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Introduction of FEA in the Introduction of FEA in the Product Design ProcessProduct Design Process
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1. Lord John William Strutt Rayleigh (late 1800s), developed a m
ethod for predicting the first natural frequency of simple struct
ures. It assumed a deformed shape for a structure and then qua
ntified this shape by minimizing the distributed energy in the st
ructure.
2. Walter Ritz then expanded this into a method, now known as t
he Rayleigh-Ritz method, for predicting the stress and displace
ment behavior of structures.
A Brief History of Computer-aided Engineering
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3. In 1943, Richard Courant proposed breaking a continuous
system into triangular segments. (The unveiling of ENIAC at
the University of Pennsylvania.)
4. In the 1950s, a team form Boeing demonstrated that complex
surfaces could be analyzed with a matrix of triangular shapes.
5. Dr. Ray Clough coined the term “finite element” in 1960. The
1960s saw the true beginning of commercial FEA as digital
computers replaced analog ones with the capability of
thousands of operations per second.
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6. In the early 1960s, the MacNeal-Schwendler Corporation (MS
C) develop a general purpose FEA code. This original code ha
d a limit of 68,000 degrees of freedom. When the NASA contr
act was complete, MSC continued development of its own vers
ion called MSC/NASTRAN, while the original NASTRAN be
come available to the public and formed the basis of dozens of
the FEA packages available today. Around the time MSC/NAS
TRAN was released, ANSYS, MARC, and SAP were introduc
ed.
7. By the 1970s, Computer-aided design, or CAD, was introduce
d later in the decade.
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8. In the 1980s, the use of FEA and CAD on the same workstation
with developing geometry standards such as IGES and DXF.
Permitted limited geometry transfer between the systems.
9. In the 1980s,CAD progressed from a 2D drafting tool to a 3D
surfacing tool, and then to a 3D solid modeling system. Design
engineers began to seriously consider incorporating FEA into
the general product design process.
10. As the 1990s draw to a place, the PC platform has become a
major force in high end analysis. The technology has become to
accessible that it is actually being “hidden” inside CAD
packages.
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Rapid Product Development Process
(1) communication,
(2) visualization, and
(3) simulation
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There enabling technologies have emerged to provide the
communication, visualization, and simulation capabilities
required by RPD. These technologies are 3D solid modeling,
finite element analysis, and rapid prototyping.
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Traditional product development process.
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Relative cost of product change at the different stages of the design.
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Cost versus knowledge dilemma.
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Product development using predictive engineering
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Improved tracking of cost versus product knowledge with simulation.
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Who Should Use FEA?
The champion or the designate. The champion was integral in the
acquisition of the technology. The designate, on the other hand,
was selected to be the FEA guy or gal once management made the
decision to bring in FEA. Many champions lose sight of their
limitations in their enthusiasm to validate their tool while some
designates proceed with methodical caution to ensure that results
are accurate. Also common to both types is isolation from peer
interaction to talk about modeling techniques and results
interpretation. While some do not know where to look for this
support, others do not know they should.
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Pointing FEA in the right Direction
Process
1. Establish a clearly defined goal.
2. Compile and qualify the inputs.
3. Solve the problem with the most appropriate means.
4. Verify and document the results.
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Substances in the Process
What is the goal of the analysis?
Predictive engineering versus failure verification
Trend analysis versus absolute data
Selecting required output data
What input is required for the solution and what level of uncertainty does it introduce?
What is the most efficient means to solve the problems?
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Common Misconceptions About FEA
1. Meshing is Everything
2. FEA Replaces Testing
3. Finite Element Analysis is Easy
4. Finite Element Analysis is Hard
5. Learning the Interface Equals Learning FEA
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FEA Capabilities and LimitationsFEA Capabilities and Limitations
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Actual Performance versus FEA Results
“How accurate are the results?”
Every variable, or price of data, that you are required to the
system is an assumption and source of error.
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Source of Errors
1. Material properties.
2. Geometry
3. Loading condition
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How FEA Calculates Data
KxF
2
1
22
221
2
1
U
U
KK
KKK
F
F
0
0
2122
212111
KUUF
KUUKUF
Basic Equation
Equilibrium
Assembly
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Correctness versus Accuracy
The Correct Answer
Correct results are results expected by those observing or
envisioning the parts or systems working in the field.
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The accurate answer
An accurate answer in FEA is considered the best result
obtainable for the properties, geometry, and boundary conditions
specified, that is, the best answer to the question posed. Typically,
the degree of accuracy refers, in large part, to convergence or the
refinement of the mesh necessary to reduce error.
H-elements versus P-elements
Elements that can assume higher edge orders are called p-
elements. H-element which typically limits the element order to
quadratic, and convergence requires mesh refinement.
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Key Assumptions in FEA for Design
Four Primary Assumptions
• Geometry
• Properties
• Mesh
• Boundary conditions
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Linear Static Assumption
Material Properties
A material is said to be linear if its stress-strain relationship is or
can be assumed to be linear.
Geometry Concerns(geometric stiffening )
The primary result of this condition is decreasing displacement
under increasing load.The primary cause of this stiffening is
increased tensile stresses in the areas being deformed.As the axial
tensile stress in a self-stiffen. This is often called stress stiffening
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Boundary Conditions
The boundary conditions do not change from the point of load
application to the final deformed shape. Loading must be constant
in magnitude, orientation, and distribution.
