Engineering Page

Finite Element Analysis of Structures

The Engineer's Golden Rule:
Never use a 1/4 inch bolt where a 1/2 inch bolt will do!

Before retiring in 1990, I worked at the Lawrence Livermore National Lab for 30 years. The last few years I was the Advanced Engineering Analysis Group Leader in Weapons Engineering Division. We analyzed very complex structures. Physics developed the concepts and engineering made them deliverable. It was a great job and it was rewarding to help win the Cold War.  Before becoming group leader, the last weapon system I worked on was the B-83. See a web page on the B-83 and here This is a page on Deployment.

The critical thinking required for engineering analysis is hard work and is like weight lifting for the brain.

BULLET IMPACT.... Here is a 38 special lead bullet traveling at 1000 fps impacting a 1/2" aluminum 1100-O plate. The aluminum plate is 5" in diameter and is free to translate, simulating its being supported by a string. The first view is at the time of contact. The second view is after about half of the bullet's energy has been dissipated. The third view is when about 90% of the energy has been delivered to the plate. The 4th view is a close up showing the bullet's mesh detail and the fringes of stress. The calculation halts at this point because the mesh has distorted too much to continue without rezoning. This calculation using John Hallquist's DYNA2D code took about 5 minutes on my Pentium 200 MMX computer.

	Web www.varmintal.com

CONSULTING.... I have my Pentium 200 MMX computer setup for Finite Element calculations. It boots up in DOS ready to make 2-D and 3-D meshes and run the NIKE and/or DYNA calculations. If you have a difficult structural problem that needs to be analyzed and/or redesigned, I can give you a preview of what can be done and an estimate of the cost. I can be contacted via Email.

STOLLE PANDA ACTION.... Here is an example 3D Finite Element Analysis using John Hallquist's NIKE3D Finite Element Code. The stress levels in a 6-PPC caliber Stolle Panda benchrest rifle action are shown at a peak internal chamber pressure of 50,000 psi. This pressure occurs during firing when the bullet has only traveled a short distance down the barrel. I have updated the calculation with the latest LS-DYNA Finite Element Code. Click Here to view the updated results. The first Figure shows the action with the bolt in the locked position. The second Figure shows only the bolt where the maximum stress level, in the lugs, is 87,700 psi. The third Figure is the action with a maximum stress level of only 41,300 psi. Note that the high stressed region of the bolt is in compression and occurs at the area of contact with the action. The stress levels are in psi, see the legend. To run this calculation out to seven time steps, took about 2 hours of number crunching. FEA Publications published my analysis in the .pdf format. Click here to view the publication. 

A more detailed analysis of the Stolle Panda action stresses and deflections here.

This is a animated deformation view as the pressure increases from 0 to 50,000 psi in 5,000 psi steps. The 243 Win brass has a friction coefficient of 0.41 between the brass and the 416 stainless steel chamber. The fringes are of effective plastic strain. Note that the primer backs out at first and then is reseated. The detailed calculation is here.

BOLT ANALYSIS.... I worked for many years at the Lawrence Livermore National Laboratory performing engineering structural analysis on complex systems. The example calculation above is a 2D Finite Element Analysis of a 4-40 socket head cap screw being loaded to its breaking point and the resulting stress levels. The FEA software used was John Hallquist's NIKE2D Finite Element Code. The number crunching took about 10 minutes of CPU time on my P5-200 MMX computer.

TRUCK LEAF SPRING.... Above is an example of a truck leaf spring analysis using John Hallquist's NIKE2D with the plane strain option. The first view is the spring mesh outline in the unloaded condition. There are slide surfaces between the leaves and between the end coils and the shafts. The slide surfaces transmit compressive loads, and allow sliding with friction. The second figure shows the stress levels with the spring deflected 5 inches. The third Figure is a close up view of one end, showing the mesh detail. The shaft is not allowed to rotate, and the spring coil rotates around the shaft with a 0.1 coefficient of friction.

