边界条件下，分别用一个描述载荷效应的小参数和一个描述问题几何性质的小参数，求解了梯度梁的非线性大挠度问题。推导了梁的挠度、转角、弧长以及梁端内力的一阶和二阶近似解析解。结果表明，两个独立参数的选取可以综合反映荷载和梯度引起的非线性效应，使近似解具有足够的精度，可用于梯度梁的大挠度分析。(C)2013 Elsevier Inc. All rights reserved.
For beams with gradient, due to the combined influences introduced by loads and gradient, the first derivative item in Euler-Bernoulli equation can not be neglected thus making the solution of the problem be a nonlinear large deflection one. In this paper, we use a new perturbation method with two small parameters, one describes the loads effect and another describes the geometrical nature of the problem, to solve the nonlinear large deflection problem of beams with gradient under the two different boundary conditions. We derive the first and second order approximate analytical solution of the deflection, the rotation and the arc length of the beam, as well as the internal forces of the beam at the end. The results indicate that the choice of two independent parameters may describe comprehensively the nonlinear effects caused by loads and gradient, which enables the approximate solution to be precise enough to be used for the analysis of large-deflection beam with gradient. (C) 2013 Elsevier Inc. All rights reserved.