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Static Assumption
A good way to interpret the static assumption is as that of
steady state and constant magnitude.
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Dynamic Simulation
There are three primary type of dynamic loading in FEA:
• Transient response or time- dependent loading
• Frequency response or sinusoidal loading
• Random response
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Transient Response
If the duration or period of the event is so small that the system
can respond quickly enough to fully deform before the load
reported by a static analysis.
Frequency Response
A frequency response analysis is also steady state,m but differs for
m a static analysis in that both the magnitude and orientation of th
e load vary sinusoidally. As the frequency of the input approaches
any natural frequency of the system, the difference between the sta
tic and dynamic responses diverges.
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Random Response
While loading in a frequency,random response input typically in p
ounds or pounds versus frequency ,random response input is in the
form of acceleration squared (G2)versus frequency. These data are
usually compiled in the form of a power spectral density (PSD) cur
ve.Random response input rally is not random at all but a preappro
ved spectrum of excitations and frequencies
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Other commonly Used Assumptions
Geometry
• The supplied CAD geometry adequately represents the physical
part.
• Nonlinear geometric stiffening will not affect the behavior of
the system.
• Stress behavior outside the area of interest is not important to
this project such that geometric simplifications in those areas
will not affect the outcome.
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• Only internal fillets in the area of interest will be included in th
e solution.
• The thickness of the part is small enough relative to its width a
nd length such that shell idealization is valid.
• The thicknesses of the walls are sufficiently constant to justify
constant thickness shell element.
• Local behavior at the corners and intersection of thin surfaces i
s not of primary interest such that no special modeling of these
areas is required.
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• The primary members of the structure are long and thin such
that a beam idealization iv valid.
• Local behavior at the joints of beams or other discontinuities are
not of primary interest such that no special modeling of these
areas is required.
• Decorative external features will be assumed insignificant to the
stiffness and performance of the part and will be omitted form
the model.
• The variation in mass due to suppressed features in negligible.
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• A 2D(plane stress or plane strain) Solution will be used.It is
assumed that any part features that violate the planar
assumption will have no impact on the behavior of interest.
• Reflective symmetry will be used. The geometry and boundary
conditions are,or can be assumed to be,equivalent across once
or more planes.
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Material Properties
• Material properties will remain in the linear regime.It is unders
tood that either stress levels exceeding yield or excessive displ
acements will constitute a component failure, that is ,nonlinear
behavior can not be accepted.
• Nominal material properties adequately represent the physical
system.
• Material properties are not affected by the load rate.
• Material properties can be assumed isotropic (or orthotropic)an
homogenous.
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• The part is free of voids or surface imperfections that can
produce stress risers and skew local results.
• Actual nonlinear behavior of the system can be extrapolated
form the linear material results.
• Weld material and the heat affected zone will be assumed to
have the same properties as the base metal.
• All simulations will assume room temperature although
temperature variation may have a significant impact on the
properties of the materials used.Unless otherwise specified, this
change in properties will be neglected.
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• The effects of relative humidity(RH) or water absorption on the
materials used with be neglected.
• The material properties used assume dry, 50% RH, or 100%
RH properties as specified in the manufacturer’s date sheets.
• No compensation will be made to account for the effects of
UV,chemicals, corrosives, wear, or other factors which may
have an impact on the long-term structural integrity of the
components.
• Material damping will be assumed negligible, constant across
all frequencies of interest, and/or a published value or one
determined form testing.
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Boundary Conditions
• Displacements will be small such that the magnitude,
orientation, and distribution of loading remain constant
throughout the deformation.
• A static solution will be used. Loading rates are expected to be
sufficiently low as to make this assumption valid.
• Frictional losses in the system will be considered negligible.
• All interfacing components will be assumed rigid.
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• The portion of the structure being studied can be assumed Deco
upled from the rest of the system such that any reactions or inp
uts form the adjacent features can be neglected.
• Symmetry may be assumed to minimized model sized and com
plexity.
• Load is to be assumed purely compressive, tensile, torsional, or
thermal .No other load components are to be included in the stu
dy.
• Pressure loading will be assumed uniform across all loaded surf
aces.
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• The components modeled as pure forces will impart no
additional rigidity in the actual system.
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Fasteners
• Residual stress due to fabrication, preloading on bolts, welding,
and/or other manufacturing or assembly processes will be
neglected.
• Bolt loading is primarily axial in nature.
• Bolt head or washer surface torque loading is primarily axial in
nature. Surface torque loading due to friction will produce only
local effects.
• Stress relaxation of fasteners or other assembly components
will not be considered.Failure is assumed to be early in the
service life of the assembly.
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• Load on the threaded portion of the part is evenly distributed
On engaged threads.
• The bolts, spot welds, welds, rivets, and/or fasteners are
numerous and stiff such that the bound between the two
components can be considered prefect.
• All welds between components will be considered ideal and
continuous.
• The failure of fasteners will not be considered.
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General
• Only the results in the area of interest are important and mesh
convergence will be limited to shit area.
• No slippage between interfacing components will be assumed.
• Any sliding contact interfaces will be assumed frictionless.
• System damping will be assumed negligible, constant across all
frequencies of interest, and/ or a published value or one
determined from testing.
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• Stiffness of bearings , radically or axially, will be considered
infinite or rigid.
• Elements with poor, or less than optimal geometry, are only
allowed in areas not expected to be of concern and do not
affect the overall performance of the model.
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