LOAD DEFLECTION CURVE.... I modeled the Truck Leaf Spring in 3D and ran an implicit quasi-static calculation with LS-DYNA to calculate the load deflection characteristics of the spring. Notice that during the early deflections there is some stick and slip as the leaves contact each other.

FULLY LOADED.... Here the spring is deflected 3" at the center and the load is 8600 pounds. The stress is high and it would be lower if the short leaves had tapered ends. The end pins are allowed to move horizontally since the spring is quite a bit longer when loaded. Very high stresses would occur if the ends were prevented from moving to allow for the increased spring length.

MOVIE.... Here is an animation of the deflection and stress levels as the spring is loaded.

CONTACT SURFACE.... This clip shows the movement as the spring increases its length and the rotation around the end pin. The pin is allowed to move to the right, but restrained from rotation and moving vertically.  If the link system in mounting the spring did not allow the increase if length the stresses in the main leaf would be very high.

TUNING FORK.... I measured a steel 440 Hz tuning fork (note "A" on the music scale) with a dial caliper to determine the dimensions for a 2D finite element plane stress model with a 0.155 inch thickness. A plane strain model (infinitely long normal to the above views) was less accurate in predicting the correct mode frequency.  I used the NIKE2D Finite Element code for the modal analysis. The blue tuning fork in its rest state and red views show the first 5 natural frequency mode shapes. The handle of the tuning fork was not modeled since is is merely a way to hold the tuning fork without dampening out the vibrations. Using the average measurements of the geometry and properties of 4140 steel, the mode 1 accuracy is within 3.2%. The frequencies are:

Mode 1    454 Hz
Mode 2  2,850 Hz
Mode 3  7,513 Hz
Mode 4 10,947 Hz
Mode 5 16,657 Hz

The tuning fork is made of steel with a modulus, E = 29 msi, Poisson ratio = .29 rho = .283 lb/in^3
These are the dimensions measured from the tuning fork. See how accurately your software calculates Mode 1.

THREE DIMENSIONAL MODEL.... The Tuning Fork modal analysis was repeated using LS-DYNA with a 3-D mesh. Here are the first 4 modes shown in animated gif files.

Mode 1 at 436.78 Hz (0.73% Error)	Mode 2 at 2739.2 Hz
Mode 3A at 7248.9 Hz	Mode 4 at 8113.8 Hz (torsion)

Notice that it was not possible to identify Mode 4 (a rotational twisting of the tuning fork tines) with the 2-D model.

HOW ACCURATE?.... How accurately do the FEA codes calculate the mode vibration frequencies? Below is a table comparing the modal frequency calculations for the first 5 mode shapes of a steel cantilever beam with a 0.5" square cross section and a length of 20". The equation in Chapter One, from the Shock and Vibration Handbook (Third Edition) should be quite accurate since it uses a "fudge factor" for each mode to normalize the results to test data.

This view of the 0.5" square beam is Mode #3 at 695 Hz. The left end condition is fixed to a rigid wall.

Mode 1 39.90 Hz	Mode 2 249.4 Hz
Mode 3 695.0 Hz	Mode 4 1353. Hz
Mode 5 2218. Hz	Torsional Mode 1395.3 Hz

Modal Analysis Accuracy Comparison
Mode Frequencies in Hz
Steel Cantilever Beam 0.5" x 0.5" x 20" long

.

MAXIMUM SPIN VELOCITY.... This is in response to some of the BBS posts about "How Fast?" can one shoot a bullet before it will explode in midair. It turns out that it is not how much velocity, but rather, how fast is it spinning that counts. A bullet with a thicker jacket will withstand higher spin velocities than the bullet I selected to model, but here are the results of the analysis.

