Finite Element Analysis of the Strain Energy Stored in Hydroxide-Catalysis Bonded Fused Silica Samples
Peter Murray Institute for Gravitational Research August 2007
Summary
Tutorial presents one way to model the strain energy stored in a hydroxide-catalysis bond between two fused silica cylinders Typically bond is ~65 nm thick, which is too thin to be modelled in Finite Element Analysis Instead, we can extract the energy ratio by running a series of models with 0.2 – 0.5 mm thick bonds and plot the energy ratios against bond thickness for each resonant mode
Case Study
2 Fused Silica Cylinders
First 65 mm diameter by 70 mm long Second 65 mm diameter by 50 mm long
Hydroxide-Catalysis Bond between two faces
~65 nm thick bond Covering entire 32.2 cm2 area of face
Material Properties
Young’s Modulus: 72 GPa Density: 2202 kg/m3 Poisson’s Ratio: 0.17
Material Properties
Young’s Modulus: 7.9 GPa Density: 2202 kg/m3 Poisson’s Ratio: 0.17
Case Study
Use Finite Element to:
Model 0.005 m thick Hydroxide-Catalysis bond between the two cylinders Apply the properties of the bond Find the resonant frequencies of the cylinder Plot the mode shapes of these resonances Extract the ratio of strain energy stored in the bond region to the total energy in the entire bonded mass
Creating the Model
Open ANSYS Create New Jobname
i.e. Bond0005mm
Select Structural GUI
ANSYS Main Menu > Preferences > Structural > OK
Creating the Model
Define Element Type
ANSYS Main Menu > Preprosessor > Element Type > Add/Edit/Delete > Add > Solid Brick 20node 95 > OK
Creating the Model
Create First Cylinder
65 mm diameter 70 mm long ANSYS Main Menu > Preprocessor > Modelling > Create > Volumes > Cylinder > Solid Cylinder
Radius: 0.065/2 Depth: 0.07
• NOTE: Units are in metres
> Apply
Creating the Model
Create Bond Region
65 mm diameter 0.5 mm long ANSYS Main Menu > Preprocessor > Modelling > Create > Volumes > Cylinder > Solid Cylinder
Radius: 0.065/2 Depth: -0.0005
• NOTE: Negative Depth
> OK
Creating the Model
Offset workplane by thickness of the bond so that front face of second silica cylinder lines up with bond
Workplane > Offset WP by increments… > Element Type > X, Y, Z Offsets: 0, 0, -0.0005 > OK
Creating the Model
Create Second Cylinder
65 mm diameter 50 mm long ANSYS Main Menu > Preprocessor > Modelling > Create > Volumes > Cylinder > Solid Cylinder
Radius: 0.065/2 Depth: -0.05
• NOTE: Still Negative
> OK
Creating the Model
Creating the Model
So far the three cylinders are in contact, but not attached together Must glue the surfaces together Select Right View and Zoom in on bond region
Creating the Model
Glue First Cylinder to Bond
ANSYS Main Menu > Preprocessor > Modelling > Operate > Booleans > Glue > Volumes
Select First Cylinder Select Bond Region
> APPLY
Creating the Model
Glue Second Cylinder to Bond
ANSYS Main Menu > Preprocessor > Modelling > Operate > Booleans > Glue > Volumes
Select Second Cylinder Select Bond Region
> OK
Define Material Properties
Properties detailed in Case Study Slide Silica
ANSYS Main Menu > Preprocessor > Material Models > Material Model Number 1 > Structural > Linear > Elastic > Isotropic
EX: 7.2E10 PRXY: 0.17
> OK > Structural > Density
Density: 2202
> OK
Define Material Properties
Hydroxide-Catalysis Bond
ANSYS Main Menu > Preprocessor > Material Models > Material > New Model… > Material Model Number 2 > Structural > Linear > Elastic > Isotropic
EX: 7.9E9 PRXY: 0.17
> OK > Structural > Density
Density: 2202
> OK
Meshing the Model
Define HydroxideCatalysis Bond Mesh
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Element Attributes: > Global > Set > Material Number
MAT: 2
> OK
Meshing the Model
Set element length to be ten times the modelled bond thickness
• NOTE: Too small an element length will create mesh with more nodes than the licence permits
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Size Controls: > Global > Set > Element Length
SIZE: 0.005
> OK
Meshing the Model
Mesh the Bond
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Mesh:
Volumes
> Shape:
Hex/Wedge Sweep
> Select Bond Region > OK
Meshing the Model
Define Silica Cylinder Mesh
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Element Attributes: > Global > Set > Material Number
MAT: 1
> OK
Meshing the Model
Remove the set element length
• NOTE: The mesh will automatically map to match the mesh on the faces of the bond
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Size Controls: > Global > Set > Element Length
SIZE: 0
> OK
Meshing the Model
Mesh the Cylinders
ANSYS Main Menu > Preprocessor > Meshing > Mesh Tool > Mesh:
Volumes
> Shape:
Hex/Wedge Sweep
> Select Both Cylinders > OK
Meshing the Model
Running a Modal Analysis
Set type of analysis to modal
ANSYS Main Menu > Solution > Analysis Type > New Analysis > Type of Analysis
Modal
> OK
Running a Modal Analysis
Set analysis options
ANSYS Main Menu > Solution > Analysis Type > Analysis Options > No. of modes to extract
25
• NOTE: This depends on how many modes you wish to find
> Expand mode shapes
Yes
> No. of modes to expand
25
> Calulate elem results?
