Static Stress with Linear Material Models
Static stress analysis with linear material models is the most common type of FEA used today.
Industrial products, manufacturing, consumer products, civil engineering, medical research, power transmission and electronic design are just a few of the areas in which static stress analysis is often performed.
The simplest of all analysis types, the static stress analysis with linear material models, should only be used in cases where all applied loads are static and all material strains are expected to be in the linear elastic range. Whenever any of the strains produced are expected to be in the nonlinear range of the materials used, a nonlinear analysis type should be specified.
Static stress analysis with linear material models enables the study of stress, strain, displacement and shear and axial forces that result from static loading. This analysis type is often sufficient for situations in which loads are known and the time of peak stress is evident.
When performing a static stress analysis with linear material models, engineers apply static loads such as forces, pressures or known "imposed" displacements to a finite element model.
Then, they add elastic material data, boundary conditions and other information such as the direction of gravity. Static forces are assumed to be constant for an infinite period of time, while resulting strain, movement and deformation are small. Engineers assume that the material will not deform beyond its elastic limit and any resulting dynamic effects from the loading are insignificant.
Natural Frequency (Modal)
Engineers have to design things to withstand vibration when it cannot be avoided. For example, tires and shock absorbers ("dampers" in technical terms) help reduce vibration in cars and trucks. Similarly, flexible couplings help isolate vibrations produced by the engines.
Vibration is about frequencies. By its very nature, vibration involves repetitive motion. Each occurrence of a complete motion sequence is called a cycle. Frequency is defined as so many cycles in a given time period.
Individual parts have, what engineers call, natural frequencies. For example, a violin string at a certain tension will vibrate only at a set number of frequencies, which is why you can produce specific musical tones. There is a base frequency in which the entire string is going back and forth in a simple bow shape. Harmonics and overtones occur because individual sections of the string can vibrate independently within the larger vibration. These various shapes are called modes. The base frequency is said to vibrate in the first mode, and so on up the ladder. Each mode shape will have an associated frequency. Higher mode shapes have higher frequencies.
The most disastrous consequences occur when a power-driven device, such as a motor for example, produces a frequency at which an attached structure naturally vibrates. This event is called resonance. If sufficient power is applied, the attached structure will be destroyed.
When vibration causes resonance in an object, destruction will result unless it has been designed to withstand the stress. The wine glass, for example, is not sound enough to withstand the resonance caused by the frequencies produced by the opera singer.
Note that ancient armies, which normally marched in step, were taken out of step when crossing bridges. Should the beat of the marching feet align with a natural frequency of the bridge, it could fall down.
Engineers must design so that resonance does not occur during regular operation of machines.
This is a major purpose of modal analysis. Ideally, the first mode has a frequency higher than any potential driving frequency.
Frequently, resonance cannot be avoided, especially for short periods of time. For example, when a motor comes up to speed it produces a variety of frequencies. So it may pass through a resonant frequency. Other vibration processes, such as time history, response spectrum, random vibration, etc., are used in addition to modal analysis to deal with this type of more complex situation. These are called transient natural frequency processors.
Transient Stress (Direct Integration)
When you strike a guitar string or a tuning fork, it goes from a state of inactivity into vibration to make a musical tone. This tone seems loudest at first, then gradually dies out. Conditions are changing from the first moment the note is struck.
When an electric motor is started up, it eventually reaches a steady-state of operation. But to get there, it starts from zero rpm and passes through an infinite number of speeds until it attains the operating speed.
Every time you rev the motor in your car, you are creating transient vibration. When things vibrate, internal stresses are created by the vibration. These stresses can be devastating if resonance occurs between a device producing vibration and a structure responding to vibration.
A bridge may vibrate in the wind or when cars and trucks go across it. Very complex vibration patterns can occur. Because things are constantly changing, engineers must know what the frequencies and stresses are at all moments in time.
Sometimes transient vibrations are extremely violent and short-lived. Imagine a torpedo striking the side of a ship and exploding, or a car slamming into a concrete abutment, or dropping a coffeepot on a hard floor. Such vibrations are called shocks, which is just what you would imagine. In real life, shock is rarely a good thing and almost always unplanned.