I have done a 2D Finite Element calculation of the spin velocity necessary to fail a .224" 40 gr. bullet with a 0.012" gilding metal jacket wall and a pure lead core. The yield stress used for the gilding metal (G21000 95Cu/5Zn) was 15 KSI. At a spin velocity of 307,500 rpm a condition of plastic instability occurs. The bullet's jacket begins to yield and the radius increases. This increase of radius puts an even higher stress on the jacket, but the jacket metal is strain hardening. Instability occurs when the radius increases at a greater rate than the jacket is strengthened due to strain hardening. The Finite Element Code could not find an equilibrium position for the next increment of spin velocity and terminated. Therefore, from the calculation, this bullet would fly apart at or near 307,500 rpm. Using this as the maximum spin velocity capability, the following are the twist rates (inches for one turn) and the associated muzzle velocity to fail this bullet:

Twist = 7 Max Vel = 2989 fps
Twist = 8 Max Vel = 3416 fps
Twist = 9 Max Vel = 3843 fps
Twist = 10 Max Vel = 4270 fps
Twist = 11 Max Vel = 4697 fps
Twist = 12 Max Vel = 5124 fps
Twist = 13 Max Vel = 5551 fps
Twist = 14 Max Vel = 5978 fps
Twist = 15 Max Vel = 6405 fps
Twist = 16 Max Vel = 6832 fps

Mesh outline.

Deformations amplified 20X.

Effective stress.

The first Figure is the outline and detail of the Finite Element mesh. The second Figure is of the deformations, amplified by 20X, at 307,500 rpm. The third Figure is the effective stress levels in the jacket gilding metal at 307,500 rpm and it shows that most of the cylindrical section of the bullet is stressed above the 15 KSI yield stress. The maximum stress is 16.46 KSI. Any damage done to the bullet during firing, such as engraving of the jacket and deformations due to torsional impulse will only reduce the bullet's spin velocity capability.

NOSLER BULLET.... This is a 2D Finite Element analysis, using the NIKE2D code, of a spinning .243" 55 gr. Nosler Ballistic Tip bullet. One would think that a bullet with a larger diameter would have less spin velocity capability than a smaller bullet. But this bullet design with the same material properties as the .224 bullet above, fails at 420,000 rpm. The good people at Nosler have cleverly strengthened the bullet to withstand high spin velocities. The first improvement is that the solid base has enough thickness so it does not dish in from the high powder pressures or after exit when the jacket wants to expand radially. Note that the base of the .224 bullet is concave. The solid base also minimizes the radial expansion of the jacket near the base. The second feature is the thick boss at the jacket mouth which provides hoop strength to reduce radial expansion. I did not include the plastic nose tip in the calculation. It is such a light material and the diameter is so small that it would put only a very small radial loading on the jacket nose. But plastic nose tip's presence during flight prevents the in flight stagnation gas pressure from radially forcing open the nose of the jacket. All of these features combined make a very stable bullet for surviving high spin velocities. Using 420,000 rpm as the maximum spin velocity capability, the following are the twist rates (inches for one turn) and the associated muzzle velocity to fail this bullet:

Twist = 7 Max Vel = 4083 fps
Twist = 8 Max Vel = 4667 fps
Twist = 9 Max Vel = 5250 fps
Twist = 10 Max Vel = 5833 fps
Twist = 11 Max Vel = 6417 fps
Twist = 12 Max Vel = 7000 fps
Twist = 13 Max Vel = 7583 fps
Twist = 14 Max Vel = 8167 fps
Twist = 15 Max Vel = 8750 fps
Twist = 16 Max Vel = 9333 fps

Mesh Unloaded

Deformed times 5X

Stress levels at 420,000 rpm

The first Figure is the FEA mesh detail in the unloaded condition. The second Figure is the deformations that occur at 420,000 rpm just before failure with the deformations amplified by 5X. Note that the solid base does not undergo the concave deformations of the thin based bullet above and remains flat. The soft lead core is radially forced outward against the jacket and the nose opening diameter of the jacket remains almost unchanged. The third Figure shows the stress levels in the jacket and a stress of 25.9 KSI is reached before the bullet fails. This, in my opinion, is a very well thought out bullet design.

