Technical Report For Solidworks r1x6r
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Technical Report 1: Stress, Strain, & Displacement Introduction The strength and composition of materials when affected by force can be calculated using specific formula theoretically. However, generating accurate values can only be achieved by means of testing, experimentation and formulation. Since the advancement of technology, this values can now be generated using a software application, this is called the Finite Element Analysis. One example of this is the Solidworks where it can generate the accurate values without experimentation. The Technical Report will compare the result of two figures with the same area and material but with different shapes (cube & cylinder) using both theoretical and solidworks results. The difference in values will be recorded for multiple trials, each having different set of forces ranging from 100 kN to 500 kN.
Software: Solidworks SolidWorks Version 2015 or higher will be used as testing medium for the software side. The FEA (Finite Element Analysis) capability of SolidWorks is integrated to the Simulations add-ins package with the capability to do linear and non-linear analysis. Stress Stress is used to express the loading in of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. Strain Strain is the ratio of change in length to the original, or quantity since it is the ratio of displacement.
. Strain is a dimensionless/unitless
Displacement It is the shortest distance from the initial to the final position of a point when a force is applied. In rigid body, the tern displacement may also include the rotations of the body. Modulus of Elasticity The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region. A stiffer material will have a higher elastic modulus. The unit of Elastic of Modulus has the same unit of stress.
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Technical Report 1: Stress, Strain, & Displacement Yield Point The yield point determines the limits of performance for mechanical components, since it represents the upper limit to forces that can be applied without permanent deformation
.
Figure 1. The slope of stress and strain is denoted by the constant E. (image from Total material website) Von Mises Yield Criterion Solidworks Simulation uses the Von Mises Yield Criterion to calculate the Factor of Safety of many ductile materials. Von Mises Criterion computes the stress along all planes. URES: Resultant Displacement Solidworks Simulation uses the URES: Resultant Displacement to calculate the elongation of the material when a force is applied. URES: Resultant Displacement computes the displacement along all planes. ESTRN: Equivalent Strain Solidworks Simulation uses ESTRN: Equivalent Strain to calculate the strain when a force is applied to a material. ESTRN: Equivalent Strain computes the strain along all planes Sensors Four sensors are placed to both specimen to measure its max Von misses, Principal Stress, Equivalent Strain, and Resultant Displacement.
Delfin
2|Page
Technical Report 1: Stress, Strain, & Displacement Model Information of the Solid Cube Figure
Model name: Cube Current Configuration: Default Solid Bodies Document Name and Reference
Treated As
Volumetric Properties
Solid Body
Mass:75060 kg Volume:27 Density:2780 kg/ Weight:735588 N Area: 9
Boss-Extrude1
Document Path/Date Modified
Figure 2. Information about the Solid Cube Figure generated in the SolidWorks through report
Delfin
3|Page
Technical Report 1: Stress, Strain, & Displacement Model Information of the Solid Cylinder Figure
Model name: Cylinder Current Configuration: Default Solid Bodies Document Name and Reference
Treated As
Volumetric Properties
Solid Body
Mass: 84685.8 kg Volume: 30.4625 Density: 2780 kg/ Weight: 829921 N Area:
Boss-Extrude1
Document Path/Date Modified
Figure 3. Information about the Solid Cylinder Figure generated in the SolidWorks through report
Delfin
4|Page
Technical Report 1: Stress, Strain, & Displacement Part 1: Stress Validation Method Materials under fixed geometry fixture with constant area of two different shapes are subjected to different values of force in compression which will result to different level of stresses. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted.
Formula The following will be used for the theoretical part of validation.
