层叠板随机瞬态温度场响应区间的近似求解

Approximate Solution of Temperature’s Interval of Stochastic Transient Temperature Field for Composite Plates

以传导、对流和辐射边界条件共同作用下的不同材料的层叠板为研究对象,利用伽辽金法得到了该结构温度场的有限元方程。研究了当参数含有随机性时,通过综合运用差分法、Monte-Carlo数值模拟法、Q-Q图法、Box-Cox幂变换法,正态假设检验以及参数区间估计,提出了近似求解温度响应区间的方法和表达式。最后以所有参数均为随机性的三层板结构为例,通过所得温度响应区间与诸多随机样本值的比较,表明所提出的分析和求解策略的有效性与合理性。

For composite plates with materials of each layer different, under heat exchange, heat convection and heat radiation boundary conditions, its temperature finite element equations were deduced by means of Galerkin method. When parameters were random, the randomicity of the nonlinear stochastic transient temperature field was analyzed, and a method was presented to obtain the approximate solution of the temperature’s interval by using synthetically the following techniques： difference method, Monte-Carlo method, Quantile-quantile plot, Box-Cox transformation, hypothesis testing and parameter interval estimation. A 3-layer plate taking all parameters as random was simulated, and the temperature’s interval was compared with lots of temperature’s random samples, which shows that the method presented is reasonable.