STAR TRACKER CAMERA.... Here is an example Finite Element Analysis using John Hallquist's NIKE3D. The Star Tracker Camera body and baffle are exposed to 100 G's of X Acceleration and the resulting stress levels are shown. In the second view, the baffle is removed from the camera

UV/VISIBLE CAMERA.... Here is another example of Finite Element Analysis using NIKE3D. The UV/Visible Camera body and baffle are exposed to 100 G's of Y Acceleration and the resulting stress levels are shown. In the second view, the baffle is removed from the camera body and rotated 180° for better viewing.

FREE SOFTWARE.... If you have made it this far, there is a reward! Here are two FREE engineering tools that I have used over the years. The first one, BOLTS.ZIP (34K) is a bolt calculator program that calculates how many bolts are required to withstand a given axial load with a specified yield safety factor. The code includes most bolt material properties and bolt data for sizes from 0-80 up to 1-1/2"-6 and for both NC and NF threads. If a bolt circle diameter is specified, it will display a CGA scale drawing of the bolt pattern. Want to forget about DOS? See the new Bolt Calculator below.

NEW BOLT CALCULATOR.... Paul Bussieres has ported the old DOS Bolt Calculator program over to Visual Basic 6.0. He has done an excellent job keeping it small plus all the instructions are right on the screen. I have checked it out and it works well and is much easier to use than the old DOS version. Click on boltsvb.zip (33K) and download the file to a temp folder on your compute. No installation is required. When you unzip it, it will create a C:\BoltsVB folder and put two files in that folder, the executable and an icon file.. Use your Find command and look for boltsvb.exe on your C: drive. Right click on boltsvb.exe and create a icon on your desktop or double click on boltsvb.exe and calculate the number and size of bolts to support a given load. If you don't like the program, merely delete the bolts folder on your C: drive. There are no other files added to your computer.

Screen view of the boltsvb.exe calculation for an axial load of 5000 lb and using bolts
made of Grade 8 steel. Once the user selects a bolt size, then he can specify how many
bolts to use.

Output from boltsvb.exe after
selecting 6 bolts instead of 5.

GAS EQUATION OF STATE.... The GASB.ZIP (26K) program is the old DOS version of a gas equation of state solver. Given a temperature and any two of PRESSURE, VOLUME, or MASS, it calculates the third. The Beattie-Bridgeman Equation of State data for 10 common gases are built into the code. The solutions are reasonable for temperatures from about -60°F to 500°F. The solutions is not valid near the triple point for a given gas.

Down load the software by clicking on the name. They are zipped and must be unzipped to be used. These codes were written a long time ago and have to be run in a DOS Box. They are not pretty, but if you need to know how many bolts or the mass of the gas, they will quickly give reasonable results.

NEW GAS PROGRAM.... Paul Bussieres has done an excellent job translating the old Gasb.exe program from BASIC to Visual Basic 6.0. Click on GasVB.zip (16K) and download the file to a temporary folder on your compute. No installation is required. When you unzip it, it will create a C:\GasVB folder and puts two files in that folder, the executable and an icon file. Use your Find command and look for GasVB.exe on your C: drive. Right click on GasVB.exe and send a shortcut Icon on your desktop or double click on GasVB.exe and calculate the properties of the listed gases. If you don't like the program, merely delete the C:\GasVB folder on your C: drive. There are no other files added to your computer.

Sample screen shot for calculating Hydrogen, given there was 100 psi
in a 10 liter container. The code calculates the mass. Then see below.

The code also calculates the pressure change for a range of temperatures that are user selected.

MATERIAL PROPERTIES DATA BASE.... I have included a material.txt data base of over 1000 structural materials. The properties are in English Units. These are the data that I have use for years as input to the Finite Element calculations. Below is a sample of the data for the first nine entries. 

