Behind the Pretty Pictures

Transcription

Behind the Pretty Pictures:
How to get the most from your Finite Element Analysis contractors
John Davidson – WorleyParsons Services Ltd: Pressure Equipment Group
10-Sep-05
Introduction
Aims of this presentation:
• To give a general awareness of finite element analysis (FEA) and its
common applications
• Highlight key issues and potential problems in the methods used
• What should be involved in the validation of FEA work?
• What should a good FEA report contain?
• How do you get the most value out of your FEA contractors?
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FEA presentation.ppt
Introduction
My FEA background:
• Pressure equipment (vessels, piping)
• Structural Components (offshore platform
connections, lifting equipment, Bussleton
Underwater Observatory)
• Mechanical and thermal, linear and
non-linear, static and transient analyses
• Use of ANSYS, Caesar II, FEPipe, SACS, USFOS, ABAQUS
• On-the-job training with some supplementary external courses.
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Introduction – The Finite Element Method
Developed in the early 1940’s by Richard Courant and Alexander Hrennikoff to
solve complex elastic structural analysis problems.
They are numerical techniques used for finding approximate solutions of partial
differential equations.
Development progressed in the middle to late 1950s for airframe and structural
analysis through the work of John Argyris and Ray W. Clough in the 1960s for
use in civil engineering.
By late 1950s, the key concepts of stiffness matrix and element assembly
existed essentially in the form used today, and NASA issued request for
proposals for the development of the first finite element software NASTRAN in
1965.
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Introduction – Common FEA Today
Structural and thermal problems are the
most common use of FEA today:
• Structural analysis calculates the mesh’s
node displacements
•Displacement components interpolated
across elements to calculate a
displacement field in the model.
•Displacement fields are differentiated to
find strains.
•Stresses calculated based on strains and
material elasticity.
•Thermal analysis is similar: an interpolated temperature field is differentiated
to find a temperature gradient. Heat flux is calculated based on gradient and
material conductivity.
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Introduction – Some key issues
• Significant increase in software accessibility and hardware power has lead to
a surge in the amount of FEA undertaken.
• Increasing costs of materials is raising the importance of design efficiency –
FEA offers potential to improve and iterate design for comparatively low cost.
• FEA being introduced in university courses – is there a danger of being too
software focussed?
•Misconception of FEA as an engineering panacea; the new primary design
tool.
• The pretty pictures are very useful for mollifying upper management
‘The “perform-FEA” syndrome often stems from bureaucratic
misunderstanding rather than engineering need for results’
Paul Kurowski – President ACOM Consulting, USA
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Who should be running your FEA?
FEA is an engineering tool and running the analysis is a specific skill:
• Training is required and the opportunity to practice extensively.
• “Garbage in = garbage out” – the black box dilemma
• Some foundation in the theory behind the method as well as sound engineering
judgment in materials and load conditions is needed as a minimum.
• Some software providers are pushing the integration of FEA with CAD –
encouraging the use of designers/draftspeople as FEA operators. This is a
potentially dangerous philosophy. Functions such as “Automeshing” still require an
experienced eye to confirm suitability.
• An FE analyst needs to decide which features need modelling, how to apply loads
and boundary conditions, what errors are acceptable, and how the results are
interpreted against the relevant codes.
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Use of recent graduates as FEA operators:
• Computer-savvy, but lack meaningful experience in the fundamentals of good
engineering design.
• “Unwillingness to ask too many
questions, graduates may withdraw into
isolated world of simulation. This is of
no benefit to their growth as a good
engineer or to the company employing
them.”
• A person eager to use newly acquired
skills and lacking a good grasp of FEA
is probably the most dangerous user.
Understanding the FE method is more important than specific software
commands, which are easily learned.
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NAFEMS (National Agency for Finite Element Methods and Standards ) has
released a quality supplement to ISO 9001 titled R0013 – “Finite element
analysis in the design and validation of engineering products”
Includes recommendations for the level of experience required to complete
certain levels of FEA:
Analysis Category
1. Vital
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Engineering
experience
5 years
Finite-element
experience after
formal training
Relevant FEA jobs
performed
6 months
2 X category 1 under
supervisory or 5 X
category 2 properly
assessed
2. Important
2 years
2 months
1 X category 1 or 2
under supervision or 3
X category 3 properly
assessed
3. Advisory
1 year
1 month
Relevant benchmarks
Codes and Standards – Which to Use?
