實驗力學研究室 1 Introduction of FEA in the Product Design Process.

實驗力學研究室

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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.

實驗力學研究室 1 Introduction of FEA in the Product Design Process.

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