Material Name and Condition.                                  Density Yng's Poiss  Yld   Ult  Elong Redu CTE   Yld
                                                              lb/in^3 Modul Ratio  Strs  Strs       Area 10^-6 off-
                                                                       msi         ksi   ksi    %    %   /degF set

acrylic lucite                                                 0.0430  0.43 0.400   6.0  10.5   6.0  0.0 36.00 0.20
aluminum pure 99.996 annealed                                  0.0970 10.00 0.330   1.8   7.0  50.0  0.0 13.20 0.20
aluminum pure 99.45-o condition                                0.0980 10.00 0.330   4.0  12.0  30.0  0.0 13.20 0.20
aluminum pure-h12 sheet                                        0.0980 10.00 0.330  12.0  14.0   8.0  0.0 13.20 0.20
aluminum pure-h16 sheet                                        0.0980 10.00 0.330  16.0  18.0   4.0  0.0 13.20 0.20
aluminum 1060-o sheet                                          0.0980 10.00 0.330   4.0  10.0  43.0  0.0 13.10 0.20
aluminum 1060-h12 sheet                                        0.0980 10.00 0.330  11.0  12.0  16.0  0.0 13.10 0.20
aluminum 1060-h18 sheet                                        0.0980 10.00 0.330  18.0  19.0   6.0  0.0 13.10 0.20
aluminum 1100-o sheet                                          0.0980 10.00 0.330   5.0  14.0  35.0  0.0 13.10 0.20

LS-DYNA USERS.... I have also calculated the material properties for the complete materials data base to be used in LS-DYNA as Mat #18 (*MAT_POWER_LAW_PLASTICITY). Click on mat18.zip (67Kb) to download the file. Once the file is downloaded and unzipped you can use your text editor to search for the material of interest. Comment cards are included for each material that give the properties data plus the calculated strain hardening power law values. Each material entry is formatted so that it can copied from the text file and pasted directly into the LS-DYNA k file. I have made the MID (material number xx) and it will need to be changed to the correct value.

Here is a typical material example showing the values for Aluminum 6061-T6

*MAT_POWER_LAW_PLASTICITY
$#    ******  Strain-Hardening Equation Material (Mat 18) ******
$# Material . . . . ALUMINUM 6061-t6
$# Material density . . . . . .      0.09800   lb/in^3
$# Young's Modulus. . . . . . .      1.000E+07 psi
$# Shear Modulus. . . . . . . .      3.759E+06 psi
$# Bulk Modulus . . . . . . . .      9.804E+06 psi
$# Poisson's ratio. . . . . . .      0.3300    
$# Yield stress at offset . . .  42200.0       psi
$# Engineering ultimate stress.  44900.0       psi
$# Elongation at failure. . . .     16.50      %
$# Reduction in area. . . . . .     50.00      %
$# CTE. . . . . . . . . . . . .      1.310E-05 1/F
$# Yield offset . . . . . . . .      0.20000   %
$# ------------------ Calculated values -----------------------
$# Strain Hardening equation       s = s0 * e^m
$# Equation constants             s0 =   54943.   m  = 0.050692
$# Yield point                    sy =   41613.   ey = 0.004161
$# Ultimate (Engineering)         SU =   44900.   EU = 0.051999
$# Ultimate (True)               sut =   47235.  eut = 0.050692
$# Failure  (True)               sft =   53931.  eft = 0.693147
$#     MID       RHO         E        PR         K         N       src       srp
        xx 0.0002539 1.0000E+7  0.330000    54943. 0.0506919
$#    sigy        vp
     0.000     0.000
     

You can purchase quality materials from Online Metals in any quantities/sizes.

Table 1: Summary of the example problems

Brief description of most of the example problems listed in the table:

DYNA2D

I357 This is a 357 magnum bullet traveling at 1000 fps and impacting a copper plate. There is a type 4 sliding interface between the bullet and the plate.