Pressure Vessels
Previously ASME VIII, Division 2 and AS1210-Supplement 1:1990.
• Almost identical in their guidance for numerical analysis
• Biased towards linear elastic analysis (written before the FEA
software boom) – the “hopper diagram”
• Although simple to analyse, interpretation of stresses requires
experience and good knowledge of differences between primary and
secondary, general and local stresses.
• Stress intensity (Max shear stress / Tresca stress theory) compared
against multiples of the material design strength. Max shear stress
theory usually more conservative and simpler to calculate.
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Codes and Standards – The ‘Hopper’ Diagram
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Pressure Vessels
ASME VIII Div 2 rewritten in 2007
• Very prescriptive section on design-by-analysis (Ch 5)
• Focussed on protection against:
- Plastic collapse
- Buckling
- Local failure
- Failure under cyclical loading
•Specifies methodology for linear (elastic) and non-linear (plastic) analyses –
now uses Von Mises stress rather than stress intensity.
AS1210 to be revised later in 2008 (?)
• Some improved guidance on FEA
• New ASME VIII Div 2 methods may be included in later amendments
Pressure Piping
AS4041 currently directs users to AS1210 for complex geometries.
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Structural Components
Far fewer codes available that give guidance on FEA use.
Some European standards (eg BS 7608, DNV-RP-C203) specify methods for
extracting suitable stresses from FEA for fatigue assessment.
Some analysts use AS3990 (or similar) based on comparing average stress
through sections against a proportion of material yield strength.
Clients and analysts must consider what form the loads are given in:
- Working Stress design
- Limit State design
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Determination of stress at FE model
singularities for strength and fatigue
purposes (DNV-RP-C203)
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Material Design Strength
Determination of material design strength is one of the key issues in
correctly interpreting FEA results (particularly for pressure
equipment).
Some variation in design strength between AS1210, ASME VIII and ASME
B31.3 etc – remember the fundamental intent behind them!
AS1210 – ‘f’ is typically lesser of Yield/1.5 and UTS/3.5 (amended from
UTS/4 except for flanges).
•Local membrane stresses limited to 1.5*f (Max = 1* yield strength)
•Local primary + secondary stresses limited to 3*f (Max = 2* yield strength).
Care must be taken with standards using different calculations for ‘f’,
eg: AS4041 Class 2P (f =0.72*Yield), AS2885 (f = 0.8*Yield)
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Material Design Strength
“Sps , is computed as the larger of the
quantities shown below.
1) Three times the average of the S values
for the material at the highest and lowest
temperatures during the operational cycle.
2) Two times the average of the Sy values
for the material at the highest and lowest
temperatures during the operational
cycle……” – ASME VIII Div 2
CAUTION – Careful consideration
of the definition of “load cycle” is
required!
For steady state conditions (say pressure + external loads at operating
temperature) it is more correct to determine the design strength at the
operating temperature.
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Modelling Techniques – Solids vs Shells
• Consider maximum stress locations
• Bending stresses at repad edges
• Weld geometry, etc…
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Modelling Techniques – Solids vs Shells
Nozzle thickness
Shell thickness
…corresponds
with…
Shell + repad
thickness
Neutral Axis
No bending stress at repad edge
accounted for!
2t
t
t
Bending stiffness ⍺ (2t)³
Bending stiffness ⍺ 2(t³)
Shell + repad?
Somewhere in between…
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Modelling Techniques – Hexahedra vs Tetrahedra
A volume built from first-order tetrahedral elements
A second-order hexahedral element
Three basic approaches to reducing % element error in FEA:
- ‘h’ method: the element order (p) is kept constant, but the mesh is
refined infinitely by making the element size (h) smaller.
- ‘p’ method: the element size (h) is kept constant and the element
order (p) is increased.
- ‘h-p’ method: the h is made smaller as the p is increased to create
higher order h elements.
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Modelling Techniques – Hexahedra vs Tetrahedra
348MPa
An 8-noded hexahedron formed
from five tetrahedrons has greater
discretisation error than a single 8noded “brick” because the five
tetrahedrons cannot assume all the
displacement fields handled by the
8-noded element. (1st order
tetrahedra elements also have
constant strain behaviour compared
to linear strain behaviour across a
1st order hexahedral element).
