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Some FEA terms ,  

Beam

A slender structural member that offers resistance to forces and bending under applied loads. Beams are found in building frames, transmission towers, bridges. The Eiffel Tower in Paris is made of beams.

A beam differs from a truss in that a beam resists moments (twisting and bending) at the connections.

finite element analysis software contains "beam elements" expressly for analyzing and predicting the behavior of structures made of beams. In this way, engineers can assure that bridges and towers will be safe prior to their construction.

Bending Load

A bending load causes an object to curve. For example a diving board will develop a pronounced curve if a person stands on one end. Note that the other end is solidly fixed so that it cannot pivot.


Boundary Element

A type of finite element sometimes used to connect the finite element model to fixed points in space. Typically this fixity is set with global boundary conditions, in which the fixity is totally rigid. A boundary element, on the other hand, allows for a flexible connection to the fixed space.

Boundary elements and boundary points are normally used to simulate the constraints that actually occur when an object is used in the real world. For example, if a coffee cup is sitting on the table and a weight is placed on top of the coffee cup, then the table is the boundary. Boundary points would be points on the plane of the table that are defined as being fixed in space and to which nodes of a finite element model of the coffee cup are attached. If the table has a spongy surface, you might want to use boundary elements to account for the flexibility.

With software, boundary elements have an additional capability of imposing and enforced displacement upon a model. The force created by this imposed displacement would be calculated automatically.

Additionally, the forces generated at a boundary by forces on the model can be obtained as output using boundary elements.


Buckling Analysis

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 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 for what the material can withstand. So they have to make a separate check to see if a product or part thereof is okay 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 mechanical engineering, designs involving thin parts in flexible structures like airplanes and automobiles are susceptible to buckling. Even though stress can be very low, buckling of local areas can cause the whole structure to collapse by a rapid series of propagating bucklings.

Sometimes, buckling is used as a characteristic part of a design. You may have seen or used the type of oil can where you pump the oil out by pressing on the bottom of the oil container. If you press a little, nothing happens. If you press harder, the bottom suddenly "snaps through", pumping out a small amount of oil. Then is snaps back when you release your thumb. This phenomena is known as "snap through" or "oil can" buckling.

Composite Material

Composite materials consist of two or more independent materials. Many composite materials contain a large amount of one substance combined with fibers, flakes or layers of another. Greater strength is obtained than what the individual materials acting alone can achieve.

For example, fiberglass reinforced plastics find use in boat hulls, building panels and truck parts.

In the 1970's Boron and Graphite (a form of Carbon) fibers were developed for intense forces and high temperatures for use in aircraft and rocket parts. Many consumer products such as power tool casings and coffee makers utilize composite materials.

Composite Elements for finite element analysis

The use of composite materials in industry led to develop special composite finite elements for stress and vibration analysis of parts made of composite materials. employs special element formulations for this purpose.

Special composite element processors are offered for stress and vibration. Other vibration analysis processors such as Time History, Response Spectrum, Frequency Response and Random Vibration can work in conjunction with the special composite element vibration processor to provide the same full range of engineering capabilities as is available for regular materials such as steel, rubber and glass.


What is an Element (in Finite Element Analysis)?

An element is the basic building block of finite element analysis. There are several basic types of elements. Which type is used depends on the type of object that is to be modeled for finite element analysis.

The most common types are truss, beam, 2-D solid, plate/shell and 3-D solid elements.

Solid elements are becoming the dominant form in mechanical engineering because most mechanical parts have a certain bulk and because can convert solid models from modern CAD solid modeling systems such as Pro/ENGINEER and CADDS5 from ComputerVision into solid brick elements automatically.

Also, solid elements can handle stress, dynamic, heat transfer, fluid flow, electrostatic and electromagnetic analysis, whereas other element types are more limited in application.

2-D solid elements are essentially obsolete. Their main function in the past was to approximate 3-Dimensional models with 2-Dimensional representations because computers were much slower and good modeling tools were not available.


What is Finite Element Analysis (FEA)?

Finite Element Analysis is a computerized method for predicting how a real world object will react to forces, heat, vibration, etc. in terms of whether it will break, not wear out or work the way it is supposed to. It is called "analysis", but in the product design cycle it is used to predict what is going to happen when the product is used.

The finite element method works by breaking a real object down into a large number (1000's or 100,000's) of elements, such as little cubes. The behavior of each little element, which is regular in shape, is readily predicted by set mathematical equations. Then the computer adds up all the individual behaviors to predict the behavior of the actual object.

The "Finite" in Finite Element Analysis comes from the idea that there are a finite number of elements in a finite element model. Previously, engineers employed integral and differential calculus which breaks objects down into an infinite number of elements.

The Finite Element Method is employed to predict the behavior of things with respect to virtually all physical phenomena:

•Mechanical stress (stress analysis) •Mechanical vibration •Heat transfer - conduction, convection, radiation •Fluid Flow - both liquid and gaseous fluids •Various electrical and magnetic phenomena •Acoustics •etc.