Yes
> OK
Running a Modal Analysis
Specify range of frequencies to be analysed
Start Frequency
1000 Hz
• NOTE: This is to eliminate displacement modes
End Frequency
100000 Hz
• NOTE: This is the upper limit of experimental measurements
Running a Modal Analysis
Save the Database
SAVE_DB
Run the Analysis
ANSYS Main Menu > Solution > Solve > Current LS > OK Warning Message > OK
Have a Cup of Coffee
Listing Resonant Mode Frequencies
To generate a list of resonant mode frequencies
ANSYS Main Menu > General Postproc > Results Summary
Picking Resonant Mode Frequencies
The element results for each individual resonant mode can be selected
ANSYS Main Menu > General Postproc > Read Results > By Pick Select result you wish to load > Read > Close
Plotting Resonant Mode Shapes
Each resonant mode picked can be plotted
ANSYS Main Menu > General Postproc > Plot Results > Contour Plot > Nodal Solu
Nodal Solution DOF Solution Displacement vector sum
> OK
Plotting Resonant Mode Shapes
Calculating Total Strain Energy
Create Strain Energy Table
ANSYS Main Menu > General Postproc > Element Table > Define Table > Add
Energy Strain Energy SENE
> OK
Calculating Total Strain Energy
List Strain Energy Element Table
ANSYS Main Menu > General Postproc > Element Table > List Elem Table
SENE
> OK
Calculating Total Strain Energy
Sum total strain energy by adding individual strain energies from table
ANSYS Main Menu > General Postproc > Element Table > Sum of Each Item > OK
Note total strain energy in Excel or MATLAB
Calculating Total Strain Energy
For the remaining resonant modes
Select Results by Pick Plot Nodal Solution Define Element Table
Update
• NOTE: For each picked set of results the element table must be updated.
List Element Table Sum of Each Item Take note of each total strain energy
Calculating Strain Energy in Bond
Select only elements that lie in the bond region
Select > Entities > Volumes > By Attributes > Material num
2
> Apply > Plot
Calculating Strain Energy in Bond
Select only elements that lie in the bond region
Select > Entities > Elements > Attached to > Volumes > From Full > Apply > Plot > OK
Calculating Strain Energy in Bond
Select Results by Pick Define Element Table
Update
• NOTE: For each picked set of results the element table must be updated.
List Element Table Sum of Each Item Take note of each total strain energy
Calculating Energy Ratios
The Ratio of strain energy stored in the bond region to the total strain energy in the sample can be calculated by: Strain Energy bond
Strain Energy t ot al
For this model the first five energy ratios should be:
Frequency Total Strain Bond Strain Ratio
1
2 3 4 5
14740
14740 15037 22917 26520
4.29E+09
4.29E+09 4.46E+09 1.04E+10 1.39E+10
2.64E+08
2.64E+08 3.07E+08 6.49E+08 9.84E+08
6.16E-02
6.16E-02 6.88E-02 6.26E-02 7.08E-02
Calculating Energy Ratio
Repeat Model for different bond thicknesses
0.00045 0.0004 0.00035 0.0003 0.00025 0.0002
Plot Energy Ratio v Thickness for each mode Calculate Energy Ratio for 65 nm