Comparison of Ritz and finite element method for stress analysis of silicon elastic elements

V. A. Gridchin, J. Lee, A. Gridchin, V. Gribov, A. Berdinsky, A. Shaporin
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引用次数: 3

Abstract

The results of elastic element (EE) modeling by the Ritz variational method (RVM) for the silicon pressure sensors are compared with the results by the finite element method (FEM) using program package such as ANSYS. The influence of types of the shape functions in RVM for the analysis of the deflection and stress distributions on rectangular diaphragms is studied for 1/spl les/m/spl les/5 where size ratio m=a/b. The comparison of calculated results of the deflection and stress distribution by RVM with those by FEM shows little difference for m=1, but for m>2 all kinds of the shape functions give errors, for example with Hermite polynomials, such as a saddle form on deflection distribution. For m/spl les/2 the difference by the two methods is less than 10%. For the evaluation of displacement of piezoresistors at the most interesting points on the diaphragm, the RVM shows that the deflection and stress distribution can be estimated easily and accurately.
硅弹性元件应力分析的Ritz法与有限元法的比较
利用ANSYS等软件对硅压力传感器进行了里兹变分法(RVM)弹性单元(EE)建模,并与有限元法(FEM)进行了比较。研究了尺寸比m=a/b的1/spl /m/spl /5矩形隔板的形状函数类型对矩形隔板挠度和应力分布分析的影响。当m=1时,RVM法与有限元法计算挠度和应力分布的结果差异不大,但当m>2时,各种形状函数都存在误差,如厄米特多项式,如挠度分布呈鞍形。对于m/spl小于/2,两种方法的差异小于10%。对于膜片上最感兴趣点的压敏电阻位移的评估,RVM表明可以方便准确地估计挠度和应力分布。
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