Example2 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.

Three analysis models are prepared.

・Before deformation (electric field analysis)

・Deformed shape (mechanical stress analysis)

・After deformation (electric field analysis)

See [Analysis with the Deformed Shape Taken into Account] for more information.

Analysis Model 1: Before Deformation

Set up analysis before the deformation. The model is named [Before deformation].

Analysis Space

Item	Setting
Analysis Space	3D
Model unit	mm

Analysis Condition

Item	Setting
Solver	Electric field 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	Setting
Open Boundary Tab	Type	Absorbing boundary
Open Boundary Tab	Order of Absorbing Boundary	1st degree

Graphical Object

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

Create the voltage-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	Setting
V0/Face	Electric	Electric wall	Voltage specified, 1[V]
V1/Face	Electric	Electric wall	Voltage specified, 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 mechanical stress analysis to calculate the deformation caused by the thermal expansion.

Copy Analysis Model 1 (before deformation) and set up as follows. The model is named [Deformed shape calculation].

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

Analysis Condition

Item	Setting
Solver	Mechanical stress analysis [Galileo]
Analysis Type	Static Analysis
Options	Thermal Load

Tab	Setting Item	Setting
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 model is named [After deformation].

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

Analysis Condition

Specify Analysis Model 2 (Deformation shape calculation) on the result import tab.

Tab	Setting Item	Setting
Result Import	Import Type	Deformed shape
Result Import	Specify Results	Specify Analysis Model [Deformed Shape Calculation]

Run Mesher/Solver

Run the solver with all analysis models. Calculation of Analysis Model 2 (deformed shape) 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 [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.