Results Cube Stress (Pa) Trial Area (
Force )
(
)
Simulated (SW) Theoretical
Von misses (
)
Difference
Percent Difference
11178.8
8897.59
44%
Principal (
)
1
9
100
11111.11
2
9
200
22222.22
40017.4
22357.6
17795.18
44%
3
9
300
33333.33
60026.2
33536.3
26692.87
44%
4
9
400
44444.44
80034.9
44715.2
35590.46
44%
5
9
500
55555.56
100044
55894.1
44488.44
44%
Table 1. Summary of 5 trials of cube using both theoretical and simulation method for stress
Delfin
5|Page
Technical Report 1: Stress, Strain, & Displacement Cylinder Stress (Pa) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
Von misses (
)
Difference
Percent Difference
11155.7
5324.79
32%
Principal (
)
1
9
100
11111.11
2
9
200
22222.22
32871.7
22311.5
10649.48
32%
3
9
300
33333.33
49307.6
33467.2
15974.27
32%
4
9
400
44444.44
65743.4
44623
21298.96
32%
5
9
500
55555.56
82179.3
55778.6
26623.74
32%
Table 2. Summary of 5 trials of cylinder using both theoretical and simulation method for stress Interpretation of the Table The values of the Von Mises stress are found to be higher than the theoretical for all the trials on both shapes. The difference of the said stresses is determined to be increasing with the increasing value of load/force. The percentage difference however is generally constant for the generated data at a certain range in the table
Figure 4. Comparison result of stress for 4 trials of cube by means of static simulation Delfin
6|Page
Technical Report 1: Stress, Strain, & Displacement
Figure 5. Comparison result of stress for 4 trials of cylinder by means of static simulation Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks. The data also denotes a constant percent difference of both Von misses and theoretical. Comparing Von misses data (max) to the principal average, the principal average has a nearer value from the theoretical rather than the Von misses. The researcher concludes that the value of Von misses is at max limit of the material rather than the average value that is computed by the theoretical. Part 2: Displacement Validation Method A material under fixed geometry fixture with constant area of two different shapes is subjected to different values of force in compression which will result to different values of displacement. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted. Formula The following will be used for the theoretical part of validation.
(7.24 x
Delfin
N/
)
7|Page
Technical Report 1: Stress, Strain, & Displacement Results Cube Displacement ( ) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
URES: Resultant Displacement ( )
Difference
Percent Difference
1
9
100
0.19%
2
9
200
0.18%
3
9
300
0.13%
4
9
400
0.18%
5
9
500
0.17%
Table 3. Summary of 5 trials of cube using both theoretical and simulation method for displacement
Cylinder Displacement ( ) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
URES: Resultant Displacement ( )
Difference
Percent Difference
1
9
100
2%
2
9
200
2%
3
9
300
2%
4
9
400
2%
5
9
500
2%
Table 4. Summary of 5 trials of cylinder using both theoretical and simulation method for displacement
Delfin
8|Page
Technical Report 1: Stress, Strain, & Displacement Interpretation of Table The values of the URES: Resultant Displacement is found to be higher than the theoretical for all the trials in cube while it is lower when in cylinder. The difference of the said displacement is determined to be increasing with the increasing value of load/force for both figures. The percentage in difference however is inconsistent for the generated data at certain range in the table. The reason for this is the miniscule value of the data. This interpretation is true for both figures.
Figure 6. Comparison result of displacement for 4 trials of cube by means of static simulation
Figure 7. Comparison result of displacement for 4 trials of cylinder by means of static simulation
Delfin
9|Page
Technical Report 1: Stress, Strain, & Displacement Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks on the solid cube figure. However, in the solid cylinder figure, the theoretical data is greater than the data that is generated on the solidworks. The reason might be because of too miniscule data of displacement. The data also denotes a constant percent difference in the solid cylinder of both URES and theoretical while an inconsistent percent difference on the solid cube figure. The minuscule data is obtained because of the high elastic modulus of the material 2024-T4.
Part 3: Strain Validation Method A material under fixed geometry fixture with constant area of two different shapes is subjected to different values of force in compression which will result to different level of strains. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted.
Formula The following will be used for the theoretical part of validation.
