ANSYS的二次开发与多维稳态导热反问题的数值解

Secondary Development of ANSYS and Numerical Solution of Multi-dimension Steady Heat Conduction Inverse Problem

由于反问题本身所具有的不适定性和复杂性,多维导热反问题的数值方法往往偏于复杂。建立了稳态导热控制方程、边界条件以及附加条件(测量温度)来表述的三维稳态导热反问题的数学模型。在此基础上,利用参数化设计语言APDL对大型通用有限元分析软件ANSYS进行简单的二次开发,从而可快速简易地求解各种复杂几何形状物体导热的反问题,而且只需知道部分点的温度值,无需对热流量进行测量,从而减小因测量误差而带来解的偏差。对一个已知导热系数的物体进行稳态导热反问题求解,误差很小,绝对误差0.055W/m2·℃,相对误差为1.72%,验证了本方法的可行性。而且,为进一步提高解的精确性,可多测量几组,求解出相对应的导热系数,然后把其平均值作为待求的导热系数。此方法同样适用于已知初始条件的多维瞬态导热问题。

Due to the uncertainty and complexity of inverse problem, numerical method of the multi-dimension heat conduction inverse problem is always complex. The mathematics model of three-dimension steady heat conduction inverse problem, including steady heat conduction control equation, boundary conditions and additional conditions (measuring temperature), is established. In virtue of the secondary development with big FEA software ANSYS with ANSYS Parametric Design Language (APDL), heat conduction inverse problem of all kind of complicated object can be solved quickly and easily. The basic step is selecting various measuring spots on the experienced object, measuring the temperatures of the spots, determining the approximate range of thermal conductivity coefficient according to the related data, selecting the suitable cycle increment, establishing parametric model with APDL and finally test calculating thermal conductivity coefficient. In view of the uncertainty of inverse problem and measurement error, all the absolute indexes of difference of calculated temperatures and measurement temperatures should be less than the error during the try calculation. In order to simplify the experiment, the measuring spots are selected among those belong to the surface. During the factual application, more accurate solution would be obtained by reasonably selecting the inner spots. Furthermore, only the temperatures of some spots are necessarily known, so the solution error due to measurement can be greatly decreased. From the result of the calculation of an example, the error is very small, the absolute error and relative error are 0.055W/m2·℃ and 1.72% respectively, which verifies the feasibility of this method. Furthermore, in order to enhance the precision of solution, more data may be measured to obtain corresponding thermal conductivity coefficients, and calculate the mean of the thermal conductivity coefficients as object index. This method is also applicable to multi-dimension transient heat conduction inverse problem with known initial conditions.