Home / Examples / Analysis with Deformed Shape Taken into Account / Example 1: Capacitance Change by Thermal Expansion

Example 1: Capacitance Change by Thermal Expansion

General

Capacitance change of a capacitor by thermal expansion is analyzed.
[Analysis with deformed shape taken into consideration] is used.
Unless specified in the list below, the default conditions will be applied.
Obtain this session's project file. (Right-click and choose 'Save link as')

Results will vary depending on Femtet version and the PC environment.

Three analysis models are prepared.

・Before Deformation (Electric Analysis)

・Deformed Shape Calculation (Stress Analysis)

・After Deformation (Electric Analysis)

See Analysis with Deformed Shape Taken into Account for the details.

Analysis Model 1: Before Deformation

Set up the analysis conditions before the deformation. The analysis model is named “Before Deformation”.

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

Analysis Conditions

Item	Settings
Solver	Electric Analysis [Coulomb]
Analysis Type	Static Analysis (Capacitance)
Options	None

In actuality, the electric field exists outside the analysis domain. Therefore, the open boundary condition below is applied initially.

Tab	Setting Item	Settings
Open Boundary Tab	Type	Absorbing Boundary
Open Boundary Tab	Order of Absorbing Boundary	1st-order

Graphical Object

Create a cubic solid body for a dielectric (Block).

Create the electric potential-setting places by the sheet bodies to set the voltage boundary condition on the top and bottom faces of the dielectric.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	Block	001_Alumina *
1/Sheet	None (imprinting body)
2/Sheet	None (imprinting body)

* Available from the material DB

Boundary Condition

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
V0/Face	Electric	Electric Wall	Specify electric potential 1 [V]
V1/Face	Electric	Electric Wall	Specify electric potential 0 [V]
Outer Boundary Condition *	Electric	Open Boundary	Set up on the open boundary tab.

To set Outer Boundary Condition, go to the [Model] tab

and click [Outer Boundary Condition] .

Analysis Model 2: Deformed Shape Calculation

Set the stress analysis to calculate the deformation caused by the thermal expansion.

Copy Analysis Model 1 (Before Deformation) and set up as follows. The analysis model is named “Deformed Shape Calculation”.

See [Copy Analysis Model into Project] for the details.

Analysis Conditions

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Type	Static Analysis
Options	Thermal Load

Tab	Setting Item	Settings
Step/Thermal Load	Step Setting	Thermal Load Analysis
	Reference Temperature	25 [deg]
	Reached Temperature	200 [deg]

Analysis Model 3: After Deformation

Set up the analysis that takes the deformed shape into account.

Copy Analysis Model 1 (Before Deformation) and set up as follows. The analysis model is named “After Deformation”.

See [Copy Analysis Model into Project] for the details.

Analysis Conditions

Specify Analysis Model 2 (Deformed Shape Calculation) on the results import tab.

Tab	Setting Item	Settings
Results Import	Import Type	[Deformed Shape]
Results Import	Specify Results	Specify the analysis model “Deformed Shape Calculation”

Run Mesher/Solver

Run solver for all analysis models. Calculation of Analysis Model 2 (Deformed Shape Calculation) must be completed before going on to Analysis Model 3 (After Deformation).

Results

To see the calculation results, go to the [Results] tab

and click [Show Numerical Summary Table] .

Results of Analysis Model 1 (Before Deformation) are as follows.

The capacitance of C1-2 is 0.884 [pF].

A displacement diagram of Analysis Model 2 (Deformed Shape Calculation) is shown as below.

The expansion due to the temperature change is observed.

Results of Analysis Model 3 (After Deformation) are as follows.

The capacitance of C1-2 is 0.892 [pF]. It confirms that the capacitance is increased due to the deformation.