But shocks occur regardless. Because of vibration, shock is always more devastating than if the same force were applied gradually.
The direct integration process works best when the time is relatively short and conditions are violent, such as conditions of shock.
Transient Stress (Modal Superposition)
The transient stress (modal superposition) analysis uses mode shapes and natural frequencies calculated through a linear natural frequency analysis to solve for time-varying loads at low frequencies. Engineers can produce the dynamic response of a structure subjected to forces, moments, temperatures or boundary accelerations.
Furthermore, ground acceleration components can be added in any or all three of the global directions to determine dynamic responses such as deflection, velocity, acceleration and stress versus time.
Modal superposition excludes the effects of high frequency modes; thus, it uses only low frequency modes of vibration and requires fewer calculations. This type of analysis is used for fluid flow, structural vibration and load testing. For example, the effects of impulsive wind loading on towers or sinusoidal loading on air purification equipment can be determined.
The transient stress (modal superposition) analysis uses the time history processor. The time history processor uses the mode shapes and natural frequencies calculated by the linear mode shapes and natural frequencies processor to perform a modal superposition solution for time-varying forcing functions. The dynamic response can be produced for two general types of input:
1. Ground acceleration input in any (or all) of the three global (X,Y,Z) directions.
2. Time-varying loads (forces/moments) applied to any (or all) nodal degrees-of-freedom.
Response Spectrum
Engineers use this type of analysis to find out how a device or structure responds to sudden forces or shocks. It is assumed that these shocks or forces occur at boundary points which are normally fixed.
An example would be a building, dam or nuclear reactor when an earthquake strikes. During an earthquake, violent shaking occurs. This shaking transmits into the structure or device at the points where they are attached to the ground (boundary points).
Response spectrum analysis is used extensively by civil engineers who must design structures in earthquake-prone areas. The quantities describing many of the great earthquakes of the recent past have been captured with instruments and can now be fed into a response spectrum program to determine how a structure would react to a past real-world earthquake.
Mechanical engineers who design components for nuclear power plants must use response spectrum analysis as well. Such components might include nuclear reactor parts, pumps, valves, piping, condensers, etc.
When an engineer uses response spectrum analysis, he/she is looking for the maximum acceleration, velocity and displacements that occur after the shock. These in turn lead to maximum stresses. Autodesk® Simulation's response spectrum analysis utilizes formulas recommended by the U. S. Nuclear Regulatory Commission (NRC).
Random Vibration
Engineers use this type of analysis to find out how a device or structure responds to steady shaking of the kind you would feel riding in a truck, rail car, rocket (when the motor is on) and so on. Also, things that are riding in the vehicle, such as on-board electronics or cargo of any kind, may need random vibration analysis.
The vibration generated in vehicles from the motors, road conditions, etc. is a combination of a great many frequencies from a variety of sources and has a certain "random" nature.
Random vibration analysis is used by engineers who design various kinds of transportation equipment. Engineers provide input to the processor in the form of a power spectral density (PSD), which is a representation of the vibration frequencies and energy in a statistical form.
When an engineer uses random vibration analysis, they are looking to determine the maximum stresses resulting from the vibration. These stresses are important in determining the lifetime of a structure of a transportation vehicle. Also, it would be important to know if things being transported in vehicles will survive until they reach the destination.
Frequency Response
Suppose an electric motor is to drive a conveyer system to move grain from the storage area to the area where it will be processed into cereal.
When the motor is switched on, the system starts up, going through a number of transient conditions, possibly with occasional rumbling and buzzing, finally reaching a steady-state condition for smooth, normal operation. Analyzing the parts of the conveyer system throughout this time and during the final running state can be done with a random vibration analysis. But this type of analysis may provide much more information than is actually needed if the engineers only want to study the normal running operation. Further, defining the input information to include the final condition would involve a large amount of data.
Frequency response analysis was invented to analyze only the steady-state operation of the system. The inputs and output are very simple and the analysis works quickly. The engineers run one modal analysis followed by all the steady-state scenarios they desire.