Delfin
10 | P a g e
Technical Report 1: Stress, Strain, & Displacement Results Cube Strain Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
ESTRN: Equivalent Strain (
Difference
Percent Difference
)
1
9
100
22%
2
9
200
22%
3
9
300
22%
4
9
400
22%
5
9
500
22%
Table 5. Summary of 5 trials of cube using both theoretical and simulation method for strain
Cylinder Strain Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
ESTRN: Equivalent Strain (
Difference
Percent Difference
)
1
9
100
7%
2
9
200
7%
3
9
300
7%
4
9
400
7%
5
9
500
7%
Table 6. Summary of 5 trials of cylinder using both theoretical and simulation method for strain
Delfin
11 | P a g e
Technical Report 1: Stress, Strain, & Displacement Interpretation of the Table The values of the ESTRN: Equivalent Strain is found to be higher than the theoretical for all the trials. The difference of the said strain is determined to be increasing with the increasing value of load/force. The percentage in difference however is generally constant for the generated data at certain range in the table. This interpretation is true for both figures.
Figure 8. Comparison result of strain for 4 trials of cube by means of static simulation
Figure 9. Comparison result of strain for 4 trials of cylinder by means of static simulation
Delfin
12 | P a g e
Technical Report 1: Stress, Strain, & Displacement Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks. The data also denotes a constant percent difference of both Equivalent Strain and theoretical. The strain also has a miniscule value because of a great modulus of elasticity of the material.
Final Conclusion and Recommendation For the comparison of the different parameters, the researcher conclude that when the given compressive force increases all the set parameters (Stress, Strain, & Displacement) and its difference also increases while the percent difference remains constant. It is also generated in the data that the solution of the Finite Element Analysis (SolidWorks) is greater than the theoretical value excluding the parameter displacement of the cylinder (refer to table 4) where the theoretical is greater than the FEA. The reason for this is still unknown but the researcher suggests that the value might be too miniscule. The strain and the displacement data is minuscule because of the high elasticity of the material 2024-T4 and its solid figure enabled it to withstand the maximum force that is given. Therefore the researcher recommends the use of the Finite Element Analysis in determining the static simulation data of a material.
Delfin
13 | P a g e
Software: Solidworks SolidWorks Version 2015 or higher will be used as testing medium for the software side. The FEA (Finite Element Analysis) capability of SolidWorks is integrated to the Simulations add-ins package with the capability to do linear and non-linear analysis. Stress Stress is used to express the loading in of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. Strain Strain is the ratio of change in length to the original, or quantity since it is the ratio of displacement.
. Strain is a dimensionless/unitless
Displacement It is the shortest distance from the initial to the final position of a point when a force is applied. In rigid body, the tern displacement may also include the rotations of the body. Modulus of Elasticity The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region. A stiffer material will have a higher elastic modulus. The unit of Elastic of Modulus has the same unit of stress.
Delfin
1|Page
Technical Report 1: Stress, Strain, & Displacement Yield Point The yield point determines the limits of performance for mechanical components, since it represents the upper limit to forces that can be applied without permanent deformation
.
Figure 1. The slope of stress and strain is denoted by the constant E. (image from Total material website) Von Mises Yield Criterion Solidworks Simulation uses the Von Mises Yield Criterion to calculate the Factor of Safety of many ductile materials. Von Mises Criterion computes the stress along all planes. URES: Resultant Displacement Solidworks Simulation uses the URES: Resultant Displacement to calculate the elongation of the material when a force is applied. URES: Resultant Displacement computes the displacement along all planes. ESTRN: Equivalent Strain Solidworks Simulation uses ESTRN: Equivalent Strain to calculate the strain when a force is applied to a material. ESTRN: Equivalent Strain computes the strain along all planes Sensors Four sensors are placed to both specimen to measure its max Von misses, Principal Stress, Equivalent Strain, and Resultant Displacement.
