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Issues to Note When Applying Linear Analysis

The piezoelectric solver does not simulate the nonlinearity. The issues when applying linear analysis are explained here by comparing the results between nonlinear analysis (having large displacement function) and linear analysis (having no large displacement function) in the stress analysis.

The linear analysis skips the nonlinear effects. The analysis with large displacement function solves the problems more strictly. It is more accurate than the linear analysis.

 

The following points were investigated by applying the static analysis to the axially symmetric disc.

1. The relationship between mesh size and convergence of displacement

2. The difference between large displacement and linear analysis

3. The influence of the disc thickness

 

The investigation was carried out with following conditions in the nonlinear stress analysis.

- Static analysis

- Axisymmetric Radius: 10mm Thickness is parameter

- Load is acceleration

- Side is fixed

 

Parameters

- Large displacement: ON (Nonlinear),OFF (Linear)

- Thickness (0.1mm, 0.08mm)

- Mesh size (3mm-0.02mm)

- Acceleration (-9.8e4, -9.8e3)

 

The displacement diagram is shown below.

 

 

The displacement is plotted in the graph below.

 

Summary

- The resulting displacement differs between the analyses with and without 'large displacement'.

- In the upper left diagram, the gap between the linear and the nonlinear analysis is almost 30% even if the displacement of the disc with radius of 10mm is as small as 0.1 [mm]. It can be said that the displacement is not necessarily linear even if the displacement is small.

- In the linear analysis, the displacement becomes twice if the load is doubled.

- Displacement tends to be large in the linear analysis.

- The influence of the thickness tends to appear significantly in the linear analysis.

Please keep in mind the issues mentioned above when executing the linear analysis.
Obtain the project file used for the test. (Save the project file before open)

 

 

• Reference data 1: A beam fixed at both ends.

A beam fixed at both ends was analyzed as well. As in the case of the disc, there was a significant difference between linear analysis and nonlinear analysis.

The upper diagram below shows the result of the linear analysis. The lower diagram below shows the result of the nonlinear analysis. Mesh size for the analysis is 0.1.

 

• Reference data 2: A beam fixed at one end.

The investigation was carried out in the same manner for the beam fixed at one end. It can be said that the difference in displacements is small compared with the case of the disc.

The upper diagram below shows the result of the linear analysis. The lower diagram below shows the result of the nonlinear analysis. Mesh size for the analysis is 0.1.

Comparing the deformation, it can be observed that the beam is extended in the linear analysis.