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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”

IBEX 2002 - SESSION 602

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

- The actual boundary conditions with the three floors.

Floor grain is vertical

Forward

White Oak floors

t=0.5”

IBEX 2002 - SESSION 602

Deformation (300x)

IBEX 2002 - SESSION 602

Stress with transverse grain floors

Max Stress = -2706 psi

43% higher!

But floor loads are more even

IBEX 2002 - SESSION 602

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

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

Solving the basic equation for the unknown degrees of freedom…

- 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”

IBEX 2002 - SESSION 602

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.

IBEX 2002 - SESSION 602

Example of Beam/Cable/Truss Elements:What they are

2 nodes,

Each node has up to 6 degrees of freedom, giving 12 per element

•

•

IBEX 2002 - SESSION 602

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

IBEX 2002 - SESSION 602

Example of Shell Elements: What they are

4 nodes,

Each node has up to 6 degrees of freedom, giving 24 DOF per element

IBEX 2002 - SESSION 602

Example of Solid Elements: What they are

8 nodes,

Each node has up to 3 degrees of freedom

(translation only), giving 24 DOF

IBEX 2002 - SESSION 602

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 SailboatIBEX 2002 - SESSION 602

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

IBEX 2002 - SESSION 602

Tsai- Wu Factors of Safety

IBEX 2002 - SESSION 602

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

Not all aspects of structres can be accounted for in FEA models

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

Working with a Consultant- and getting good value from it -an overview

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

IBEX 2002 - SESSION 602

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

IBEX 2002 - SESSION 602

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.

IBEX 2002 - SESSION 602

Interior

IBEX 2002 - SESSION 602

Interior FOS

IBEX 2002 - SESSION 602

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

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