Delfin
2|Page
Technical Report 1: Stress, Strain, & Displacement Model Information of the Solid Cube Figure
Model name: Cube Current Configuration: Default Solid Bodies Document Name and Reference
Treated As
Volumetric Properties
Solid Body
Mass:75060 kg Volume:27 Density:2780 kg/ Weight:735588 N Area: 9
Boss-Extrude1
Document Path/Date Modified
Figure 2. Information about the Solid Cube Figure generated in the SolidWorks through report
Delfin
3|Page
Technical Report 1: Stress, Strain, & Displacement Model Information of the Solid Cylinder Figure
Model name: Cylinder Current Configuration: Default Solid Bodies Document Name and Reference
Treated As
Volumetric Properties
Solid Body
Mass: 84685.8 kg Volume: 30.4625 Density: 2780 kg/ Weight: 829921 N Area:
Boss-Extrude1
Document Path/Date Modified
Figure 3. Information about the Solid Cylinder Figure generated in the SolidWorks through report
Delfin
4|Page
Technical Report 1: Stress, Strain, & Displacement Part 1: Stress Validation Method Materials under fixed geometry fixture with constant area of two different shapes are subjected to different values of force in compression which will result to different level of stresses. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted.
Formula The following will be used for the theoretical part of validation.
Results Cube Stress (Pa) Trial Area (
Force )
(
)
Simulated (SW) Theoretical
Von misses (
)
Difference
Percent Difference
11178.8
8897.59
44%
Principal (
)
1
9
100
11111.11
2
9
200
22222.22
40017.4
22357.6
17795.18
44%
3
9
300
33333.33
60026.2
33536.3
26692.87
44%
4
9
400
44444.44
80034.9
44715.2
35590.46
44%
5
9
500
55555.56
100044
55894.1
44488.44
44%
Table 1. Summary of 5 trials of cube using both theoretical and simulation method for stress
Delfin
5|Page
Technical Report 1: Stress, Strain, & Displacement Cylinder Stress (Pa) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
Von misses (
)
Difference
Percent Difference
11155.7
5324.79
32%
Principal (
)
1
9
100
11111.11
2
9
200
22222.22
32871.7
22311.5
10649.48
32%
3
9
300
33333.33
49307.6
33467.2
15974.27
32%
4
9
400
44444.44
65743.4
44623
21298.96
32%
5
9
500
55555.56
82179.3
55778.6
26623.74
32%
Table 2. Summary of 5 trials of cylinder using both theoretical and simulation method for stress Interpretation of the Table The values of the Von Mises stress are found to be higher than the theoretical for all the trials on both shapes. The difference of the said stresses is determined to be increasing with the increasing value of load/force. The percentage difference however is generally constant for the generated data at a certain range in the table
Figure 4. Comparison result of stress for 4 trials of cube by means of static simulation Delfin
6|Page
Technical Report 1: Stress, Strain, & Displacement
Figure 5. Comparison result of stress for 4 trials of cylinder by means of static simulation Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks. The data also denotes a constant percent difference of both Von misses and theoretical. Comparing Von misses data (max) to the principal average, the principal average has a nearer value from the theoretical rather than the Von misses. The researcher concludes that the value of Von misses is at max limit of the material rather than the average value that is computed by the theoretical. Part 2: Displacement Validation Method A material under fixed geometry fixture with constant area of two different shapes is subjected to different values of force in compression which will result to different values of displacement. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted. Formula The following will be used for the theoretical part of validation.
