Journal of Electrical Engineering
Vol.2 No.02(2014), Article ID:13482,6 pages
DOI:10.12677/JEE.2014.22003

Study on the Laguerre Integral Multivariate Stochastic Finite Element Method

Zonghe Zhou, Zhao Zhang

Military Representative Office of Navy Stationed in 438 Factory, Wuhan

Email: zhouzonghe1982@126.com

Copyright © 2014 by authors and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received: Apr. 2nd, 2014; revised: Apr. 16th, 2014; accepted: Apr. 30th, 2014

ABSTRACT

In the existing single variable Laguerre integral stochastic finite element method, based on Laguerre integral multivariate stochastic finite element formula, the author proposed variable Lagurre integral stochastic finite element method (LISFEM). By using APDL of ANSYS, LISFEM was embedded into ANSYS, and corresponding calculation program module was generated, then using the postprocessing program of ANSYS, the mean and variance of the whole node’s stress and deformation was realized by the cloud image displaying. Finally, took the turbine blade of the two loop as an example, chose different Laguerre integral point number and calculated, then compared with the analytical solution, the calculation results showed that the efficiency of calculating was high, and the less integral point could get high accuracy, so as to test the correctness of this method.

Keywords:Laguerre Integral, Stochastic Finite Element, Straight Blade

Email: zhouzonghe1982@126.com

Laguerre积分，随机有限元，等直叶片

1. 引言

2. 多变量Laguerre积分随机有限元方法

(1)

(2)

(3)

3阶中心矩

(4)

4阶中心矩

(5)

5阶中心矩

(6)

6阶中心矩

(7)

3. 积分随机有限元方法嵌入ANSYS

ANSYS具有很好的二次开发功能，主要的二次开发工具有四种，分别是APDL语言、UIDL界面设计工具、UPFs用户程序和数据接口。利用APDL语言编写积分随机有限元方法的用户程序，只需开发2个程序模块就可实现随机有限元分析的全过程。下面介绍各个模块的功能。

4. 汽轮机叶片的随机响应分析

Figure 1. Straight blade model

Table 1. Variable parameter

Table 2. Integral point and weight after density transformed

Figure 2. The mean deformation’s image of the straight blade

Figure 3. The variance of deformation’s image of the straight blade

Figure 4. The mean stress’s image of the straight blade

Figure 5. The variance of stress’s image of the straight blade

Table 3. The mean of the maximum stress and deformation

Table 4. The variance of the maximum stress and deformation

5. 结论

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