510MPa
Element selection can be a matter of preference – but there are some key
issues to be aware of.
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Modelling Techniques – Element selection
The mesh and results from the finite-element analysis of a bracket
Model 1 • 1st order tetrahedra – constant stress across element
• one element through thickness – cannot represent bending stress
• elements will be highly distorted
• shows a maximum Von Mises stress of 18,000 psi.
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From “When Good
Engineers Deliver
Bad FEA” - by Paul
Kurowski – ACOM
consulting
Model 2 • 2nd order tetrahedra – linear stress across element
• one element through thickness – mesh still too coarse to model stress
concentrations
• some elements will be highly distorted
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Model 3 • 2nd order tetrahedra, enough elements to model stress distribution reasonably
accurately (good starting point)
• analyst needs to successively refine mesh to check that % error in stress is
within permissible limits (stress will increase with each refinement)
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Model 4 • Adaptive-order ‘p’ elements – software automatically iterates element order at
each location until a user-specified accuracy is achieved (accuracy based on
local strain energy, local displacements or global RMS stress etc)
• Shows a maximum Von Mises stress of 62,000 psi.
• Not all software handles adaptive-order elements.
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Validating third party results
Due to general incompatibility between software packages, it is often difficult to get
models validated.
• Not necessarily cost-effective to re-build and re-analyse a model from scratch.
• Some gains are being made in FE software’s ability to export CAD-type geometry
files (.IGES, .SAT) which may be imported into client’s CAD packages to allow
geometry checking (and vice-versa for model development….)
• Often have to wait until receipt of final reports to highlight any possible problems
with the analysis and assumptions – by then is it too late?
• Can be totally reliant on contractor’s internal checking procedures
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Validating third party results
As part of the contractor’s checking process, the following should be done:
• Confirmation of use of correct element type (shell vs solid, 1st or 2nd order…)
• Confirmation of use of correct analysis type (linear vs non-linear, small vs large deflection)
• Check of material properties, loads, boundary conditions and sum of reaction forces
• Hand calculation of results away from geometric discontinuities (PD/2t, Roark’s Formulae…)
• Check that stress variation across elements is within acceptable limits (mesh density)
Element Order
% Stress Variation across element
0
10%
1
20%
2
30%
>2
40%
• Check that units are consistent
• Check contact (if applicable)
• Check model for “free edges”
• Check for solution convergence
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What should a good FEA report contain?
• Software package and version
• List of assumptions:
• Codes/Standards applied
• Design strengths applied
• Description of failure modes considered
• Material Properties
Longitudinal and
circumferential
restraint at free
end
Nozzle loads
applied at centre of
flange face and
transferred to face
via rigid constraint
equations
Symmetry
constraints
applied on Y-Z
plane
14MPa pressure
applied to all
internal surfaces
0.3MPa pressure
applied to bottom
surface of upper
support plate and
top surface of
lower support plate
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Plot c/o Contract
Design and
Management
Services Pty Ltd
• Plot of model geometry (including list of
thicknesses if shell elements used)
• Plot(s) of FE mesh at critical areas
•Type of elements used (shape and
order)
• Plot of applied loads and boundary
conditions (including notation for clarity)
What should a good FEA report contain?
• Plots of the final deflected shape with
colour contouring
• Key results plots
• Stress / Strain / Temperature etc
• Clearly indicating type of stress (Von
Mises, Tresca…) or strain (‘true’,
‘engineering’…)
Other helpful information:
• Summary of reaction forces at
boundaries.
• Additional hand calculations to verify
results away from discontinuities
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Getting the most value from your contractor
Avoid the “Perform FEA” syndrome..
• Stay involved with the FE contractor during the process
• Develop and agree on a design basis with the key assumptions addressed
(loads, materials, failure criteria, critical regions in the component/assembly…)
• Review preliminary results to ensure that the output is as expected.
• Understand that, what may seem like a “minor” design change at your end,
can be significantly more complex to implement in an existing model.
• Review your contractor’s internal auditing:
• Do they have other analysts with enough experience to independently check the
analysis?
• Do they have an analysis verification checklist?
• Documentation should contain enough information that a third party can replicate
the analysis long after the original author is gone.
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Questions?
….. and the obligatory cartoon
Feel free to contact me at John.Davidson@worleyparsons.com for further discussion.
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Behind the Pretty Pictures

Transcription

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