1. Rene Herrmann Compounding and Composites

2. FEM static load analyzes The purpose of the static test is to define areas of large strain. It is these areas that need stiffering in order to prevent formation of stress. For developing light weight structures the engineer should try to keep the mass to a minimum and maximize stiffness while keeping the complexity for manufacturing low. The next slides will illustrate HOW such an analysis could proceed. The user is however required to have an basic understanding of beam deflection theory.

3. FEM static loading (comsol 1) Start COMSOL and load Exercise02.mph The plate dimensions are 250 x 250 mm, the thickness is 5mm Select under SOLVE the Solver parameter option and choose Static Select in PHYSICS the Boundery Settings option and arrest the sides of the panel in all directions by selecting surfaces 1, 2,5 and 6. For these surfaces the CONSTRAINT seen in the right field must be ticked. Select under PHYSICS the Point Settings option and select point 5 which then turns red in color. Select on the right side the load option and apply a 555555N load in Z – direction.

4. FEM static loading (comsol 2) Select under PHYSICS the Subdomain Settings (F8) and choose object 1 and define the material properties as 10000000000Pa and Poission ratio as 0.33 and Density as 2300kg/m^3 Select under POSTPROCESSING the Plot Parameters option (F12) and select under General only the Subdomain and Max/Min Marker plot type option. Select also under Subdomain the predefined quantities as Strain energy density or (later) First principle strain. Select under Max/Min predefined quantities as First principle strain.

5. FEM static loading (comsol 3) Select under MESH the Free Mesh Parameters Option (F9) and select under Global a predefined mesh size of NORMAL and choose APPLY before pressing OK Choose under MESH the Initialze Mesh option Select under SOLVE the Solve problem option. Verify that the strain energy density is largest in the center of the plate where the point force is applied. Realize ALSO that the diagonal direction of the plate is less strained than the ortogonal direction. Ortogonal direction has to be stiffened and the fibers must therefore have diagonal directions. To stiffeners however should be ortogonal. (Use different view options)

6. FEM static loading (comsol 4) Redo this static load analysis and plot instead First principle strain. To do this select POSTPROCESSING and Plot parameter option and field Subdomain where predefined quanties is First principle strain. Verify that the Strain maximum in the center of the plate is about 3.257 meaning the plate has surely broken because the material increased its length 3.2 fold. The realistic limit is 100 times less.

7. FEM Eigenfrequency analysis The purpose of the Eigenfrequency analysis is to find the resonance frequencies and the modes of vibration. The result will depend on the DENSITY of the material defined in PHYSICS, Subdomain Settings. The angular frequency of a mass spring system analyzed by FEM calculates the mass by using volumen and density of the material. The following slides will illustrate HOW such an analysis could proceed.

8. Eigenfrequency analysis (1) Select under SOLVE the Solver Parameter option and choose as Analysis type Eigenfrequency. Choose to the right side in General the Desired numbers of Eigenfrequencies as 20. Press APPLY and OK. Select under SOLVE the Solve Problem option. Select then the POSTPROCESSING and Plot parameter option. Find under General on the right top side the field Solution to use and the field Eigenfrequency. In the drop down menu you find the first 20 resonant frequencies calculated. The lowest frequency is found to be 294.5 Hz.

9. Eigenfrequency analysis (1) Redo this analysis but change in PHYSICS under Subdomain Settings (F8) the materials density from 2300 to 1150. Find that an deceased density means less mass and therefore higher frequencies. Find the lowest frequency to be 416.5 Hz Test the opposite to produce lower frequencies by selecting a high density.

10. FEM transient analysis The transient analysis is the most complex analysis because it is time dependent. The test analyses how an vibration decreases in amplitude when caused by an extrenal time dependent excitation. The following slides will analyse HOW a vibration caused by an impacting hammer in the center of the plate will cause vibrational oscillations and how they are damped.

11. Transient analysis (1) Choose under PHYSICS the Subdomain Option and verify that the density of the plate is 2300. Redo the Eigenfrequency analysis and measure the first Eigenfrequency to 294.5 Hz. Calcualte that teh inverse of this frequency is the oscillation time, meaning about 0.0034s. We make an transient analysis for 10 periods with 10 points per period. Time t will therefore be defined from 0:0.00034:0.034. (Very important!!!) Select SOLVE and Solver Parameters to Analysis type Transient. For General select Time Stepping, Times as the above example. Select also Time Steps taken by solver to INTERMEDIATE. Select APPLY and OK.

12. Transient analysis (2) Select under OPTIONS the Function menu. Press New. Give as Function name: My_first_hammer and select interpolation, Use data from: Table and press OK. You are no provided with a table to be filled in. X is the time and f(x) is RELATIVE AMPLITUDE, meaning 1 is 100% and -0.3 is 30% in opposite direction. Define an piecewise function that fullfills the follwing pairs, (x,f(x)=(0,0);(0.00034,0.5); (0.00068,1);(0.00102,-0.2); (0.00136,0) Select under PHYSICS and Subdomain Settings option the materials Damping as No damping (important you return to this).

13. Transient analysis (3) Select SOLVE and Solve Problem (Now you really can have small pause – no smoking please!) Select POSTPROCESSING and Domain Plot Parameters, find under General, Point Plot which you tick and select under Solutions to use all points given. Use in the same window the folder POINT and select for point plot for Predefined quantities the z-displacement and Point selection is Point 5. When pressing APPLY you are provided with a window showing you 10 undamped oscillations at the center of the plate because the time of analysis is 10 periods with 10 points per period.

14. Transient analysis (4) Redo the same analysis but change in PHYSICS, Subdomain Settings the Damping of the Material from No Damping to Rayleigth Damping. Parameter alfa=0.003 and beta 0.0003 and find that the oscillation now dies out after 2-3 vibrations. For composite light weight materials the value alfa is between 0.15 and 0.45. Beta can be calculated using beta=alfa/w_res^2.