CUTV This is a high explosive actuated valve cutting a 20 mil thick stainless steel burst disk. The disk has 9000 psi of gas pressure behind it. The force acting on the cutting end of the plunger is much less than the approximately 4000 lb of driving force of the cutter.

NIKE2D

ADISK4 This is an analysis of a machined burst disk to determine the burst pressure.

B440 This is the analysis of a high strength 4-40 heat treated cap screw under axial load. The thread form is standard UNC sized for minimum material condition. The load is applied by a displacement boundary. The thread contact is implemented with the type 4 sliding interface with a 0.3 friction factor to simulate clean, dry threads. The failure load agrees with the minimum tested tensile strength listed in the specifications. The bolt material is implemented with the material model number 10, which is the power law hardening isotropic plasticity material model. The STRAIN code was used to format the material properties and then a block copy was used to insert the material properties in the NIKE2D input deck.

BDISK This is a simple fine mesh burst disk bending over the sharp corner of the bore diameter of the backup piece. A sliding interface between the disk and the support allows sliding between the disk and the backup piece. There is a conical dimple at the center of the burst disk. Even with the sharp corner, the highest stresses and failure occur at the center of the disk.

BELLOW This is a thin wall bellows that is under simultaneous axial extension and internal gas pressure. The pressure capability decreases as the axial extension increases.

BELLV1 This is a belleville spring washer being compressed between two plates. The contact between the washer and the plates is implemented with type 4 sliding interfaces and the load is applied with a displacement boundary on the top plate. The displacement boundary loading is more stable than a pressure boundary loading. The forces at a given displacement can readily be found while post-processing with ORION. This particular spring cannot be loaded to the flat position and remain elastic. For the spring to remain elastic, this spring should be redesigned.

CAP25 This is a 1/4-20 UNC high strength heat treated cap screw with nominal dimensions. It is similar to B440. I have written a small BASIC program that uses Machinery's Handbook data and generates the thread form MAZE line definitions for any standard UNC, UNF, or UNEF thread.

CORE This is an annealed aluminum weld bead under gas pressure loading.

COREWP This a titanium weld with the weld residual stress state simulated by a thermal cool-down of the weld bead. After cool-down, the pressure is applied to determine the failure pressure. The time step needs to be increased by typing SW6. after a time of 1.0 when the weld bead cool-down is complete. The weld bead is merged to the base metals "by hand" in a node by node process in the maze input deck.

COREHP This is a problem similar to COREWP, but with a leaking burst disk. By allowing gas pressure on both sides of the burst disk, the pressure capability of the fitting, after the disk bursts, can be calculated.

FILLP A threaded fitting is given a preload force that would result from the assembly torque and then loaded with an internal gas pressure. The thermal expansion of a number of elements in the load path are forced to expand thermally with material model #7. The CTE of the thermal material is adjusted to give the correct preload force that the assembly torque would produce. When the gas pressure is applied, the preload force is reduced as the pressure is increased. The pressure that caused a zero contact force can be calculated and at higher pressures, the gap at the contact surfaces can be calculated. This is a very powerful method of analyzing pressure fittings.

LEVEE This problem is a plane strain section of an earth levee or dam with water on one side and a three-to-one slope on the other side. The loading is a one G vertical acceleration. The location of peak shear stress in the levee indicates where possible failures could occur at high tide. The soil is implemented with material model #5. Three sided parts are used in the MAZE input deck.

NOZZ2DF The axisymmetric mode shapes and natural frequencies are found for a thruster nozzle fixed at its base.

OLDWELDA The first weld design failed due to the weld residual stresses and the location of the weld undercut. This calculation uses the thermal material model #12 and temperature dependent material properties to calculate the residual weld stresses during the weld bead cool-down.