More than 14,000 engineers in more than 60 countries use Finite Element Analysis software for mechanical engineering design and optimization. It is virtually impossible to spend a day without using a product software helped to engineer. Products as diverse as fast food restaurant furniture and food containers, Black and Decker's "Dustbuster," Nautilus exercise equipment and B.F. Goodrich tires were all engineered with the help of Software.

See also Finite Element Theory Made Easy.


Finite Element Theory Made Easy

In 1678, Robert Hooke set down the basis for modern finite element stress analysis as Hooke's Law. Simply, an elastic body stretches (strain) in proportion to the force (stress) on it." Mathematically:

F=kx.


•F = force •k = proportional constant •x = distance of stretching


This is the only equation you need to know to understand finite element stress analysis. Hooke proved it out by using weights to stretch wires hanging from the ceiling. This experiment is repeated every year in virtually every high school laboratory by students who study physics.

Other physical phenomena such as heat transfer, fluid flow and electrical effects can be handled in a similar way by analogy.

Imagine that a coffee cup is sitting on a table. It is broken down into 2000 little "brick"elements. Each element has 8 corners, or nodes. All nodes on the bottom of the coffee cup are fixed (we force in zero movement of these nodes) so they cannot move. Now, let us press down on just one node near the top of the cup.

That one node will move a little bit because all materials have some elasticity. That movement would be described by F=kx for that element except that other elements are in the way or are tending to hold it back. In fact, as the force is transmitted through the first element, it spreads out to other nodes, and so on. Without a computer, we would loose track of events very quickly.

In the finite element method, a step occurs called "element stiffness formulation." What happens is that a "k" is created for the relationship between every node on each element. Thus, every node is connected to every other node on each element by a spring, which will behave like F=kx. By so doing, we reduce the coffee cup to a large system of springs. When the "analysis" is done, a step known as "processing", a value for each "x" and "F" is determined for each node by the formula F=kx. Note: "F" and "x" are vectors as each has a value and a direction.

In the final step, which is frequently called post processing, the stress are determined by knowing the "F" at each node and the geometry of each element.


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 Cheerios.

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 Transient 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 it works quickly. The engineers run one Modal Analysis followed by all the steady-state scenarios they desire.

The 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.

To obtain the capability for Frequency Response Analysis we recommend the following parts as a minimum:


Understanding Vibration


Buckling Analysis

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 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 for what the material can withstand. So they have to make a separate check to see if a product or part thereof is okay 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 mechanical engineering, designs involving thin parts in flexible structures like airplanes and automobiles are susceptible to buckling. Even though stress can be very low, buckling of local areas can cause the whole structure to collapse by a rapid series of propagating bucklings.

Sometimes, buckling is used as a characteristic part of a design. You may have seen or used the type of oil can where you pump the oil out by pressing on the bottom of the oil container. If you press a little, nothing happens. If you press harder, the bottom suddenly "snaps through", pumping out a small amount of oil. Then is snaps back when you release your thumb. This phenomena 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 straight forward solution is available -- Buckling Analysis Processor for Beam and Plate/shell elements[6014].


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 Cheerios.

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 Transient 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 it works quickly. The engineers run one Modal Analysis followed by all the steady-state scenarios they desire.

The 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.



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 mechanical 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 he/she is 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.


Response Spectrum Analysis

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 of the world. 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 stresses or acceleration, velocity and displacements that occur after the shock. These in turn lead to maximum stresses. response spectrum analysis utilizes formulae recommended by the U. S. Nuclear Regulatory Commission (NRC).


Transient Vibration Analysis

When you strike a guitar string or a tuning fork, it goes from a state of inactivity into a 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 (see "Vibration (Modal Analysis)").

A bridge may vibrate in the wind or when cars and trucks go across it. Very complex vibration patters 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 coffee pot on a hard floor. Such vibrations are called "shock, " which is just what you would imagine. In real life, shock is rarely a good thing and almost always unplanned. But shocks occur anyhow. Because of vibration, shock is always more devastating than if the same force were applied gradually.


The Direct integration process works better when the time is relatively short and conditions violent, such as conditions of shock.

Modal Superposition is not well suited for shock, but is fine when times are longer (bridge analysis, for example). The main advantage of Modal Superposition is that you begin by doing a modal analysis, and then additional transient analyses on the same structure can be performed very rapidly as compared with Direct Integration, which requires a "full" analysis for every case.

The Accupak/VE Nonlinear Transient Processor is a Direct Integration processor but considers the effects of nonlinear materials such as rubber and many kinds of plastics and composite materials. Additionally this processor considers the effects of any loadings that may be applied, such as the tension in a violin string or the weight of a bridge deck on a support column.


Vibration Analysis (Modal Analysis)

All things vibrate. Think of musical instruments, think of riding in a car, think of the tires being out of balance, think of the rattles in an airplane when they are revving up the engines, or the vibration under your feet when a train goes by.

