4、纳米增强梁在火灾与地震作用下的性能研究

纳米增强梁在火灾与地震作用下的性能研究

1. 火灾中纳米颗粒增强梁的屈曲分析

在火灾环境下，纳米颗粒增强梁的性能分析至关重要。首先，弹性介质和火灾所做的功可表示为：
[
W = \int_{0}^{L} (F - LP)Wdx
]

基于哈密顿原理，可以推导出结构的控制方程。哈密顿原理表达式为：
[
\int_{t_0}^{t_1} (\delta U - \delta K + \delta W)dt = 0
]

由此得到的控制方程如下：
[
C_{11}\frac{\partial^2 U}{\partial x^2}-C_{11}\frac{\partial^2 W}{\partial x^2}=-\rho h\frac{\partial^2 U}{\partial t^2}
]
[
A_{55}\left(\frac{\partial^2 \psi}{\partial x^2}-\frac{\partial^2 W}{\partial x^2}\right)-N_x\frac{\partial^2 W}{\partial x^2}+A_{11}\alpha_x T + LP + K_w W - G\frac{\partial^2 W}{\partial x^2}=\rho h\frac{\partial^2 W}{\partial t^2}
]
[
I_{11}\frac{\partial^2 \psi}{\partial x^2}-K_s A_{55}\left(\psi - \frac{\partial W}{\partial x}\