PCUTW The preload resulting from the assembly torque is applied with a row of thermal elements modeled with material #7. After one time step, the preload is applied. SW6. is used to change the time step to 1000 or a reasonable gas pressure increment. Gas pressure is increased until failure occurs. Failure occurs when NIKE2D is unable to find an equilibrium condition for the next increment of pressure. At failure, the thread relief section of the fitting separates when plastic instability occurs. Plastic instability occurs when a small increase in pressure causes the load at the thread relief section to increase at a greater rate, both due to the increased pressure and to the reduced thread relief section, as it necks, than the material can increase its strength, as it strain hardens. At the 26,000 psi failure pressure, the gap at the seating surfaces is 7 mils and the "O" ring would be extruded because it could not possibly maintain a seal at such a high pressure with such a large gap.

PISTON This is a thin wall piston inside a thin wall tube. The piston has an "O" ring at each end and the analysis was used to calculate the pressure at which the center of the piston deforms and contacts the tank wall.

PISTON1 is a design with a stiffening ring in its center that functions at the higher pressure without contacting the tank wall. Two nodes on the inner surface of the piston were moved by hand to create the stiffening ring.

PRIMER This is a rifle primer being dented and pressurized during the firing of a rifle. The firing pin dents the primer cup and then a 55,000 psi internal pressure is applied and removed. The firing pin is then extracted to get the final shape. Loading is controlled with two separate load curves. The final shape agrees with a standard load in a 243 Winchester cartridge.

PULLA This is a test of material model #10. The properties for aluminum 6061-T6 are input into the STRAIN code to calculate the constants for the material model. A standard pull specimen is loaded to failure with NIKE2D. The 0.2% offset yield stress and the ultimate engineering stress are calculated with NIKE2D and plotted with ORION.

Sy = 42,200 psi input data

Su = 44,900 psi input data

Sy = 42,277 psi calculated with NIKE2D

Su = 44,945 psi calculated with NIKE2D

RDISK This is a 2 mil thick burst disk machined into a stainless steel slug that is similar to BDISK. The failure pressure is 4600 psi where plastic instability occurs.

RIVET This is the forming of a mild steel rivet to fasten two plates together. The rivet fills the hole and has a high axial preload after forming. The sliding interface #4 is used between contacting surfaces. After the rivet is formed, the rivet set is lifted. For a better design, the rivet set should be more of an elliptical shape to cause a larger diameter rivet head. This calculation uses the "auto" command on card #1 to allow NIKE2D to select the optimum time step size and to automatically restart if a time step is too large.

SHEET22 This is a copper burst disk clamped in place with a steel bull-nose clamp. This burst disk requires no machining like the earlier problems and can be punched out by the gross. The first two time steps only apply the clamping force. Typing SW6. allows the changing of the time step to 100 psi, which is a reasonable pressure increment. The clamping force is maintained with a constant displacement during the application of the gas pressure. The burst pressure can be adjusted and calculated simply by changing the bore diameter of the backup ring.

SNAP This is a calculation to determine the snap ring's ability to support an axial load produced by a gap pressure. The snap ring is implemented with material model #14 (circumferentially cracked isotropic/kinematic plasticity). Sliding interface #4 with friction was used at the contact surfaces.

SPRING This is a truck leaf spring that is loaded by displacing the pinned end and holding the center section fixed. After displacing 5 in., the displacement is forced back to its initial position. There is plastic deformation in the bottom leaf. The load deflection curve for the spring is plotted. The calculation uses sliding interface #4 with friction between the leaf sections and type #3 at the lubricated pinned end. The pin is free to rotate relative to the end of the spring.

TANKW45 This is a titanium tank with a threaded end cap. Internal gas pressure is sealed at the first "O" ring and the end cap loads the threads. This analysis also uses a type #4 sliding interface between all contacting surfaces. The tank fails by expelling the end cap as the threads rotate and slip free.

TUNE This is a musical tuning fork for tuning to the "A" tone (440 Hz). The fork is magnetic and assumed to be steel. The dimensions were measured with a micrometer. NIKE2D calculates the first mode shape to have a natural frequency of 465 Hz, or an error of 3.7%.

