Transcript Finite Element Analysis for Small Craft

IBEX 2002 - Session 602
Finite Element Analysis
Paul H. Miller, D. Engr.
Assistant Professor of Naval Architecture
United States Naval Academy
IBEX 2002 - SESSION 602
Slide 1
Presentation Overview
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What is FEA and what will it do for us
What FEA will not do for us
Limitations of FEA
Working with Finite Element Analysts
Case Studies
IBEX 2002 - SESSION 602
Slide 2
Getting started with a simple example
A new mast step for an old wooden sailboat
• Designer: L. Francis
Herreshoff, 1955
• Built: 1962
Lunenberg, N.S.
• Original Mast Step
was Red Oak (not
designed that way)
• It broke at a bad
moment!
t=0.5”
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Slide 3
The Mast Step
As it’s thickness is about the same dimension
as its width, we must use solid elements.
• Loads – 7000 lb
down
• Geometry –
24”x4”x4”
• Material – Black
Locust
• Boundry Conditions
– supported by 3
oak floors
The grain is longitudinal
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Slide 4
• The actual boundary conditions
with the three floors.
Black Locust mast step
Floor
grain is
vertical
Forward
White Oak
floors
t=0.5”
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Slide 5
Deformation (300x)
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Slide 6
Displacement
Maximum displacement
is 0.0084”
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Slide 7
Stress with vertical grain floors
Max Stress = -1889 psi
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Slide 8
Stress with transverse grain floors
Max Stress = -2706 psi
43% higher!
But floor
loads are
more even
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Slide 9
Rolling Shear Stress
Maximum shear
stress is 559 psi
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Slide 10
Mast Step Analysis Results
• The analysis took 5 hours
• The predicted weight was 7.5 pounds
• The minimum factor of safety for
bending was 10.2
• The minimum factor of safety for shear
was 4.4
• The recommended minimum FOS is 4
• Therefore LFH over-designed it by 3/8”!
• I built it to LFH’s drawing…
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Slide 11
What is Finite Element Analysis?
In the real world of structural response…
Objects with loads on them:
• Deform – strain (in/in)
– If the strains are always
proportional to the load it
is “linear deformation”
– If not, then “non-linear”
• Have internal stress
(psi)
• Are made of materials
– Which could be linear or
non-linear themselves
Loads include:
• Discrete Forces
• Pressures
• Vibrations (or
fatigue)
• Accelerations
– Gravity
– Dynamics
• Temperature
• Moisture
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Slide 12
In the world of mathematics…
• FEA divides the object up into multiple
small parts (up to 100K+!)
• Each part is represented by stiffness
constants (like springs, f=k·x
• All the parts are combined mathematically
(by matrix algebra) into a global structure
• The solution is found from equilibrium
(ΣF=0, ΣM=0)
Stiffness
matrix
Loads
K D  R
Displacements and Rotations (DOFs)
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Slide 13
Solving the basic equation for the
unknown degrees of freedom…
D
1
 R K 
1
1. Finding the final displacement gives us
the elongation
2. Elongation gives us the strain
3. Strain and area gives us the stress
4. Stress and failure criteria give us the
Factors of Safety!
OK, Ready for the quiz?!
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Slide 14
Physical modeling of structures
• An FEA model is made of simple structural
“elements” connected at “nodes”
• The basic building blocks (elements) are:
– Beams (1 primary dimension)
– Plates/shells (2 primary dimensions)
– Solids (3 primary dimensions)
“Primary” means “much bigger than the
other dimensions”
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Slide 15
Just To Avoid Confusion!
An element with 2 Primary Dimensions, a
shell element, has a length and a width,
but is thin compared to the other two
dimensions.
It can be either used in either 2-D analysis
(x and y axes) or in 3-D analysis (x, y and
z axes).
