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IBEX 2002 - Session 602 Finite Element Analysis

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IBEX 2002 - Session 602 Finite Element Analysis. Paul H. Miller, D. Engr. Assistant Professor of Naval Architecture United States Naval Academy. Presentation Overview. What is FEA and what will it do for us What FEA will not do for us Limitations of FEA

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IBEX 2002 - Session 602Finite Element Analysis

Paul H. Miller, D. Engr.

Assistant Professor of Naval Architecture

United States Naval Academy

IBEX 2002 - SESSION 602

Presentation Overview
• 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

Getting started with a simple exampleA 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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The grain is longitudinal

The Mast StepAs 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

IBEX 2002 - SESSION 602

Black Locust mast step

• The actual boundary conditions with the three floors.

Floor grain is vertical

Forward

White Oak floors

t=0.5”

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Deformation (300x)

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Displacement

Maximum displacement is 0.0084”

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Stress with vertical grain floors

Max Stress = -1889 psi

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Stress with transverse grain floors

Max Stress = -2706 psi

43% higher!

But floor loads are more even

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Rolling Shear Stress

Maximum shear stress is 559 psi

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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…

IBEX 2002 - SESSION 602

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

Discrete Forces

Pressures

Vibrations (or fatigue)

Accelerations

Gravity

Dynamics

Temperature

Moisture

What is Finite Element Analysis?In the real world of structural response…

Loads include:

Objects with loads on them:

IBEX 2002 - SESSION 602

Stiffness matrix

Loads

Displacements and Rotations (DOFs)

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)

IBEX 2002 - SESSION 602

• Finding the final displacement gives us the elongation
• Elongation gives us the strain
• Strain and area gives us the stress
• Stress and failure criteria give us the Factors of Safety!

OK, Ready for the quiz?!

IBEX 2002 - SESSION 602

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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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).

IBEX 2002 - SESSION 602

Common Structural Element Types
• Mass
• Gap
• Immersed pipe
• Buoy
• Magnetic
• Fluid/heat
• Solid
• Shell
• Beam
• Cable
• Truss
• Radiation

IBEX 2002 - SESSION 602

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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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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Example of Beam Elements: A Mast tube is shells, spreaders are beams, rigging is cables

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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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Example of Shell Elements: A 77-foot Hull

Note the beam elements

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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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Example of Solid Elements:The Mast Step (again)

Solids are sometimes called “brick elements”

IBEX 2002 - SESSION 602

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%!

IBEX 2002 - SESSION 602

Complex materials

Composites

Wood

Non-linear static deformation (x5)

Buckling of isotropic materials (x2)

Increased uncertainty

From 1-5% potential error

To 3-30% error

HIGHER MIN FOS!

Increased manhours required to prepare model

What FEA does “OK”…

This means:

Examples:

IBEX 2002 - SESSION 602

Model took 127 manhours to build

Predicted deformations within 4% for static loads

Static strains within 6%

Example: A Composite Sailboat

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Composite Sailboat
• Fatigue-influenced dynamic strains were predicted within 14% when compared to strain gages and coupons.

IBEX 2002 - SESSION 602

Non-linear deformationHigh 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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Tsai- Wu Factors of Safety

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Non-linear Mast Deformation
• Small dinghy mast
• Used to size spreaders, wire and pretension
• Input was gust spectrum
• 8% error in deformation

IBEX 2002 - SESSION 602

What FEA does not do well
• 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%!

IBEX 2002 - SESSION 602

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.

IBEX 2002 - SESSION 602

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.

IBEX 2002 - SESSION 602

Joint Design with FEA(some variation with programs)
• Normal FEA solution assumes joint is perfect
• Either a) list nodal forces
• b) use nodal stresses and area
• Determine stress concentration factors for specific joint geometry
• Calculate joint loads by spreadsheet (isotropic or wood) or
• Use laminate analysis program and spreadsheet (for composites)

IBEX 2002 - SESSION 602

IBEX 2002 - SESSION 602

Failure mode prediction is only as good as it’s modeling.

This means realistic material testing to support the FEA.

“Special” failure mode analysis (post-processing) using spreadsheets or macros

IBEX 2002 - SESSION 602

Uncertain loads

Slamming

Impact

Transient

Unanalyzed loads!

IACC cockpit example

Uncertain materials

Testing

QA/QC from builder

Model Errors

Mesh density

Linear or non-linear analysis

Wrong elements

Boundary conditions

Results analysis

Limitations of FEA= High Error Possibility!

IBEX 2002 - SESSION 602

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 110%.

IBEX 2002 - SESSION 602

• Choosing a consultant
• What you’ll be asked to supply
• Getting what you expect
• Several projects outlined

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Choosing a ConsultantQuestions 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)

IBEX 2002 - SESSION 602

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!

IBEX 2002 - SESSION 602

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?

IBEX 2002 - SESSION 602

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!

IBEX 2002 - SESSION 602

Another Case Study
• A 77-foot performance cruiser
• Designed by Carl Schumacher
• Under Construction in Seattle

IBEX 2002 - SESSION 602

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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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

IBEX 2002 - SESSION 602

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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Upwind in 30 knots on port tack

Rig loads supplied by mast maker

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Displacements (25x)

Maximum displacement = 3.32”

Max rotation 0.5 degrees

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Not “real”!

Factors of SafetyTsai-Wu or Max Stress or Hashin

Minimum “real” FOS = 2.25

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Interior

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Interior FOS

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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

IBEX 2002 - SESSION 602

Final Thoughts
• Good FEA programs used in the marine industry include:
• 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