(7.24 x
Delfin
N/
)
7|Page
Technical Report 1: Stress, Strain, & Displacement Results Cube Displacement ( ) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
URES: Resultant Displacement ( )
Difference
Percent Difference
1
9
100
0.19%
2
9
200
0.18%
3
9
300
0.13%
4
9
400
0.18%
5
9
500
0.17%
Table 3. Summary of 5 trials of cube using both theoretical and simulation method for displacement
Cylinder Displacement ( ) Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
URES: Resultant Displacement ( )
Difference
Percent Difference
1
9
100
2%
2
9
200
2%
3
9
300
2%
4
9
400
2%
5
9
500
2%
Table 4. Summary of 5 trials of cylinder using both theoretical and simulation method for displacement
Delfin
8|Page
Technical Report 1: Stress, Strain, & Displacement Interpretation of Table The values of the URES: Resultant Displacement is found to be higher than the theoretical for all the trials in cube while it is lower when in cylinder. The difference of the said displacement is determined to be increasing with the increasing value of load/force for both figures. The percentage in difference however is inconsistent for the generated data at certain range in the table. The reason for this is the miniscule value of the data. This interpretation is true for both figures.
Figure 6. Comparison result of displacement for 4 trials of cube by means of static simulation
Figure 7. Comparison result of displacement for 4 trials of cylinder by means of static simulation
Delfin
9|Page
Technical Report 1: Stress, Strain, & Displacement Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks on the solid cube figure. However, in the solid cylinder figure, the theoretical data is greater than the data that is generated on the solidworks. The reason might be because of too miniscule data of displacement. The data also denotes a constant percent difference in the solid cylinder of both URES and theoretical while an inconsistent percent difference on the solid cube figure. The minuscule data is obtained because of the high elastic modulus of the material 2024-T4.
Part 3: Strain Validation Method A material under fixed geometry fixture with constant area of two different shapes is subjected to different values of force in compression which will result to different level of strains. Results for both the theoretical and simulated will be presented in tabular form. This is later compared and interpreted.
Formula The following will be used for the theoretical part of validation.
Delfin
10 | P a g e
Technical Report 1: Stress, Strain, & Displacement Results Cube Strain Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
ESTRN: Equivalent Strain (
Difference
Percent Difference
)
1
9
100
22%
2
9
200
22%
3
9
300
22%
4
9
400
22%
5
9
500
22%
Table 5. Summary of 5 trials of cube using both theoretical and simulation method for strain
Cylinder Strain Trial
Area
Force
(
(
)
)
Simulated (SW) Theoretical
ESTRN: Equivalent Strain (
Difference
Percent Difference
)
1
9
100
7%
2
9
200
7%
3
9
300
7%
4
9
400
7%
5
9
500
7%
Table 6. Summary of 5 trials of cylinder using both theoretical and simulation method for strain
Delfin
11 | P a g e
Technical Report 1: Stress, Strain, & Displacement Interpretation of the Table The values of the ESTRN: Equivalent Strain is found to be higher than the theoretical for all the trials. The difference of the said strain is determined to be increasing with the increasing value of load/force. The percentage in difference however is generally constant for the generated data at certain range in the table. This interpretation is true for both figures.
Figure 8. Comparison result of strain for 4 trials of cube by means of static simulation
Figure 9. Comparison result of strain for 4 trials of cylinder by means of static simulation
Delfin
12 | P a g e
Technical Report 1: Stress, Strain, & Displacement Conclusion The theoretical data that has been gathered from the formula given is less than the data gathered from the solidworks. The data also denotes a constant percent difference of both Equivalent Strain and theoretical. The strain also has a miniscule value because of a great modulus of elasticity of the material.
Final Conclusion and Recommendation For the comparison of the different parameters, the researcher conclude that when the given compressive force increases all the set parameters (Stress, Strain, & Displacement) and its difference also increases while the percent difference remains constant. It is also generated in the data that the solution of the Finite Element Analysis (SolidWorks) is greater than the theoretical value excluding the parameter displacement of the cylinder (refer to table 4) where the theoretical is greater than the FEA. The reason for this is still unknown but the researcher suggests that the value might be too miniscule. The strain and the displacement data is minuscule because of the high elasticity of the material 2024-T4 and its solid figure enabled it to withstand the maximum force that is given. Therefore the researcher recommends the use of the Finite Element Analysis in determining the static simulation data of a material.
Delfin
13 | P a g e
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