WASH This is a large washer with an edge load.

WIRE This is a calculation of one of the forming processes in making a wire. The initial condition of the wire is annealed copper. The wire is pulled through the die at a tensile force of 45 lb. The sliding interface #3 between the die and wire simulates a lubricated die.

If you are interested in more information on some of these examples or would like the MAZE input and/or output file, send me email.

Comprehending Engineers - Take One
Two engineering students were walking across campus when one said, "Where did you get such a great bike?" The second engineer replied, "Well, I was walking along yesterday minding my own business when a beautiful woman rode up on this bike. She threw the bike to the ground, took off all her clothes and said, "Take what you want." "The second engineer nodded approvingly, Good choice; the clothes probably wouldn't have fit."

Comprehending Engineers - Take Two
To the optimist, the glass is half full. To the pessimist, the glass is half empty. To the engineer, the glass is twice as large as necessary.
Take 2.50: To the engineer, the capacity of the container has been over designed by a factor of approximately 1.905 assuming a 5% volume for the sloshing safety factor.

Comprehending Engineers-Take Three
A pastor, a doctor and an engineer were waiting one morning for a particularly slow group of golfers. The engineer fumed, "What's with these guys? We must have been waiting for 15 minutes!" The doctor chimed in, "I don't know, but I've never seen such ineptitude! "The pastor said, "Here comes the greens keeper, let's have a word with him. " (dramatic pause) "Hi George. Say, what's with that group ahead of us? They're rather slow, aren't they?" The greens keeper replied, "Oh, yes, that's a group of blind firefighters. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free anytime." The group was silent for a moment. The pastor said, "That's so sad. I think I will say a special prayer for them tonight." The doctor said, "Good idea. And I'm going to contact my ophthalmologist buddy and see if there's anything he can do for them." The engineer said, "Why can't these guys play at night?"

Comprehending Engineers - Take 4
There was an engineer who had an exceptional gift for fixing all things mechanical. After serving his company loyally for over 30 years, he happily retired. Several years later the company contacted him regarding a seemingly impossible problem they were having with one of their multimillion dollar machines. They had tried everything and everyone else to get the machine to work but to no avail. In desperation, they called on the retired engineer who had solved so many of their problems in the past. The engineer reluctantly took the challenge. He spent a day studying the huge machine. At the end of the day, he marked a small "x" in chalk on a particular component of the machine and stated, "This is where your problem is". The part was replaced and the machine worked perfectly again. The company received a bill for $50,000 from the engineer for his service. They demanded an itemized accounting of his charges. The engineer responded briefly...
One chalk mark:
$1
Knowing where to put it:
$49,999.
It was paid in full and the engineer retired again in peace.

Comprehending Engineers-Take Five
What is the difference between Mechanical Engineers and Civil Engineers?
Mechanical Engineers build weapons, Civil Engineers build targets.

Comprehending Engineers-Take Six
The graduate with a Science degree asks, "Why does it work?"
The graduate with an Engineering degree asks, "How does it work?"
The graduate with an Accounting degree asks, "How much will it cost?"
The graduate with a Liberal Arts degree asks, "Do you want fries with that?"

Comprehending Engineers-Take Seven
"Normal people ... believe that if it ain't broke, don't fix it. Engineers believe that if it ain't broke, it doesn't have enough features." ----- Scott Adams, The Dilbert Principle

Comprehending Engineers-Take Eight
An artist, an architect and an engineer were discussing whether it was better to spend time with the wife or a mistress. The architect said he enjoyed time with his wife, building a solid foundation for an enduring relationship. The artist said he enjoyed time with his mistress, because of the passion and mystery he found there. The engineer said, "I like both." "Both?" Engineer: "Yeah. If you have a wife and a mistress, they will each assume you are spending time with the other woman, and you can go to the lab and get some work done!"

Engineering requires an understanding of mathematics

Last Updated: 08/18/2008
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