材料的温度依赖性对功能梯度梁热弯曲行为的影响—论文简介.doc

材料的温度依赖性质对功能梯度梁 热弯曲的影响 工程力 口永刚 指导老师： 马连生教授 摘 要 本文研究了均匀热载荷作用下，梁的热弯曲问题。首先基于非线性经典梁理论，建立该问题的控制方程。然后将它化简为一个关于横向挠度方向的四阶非线性积分-微分方程。对于本文所考虑的径向不可移两端简支的边界条件，该方程与相应的边界条件构成了微分特征值问题。求解该四阶非线性积分-微分方程，得到热弯曲问题的解析解，该解是外加热载荷的非线性函数。利用求得的解析解，用图形表示出了在径向不可移两端简支边界条件下热载荷与梁弯曲的关系曲线，而且通过图形表示出了屈曲点与临界屈曲载荷。 关键词：功能梯度材料；经典梁理论；热弯曲；解析解；温度依赖性质 Abstract This paper studies the thermal bending of the beam under uniform thermal loads, First, the equations governing of the beams are derived based on the nonlinear classical beam theory (CBT). The two equations are reduced to a single nonlinear fourth-order integral differential equation governing the transverse deformations. The equation and the corresponding boundary conditions lead to differential eigenvalue problem. To solve the four order nonlinear integral differential equation, the analytical solution get thermal bending structure and the solution is heating load of the nonlinear function. Based on the analytical solution, graphing out thermal loading and thermal bending relation curves. And through the graphic indicates the buckling critical buckling load and points. Keywords: Functionally graded material；Classic beam theory；Thermal bending；Analytical solution；Temperature-dependent 一、引言 Euler-Bernoulli）忽略了横向剪力和横向正应变的影响。马连生，顾春龙【3】经典梁热过屈曲问题解析解李世荣，宋江涛,杨静宁【】两端不可移简支弹性梁在横向非均匀升温下的热屈曲二、基本方程 以矩形梁为准,梁尺寸及坐标如图 2.1 位移场 () 2.2 几何方程 (2) 2.3 物理方程 (3) (4) 2.4 静态平衡方程 () (6) (7) 2.5 位移形式的平衡方程 ()