摘要
为了更明确地揭示薄板耦合热冲击问题的耦合性质,本文对在上表面受阶跃加热,下表面绝热及侧面等温条件下的四边简支矩形薄板的热弹耦合问题进行了较详尽的分析.首先通过对空间量的双三角函数展开,把该问题归结成一个对时间量的三阶常微分方程的求解问题.然后将求得的颇为繁杂的解,对热弹耦合小参数δ作幂级数展开,从而得到了能清晰地表达耦合问题特征的解析表达式,并基于该解析式,提出了关于该类问题的一系列于数值解难以反映出来的结论.
For the purpose of revealing the thermoelastic-coupling characters
of rectangular plates,this paper discusses in detail the thermal shock of the
rectangular plate that is subjected to step-rising heat on the top side,heat
insulation on the bottom side,isothermal temperature on the four flanks,and
that is simply supported on the four sides.With the double Fourier's expe-
nsion on the space field,the above problem is reduced to only a time-
depending one.Finally,the theoretical solutions,showing the characters
of the coupled problem clearly,is deduced from expending the more confus-
ing solutions into the power series according to the thermoelastic coupling
coefficient δ.Based on that,a series of conclusions which are difficult for
numerical methods to arrive at are suggested.
出处
《上海交通大学学报》
EI
CAS
CSCD
北大核心
1990年第5期117-128,共12页
Journal of Shanghai Jiaotong University
关键词
薄板
耦合热冲击
解析解
coupled thermal shock
thin plate
analytical solution