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Slide 16
Common Structural Element Types
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Solid
Shell
Beam
Cable
Truss
Radiation
• Mass
• Gap
• Immersed
pipe
• Buoy
• Magnetic
• Fluid/heat
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Slide 17
FEA can handle almost any
structure
• It’s greatest power (and cost) is with
complex structures.
• The structure needs to be envisioned in
terms of element types which are
available, and suitable.
• The structure is then represented with
many (often thousands) of these
elements.
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Slide 18
Example of Beam/Cable/Truss Elements:
What they are
2 nodes,
Each node
has up to 6
degrees of
freedom,
giving 12 per
element
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Slide 19
Example of Beam Elements: A Mast
tube is shells, spreaders are beams, rigging is cables
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Slide 20
Example of Shell Elements: What they are
4 nodes,
Each node
has up to 6
degrees of
freedom,
giving 24
DOF per
element
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Slide 21
Example of Shell Elements: A 77-foot Hull
Note the beam elements
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Slide 22
Example of Solid Elements: What they are
8 nodes,
Each node has up to 3 degrees of freedom
(translation only), giving 24 DOF
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Slide 23
Example of Solid Elements:
The Mast Step (again)
Solids are sometimes
called “brick
elements”
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Slide 24
What FEA does beautifully!
• Handles complex geometry.
(Indeterminate structures)
• Isotropic materials (materials with
consistent properties in all directions)
• Static and simple dynamic problems
• Examples
– A steel keel, a bronze rudder shaft
– Metal hulls (tanker fatigue)
• Accuracy is within 0-5%!
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Slide 25
What FEA does “OK”…
This means:
Examples:
• Complex
materials
• Increased
uncertainty
– From 1-5%
potential error
– To 3-30% error
– HIGHER MIN FOS!
• Increased
manhours
required to
prepare model
– Composites
– Wood
• Non-linear static
deformation (x5)
• Buckling of
isotropic
materials (x2)
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Slide 26
Example: A Composite Sailboat
• Model took 127
manhours to build
• Predicted
deformations
within 4% for
static loads
• Static strains
within 6%
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Slide 27
Composite Sailboat
• Fatigue-influenced
dynamic strains were
predicted within 14%
when compared to strain
gages and coupons.
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Slide 28
Non-linear deformation
High Aspect Ratio Rudder
• 8 foot span/16 lb
• 20” of tip deflection
• High membrane
stresses reduce
predicted deflection
and stress
• 5% error in
deflection
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Slide 29
Tsai- Wu Factors of Safety
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Slide 30
Non-linear Mast Deformation
• Small dinghy
mast
• Used to size
spreaders, wire
and pretension
• Input was gust
spectrum
• 8% error in
deformation
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Slide 31
What FEA does not do well
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Dynamic impact (slamming loads)
Joints ( composites or metal )
Buckling of “real world” composites.
Misc details unaccounted for in element
formulations.
• Error can be 30-300%!
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Slide 32
Dynamic Analysis
• FEA has great strengths in dynamic
analysis for certain types of problems.
• Standard FEA doesn’t handle slamming
impacts well.
• One of the major difficulties are in the
definition of the loads.
• The other is in the speed of the
transient nature of the load.
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Slide 33
Joint Analysis with FEA
• FEA is good for extracting loads at
joints.
• FEA is weak in micro analyzing joint
designs
• This is primarily due to difficulty with
material properties and failure
mechanisms.
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Slide 34
Joint Design with FEA
(some variation with programs)
1. Normal FEA solution assumes joint is perfect
2. Either a) list nodal forces
b) use nodal stresses and area
3. Determine stress concentration factors for
specific joint geometry
4. Calculate joint loads by spreadsheet (isotropic
or wood) or
5. Use laminate analysis program and
spreadsheet (for composites)
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Slide 35
Not all aspects of structres can be
accounted for in FEA models
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Slide 36
Failure mode
prediction is only as
good as it’s modeling.
This means realistic
material testing to
support the FEA.