This type of analysis is recommended whenever the transient phase of operation is either very short in relation to the total operating time or is of no interest.
Critical Buckling Load
If you press down on an empty soft drink can with your hand, not much will seem to happen.
If you put the can on the floor and gradually increase the force by stepping down on it with your foot, at some point it will suddenly squash. This sudden scrunching is known as buckling.
In the normal use of most products, buckling can be catastrophic if it occurs. The failure is not one of stress, but of geometric stability. Once the geometry of the part starts to deform, it can no longer support even a fraction of the force initially applied.
The worst part about buckling for engineers is that buckling usually occurs at relatively low stress values compared to what the material can withstand. So a separate check must be performed to see if a product or section is acceptable with respect to buckling.
Buckling almost always involves compression. In civil engineering, buckling is to be avoided when designing support columns, load bearing walls and sections of bridges which may flex under load. For example an I-beam may be perfectly "safe" when considering only the maximum stress, but fail disastrously if just one local spot of a flange should buckle.
In engineering, designs involving thin parts in flexible structures like airplanes and automobiles are susceptible to buckling. Even if the stress is very low, buckling of local areas can cause the whole structure to collapse by a rapid progression of propagated buckling.
Sometimes, buckling is used as a characteristic part of a design. You may have seen or used the type of oilcan where you pump the oil out by pressing on the bottom of the oilcan. If you press a little, nothing happens. If you press harder, the bottom suddenly "snaps through", pumping out a small amount of oil. Then it snaps back when you release your thumb. This phenomenon is known as "snap through" or "oil can" buckling.
For situations involving linear materials such as steel or glass and small deflections or deformations prior to buckling, a straightforward solution is available – Autodesk ® Simulation’s Critical Buckling analysis type.
For nonlinear situations, buckling can be determined as part of a nonlinear stress analysis using the Mechanical Event Simulation (MES) analysis type.
Natural Frequency (Modal) with Load Stiffening
The natural frequency (modal) with load stiffening analysis is very similar to natural frequency (modal) analysis. However, it can handle a situation when a part is under compression or tension at the same time that vibration is induced. Think of a violin or guitar string. If you tighten or loosen the screw, nothing is done to the string to change its mass or length, but the tone changes anyway. This effect makes music possible and engineers call it load stiffening.
Dynamic Design Analysis Method (DDAM)
The Dynamic Design Analysis Method (DDAM) enables engineers to analyze models using U.S. Navy procedures for shock design. All mission-essential equipment onboard surface ships and submarines must be qualified for shock loads, such as from depth charges, mines, missiles and torpedoes.
This analysis can determine the characteristics of underwater explosion phenomena including the effects of shock waves, surface ship or submarine body response to shock loading and application of shock spectra to component design. Engineers can use DDAM to analyze the shock response at the mountings of shipboard equipment such as masts, propulsion shafts, rudders, exhaust uptakes and other critical structures.
MES with Nonlinear Material Models
Engineers often need to check a design while it is moving in a dynamic event such as buckling, swinging, rotation or oscillation. MES combines kinematic, rigid- and flexible-body dynamics and nonlinear stress analysis capabilities. As a result, MES can simultaneously analyze mechanical events involving large deformations, nonlinear material properties, kinematic motion and forces caused by that motion and then predict the resulting stresses.
One of the main advantages of MES is the need to make fewer assumptions. With MES, there is no need for elaborate hand calculations, interpretation of results or experiments to determine equivalent loading. The fewer the assumptions that need to be made, the lesser the chance for errors will be.
Static Stress with Nonlinear Material Models
Like MES, this analysis type supports nonlinear material behavior. However, the inertial and damping effects included in a full, dynamic analysis are excluded. Therefore, all parts must be statically stable. However, geometric nonlinearity is accounted for in Static/NLM analyses. So, the results will correctly reflect changes in load location, load orientation, and part cross-section that occur as the structure deforms.
Riks Buckling Analysis
A Riks analysis is specifically intended to capture post-buckling and collapse events. An example of post-buckling behavior is the snap-through action of the bottom of an old style oil