Sometimes vibration is good. Our ears enable us to hear because they respond to the vibrations of sound waves.

Many times things are made to vibrate for a purpose. For example, a special shaking device is used in foundries to loosen a mold placed in sand. Or, in the food and bulk materials industries, conveyors frequently work by vibration.

Usually, however, vibration is bad and frequently unavoidable. It may cause gradual weakening of structures and the deterioration of metals (fatigue) in cars and airplanes. Rotating machines from small electric motors to giant generators and turbines will self destruct if the parts are not well balanced.

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. "Cycles per second" was a common measurement until 1960 when this quantity was renamed "Hertz", who in 1886 discovered electromagnetic waves. So nowadays, for example, 1000 Hertz is the same as 1000 cycles per second.

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 kinds of 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.

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.

Most applications are readily handled by the regular Linear Natural Frequency (Modal) Analysis module.

Often, however, a part is under compression or tension at the same time as 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. To account for this effect, engineers would use the Linear Natural Frequency Analysis with Load Stiffening module.

Sometimes, materials such as rubber, certain plastics and composite materials do not respond in the usual linear fashion. The Accupak Nonlinear Natural Frequency Analysis Module will consider these nonlinear material effects.

What is a Node (in Finite Element Analysis)?

In Finite Element Analysis, solid things like coffee cups or bearing housings are broken down into lots of little elements. For example, these might be "brick" elements.

Brick elements are sometimes called hexahedral elements or hexahedra, the plural form of the Greek word hexahedron, which means "having six sides."

An item having six sides, such as a brick, also has eight corners. These corner points are referred to as "nodes". In Finite Element Analysis, input quantities such as forces and temperatures are specified at nodes. Also, the solution obtained in a Finite Element Analysis is obtained at the node points.


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 mechanical 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 he/she is 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.

Using , the process is as follows:


1.Model the structure. 2.Perform a vibration (modal) analysis. 3.Perform the Random Vibration Analysis. 4.Analyze the results with Superview.


Response Spectrum Analysis

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 of the world. 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 stresses or acceleration, velocity and displacements that occur after the shock. These in turn lead to maximum stresses. response spectrum analysis utilizes formulae recommended by the U. S. Nuclear Regulatory Commission (NRC).


Stress Analysis

The front wheel spindle on your car breaks off when you go around a corner too fast while hitting a pothole causing you to crash into a gasoline truck which explodes and . . .

This scenario could happen if the spindle was overstressed. But, probably, the science of stress analysis has enabled the automobile designers to design the spindle so that overstressing does not occur, even when you corner too fast and hit potholes.

But how does anyone know if a part will be overstressed?

If a number of identical samples of an identical material, such as a certain type of steel, are all stretched in a machine, clamped in precisely the same way, then they will all break at the same applied force or stress level. If the samples are shaped differently, the force required to break them may be different, but the stress level will be the same. This stress level may be called the ultimate stress for that material. It is said to be a property of that material, an inherent characteristic. Ultimate stress levels for all materials are determined in laboratories and printed in handbooks for future reference.

Thus, determining the stress which a material can withstand is a simple, straight forward process. The trick is to apply this knowledge to real things in the real world, not just laboratory samples. This effort can become quite involved because most real things typically cannot be simply tested by a machine. There are too may complicated effects all going on at the same time.


Transient Vibration Analysis

When you strike a guitar string or a tuning fork, it goes from a state of inactivity into a 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 (see "Vibration (Modal Analysis)").

A bridge may vibrate in the wind or when cars and trucks go across it. Very complex vibration patters 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 coffee pot on a hard floor. Such vibrations are called "shock, " which is just what you would imagine. In real life, shock is rarely a good thing and almost always unplanned. But shocks occur anyhow. Because of vibration, shock is always more devastating than if the same force were applied gradually.

offers three software processors to help engineers predict the effects of transient vibration:


1.Linear Transient Stress Analysis (by Direct Integration) [6024] 2.Time History Analysis (by Modal Superposition) [6122] 3.Accupak/VE Nonlinear Transient Stress Analysis [6714].


In theory, all three will do the same job. However, each is better suited to a particular class of problems.

The Direct integration process works better when the time is relatively short and conditions violent, such as conditions of shock.

Modal Superposition is not well suited for shock, but is fine when times are longer (bridge analysis, for example). The main advantage of Modal Superposition is that you begin by doing a modal analysis, and then additional transient analyses on the same structure can be performed very rapidly as compared with Direct Integration, which requires a "full" analysis for every case.

The Accupak/VE Nonlinear Transient Processor is a Direct Integration processor but considers the effects of nonlinear materials such as rubber and many kinds of plastics and composite materials. Additionally this processor considers the effects of any loadings that may be applied, such as the tension in a violin string or the weight of a bridge deck on a support column.

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