“Special” failure mode
analysis (postprocessing) using
spreadsheets or
macros
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Slide 37
Limitations of FEA
= High Error Possibility!
• Uncertain loads
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Slamming
Impact
Transient
Unanalyzed loads!
• IACC cockpit example
• Uncertain materials
– Testing
– QA/QC from builder
• Model Errors
– Mesh density
– Linear or nonlinear analysis
– Wrong elements
– Boundary
conditions
– Results analysis
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Slide 38
A Multiple Issue Problem!
• Loads, materials and boundary conditions
• FEA assumes “continuum mechanics”
Eventually we got the deflections to match within
10%,But the strength was under predicted by
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Slide 39
110%.
Working with a Consultant
- and getting good value from it an overview
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Choosing a consultant
What you’ll be asked to supply
Getting what you expect
Several projects outlined
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Slide 40
Choosing a Consultant
Questions to Ask
• Analyst versus engineer or designer
– Their experience/education
– Your relationship (micromanagement?)
• Experience with similar projects
– Loads
– Materials (isotropic or orthotropic?)
• Track record of success and failure
• Rates and availability (current range is
$25-275/hour)
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Slide 41
Information You’ll Be Asked To
Supply:
• Geometry
• Loads (are they biased or real?) SES
• Material types and properties (guess or
test?)
• Goals
• Deliverables
• Any guesses increase the error and may
make using FEA uneconomical!
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Slide 42
Deliverables:
• Do you expect guidence in making
decisions?
• Do you want a specifc question
answered or do you want design work?
• Do you expect formal documentation?
– If so, then in what form?
– Report, e-mail, spreadsheet, tables,
drawings (dxf, dwg, igs, etc)
• Do you want nice color stress plots?
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Slide 43
Extra hints to make your life
easier
• Be specific on the design criteria
– Stiffness, deflection, strength, FOS
• Be flexible on the geometry
• Don’t be stuck on a particular
design (just because it worked in
the past doesn’t mean it is the best)
• Keep the design simple!
• Communicate!
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Slide 44
Another Case Study
• A 77-foot
performance
cruiser
• Designed by
Carl
Schumacher
• Under
Construction in
Seattle
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Slide 45
Project Overview
• Began in January 2000
• Structures to meet ABS and
realistic loads if not specified
• Multiple materials intended
• Goal is “ULDB” cruiser
– Light but strong with a deep bulb keel
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Slide 46
FEA work
• Designer subcontracted out structural
FEA design
• Designer provided dxf files for all
geometries (hull, appendages)
• FEA consultants optimized and specified
construction
• Designer did hull structure drawings
• Consultants did keel structure drawings
and interfaced with keel and hull
manufacturer to ease construction
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Slide 47
Design Limit Load Cases
• Upwind in heavy air, wave height
equal to freeboard, wave length
equal to boat length
• Slamming
• Grounding
• Lifting
Each load case drove the design of
different parts of the boat.
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Slide 48
Upwind in 30 knots on port tack
Rig loads
supplied by
mast maker
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Slide 49
Displacements (25x)
Maximum displacement = 3.32”
Max rotation 0.5 degrees
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Slide 50
Factors of Safety
Tsai-Wu or Max Stress or Hashin
Minimum “real” FOS = 2.25
Not “real”!
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Slide 51
Interior
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Slide 52
Interior FOS
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Slide 53
Project Summary (to date)
• Smooth transition of files (AutoCad,
GenericCad, Excel, Word)
• Communication is 50% phone, 45%
email, 5% meetings
• FEA has been approximately 300
hours and is 95% complete
• A third of that was redesign due to
the owner’s wishes
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Slide 54
Final Thoughts
• Good FEA programs used in the marine
industry include:
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COSMOS
Ansys
Algor
Abaqus
Costs range from $400-30,000
Free demo’s available on the web
Short courses are also available
Be realistic about your needs…
Do you need this tool?
IBEX 2002 - SESSION 602
Slide 55