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

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⩽m⩽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⩽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