Integrating Finite Element Analysis with Systems ......Integrating Finite Element Analysis with...
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nafems.org/americas 1 Integrating Finite Element Analysis with Systems Engineering Models • KONEKSYS – Jerome Szarazi, Axel Reichwein July 26, 2016 This work was performed under the following financial assistance award NIST Grant 2014-NIST-MSE-01 from U.S. Department of Commerce, National Institute of Standards and Technology (U.S. NIST contact: Conrad Bock)
Transcript of Integrating Finite Element Analysis with Systems ......Integrating Finite Element Analysis with...
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Integrating Finite Element Analysis with Systems
Engineering Models
• KONEKSYS – Jerome Szarazi, Axel Reichwein
July 26, 2016
This work was performed under the following financial assistance award NIST Grant 2014-NIST-MSE-01 from
U.S. Department of Commerce, National Institute of Standards and Technology (U.S. NIST contact: Conrad Bock)
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FE mathematics description
• Validation
• Next steps and summary
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FE mathematics description
• Validation
• Next steps and summary
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Integration between Systems
Engineering and FEA
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Systems Engineering
Requirement Behaviour
Structure Parametric
Software engineering
PRODUCTMechanical engineering
Electrical engineering
Manufacturing engineering
FEA
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Motivation: Communication and archiving
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Cross-disciplinary communication
What has been simulated?
Can I reuse the simulation?
Archiving and reuse
Defining concepts
What do you want me to simulate?
Are my requirements validated?
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Motivation: traceability and impact analysis
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Requirement traceability Impact analysis
e.g. Customization request
e.g. Cost reduction program…
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Motivation: Tool interoperability
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FEA
Domain specific tool interoperability
Interdisciplinary tool interoperability
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The challenge
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Many Artifacts
Multiphysics
Many Vendors
FEA is complex
CAD Sim file MaterialResults
Custom code
Electrical Fluid ThermalMechanical
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The requirement to success
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Systems Engineering
FEA
Mechanicalengineering
Interdisciplinary standardized interface Discipline specific
standards
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SysML – Standard for Systems Engineering
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• SysML: Systems Modeling Language
• Defined by the OMG as standard in 2007
• Widely adopted for Model-Based Systems Engineering (MBSE)
• Current version: 1.4 (2015)
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FEA-related Standards
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AP209 (v2014)-based FEA model description
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Ref: ISO 10303-209:2014(E) - Application protocol: Multidisciplinary analysis and design
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Impact of missing FEA standard
• Interoperability is compromised
• Impact on reusability (custom code)
• communication between system and FEA engineers is not efficient
• No open-standard
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FE mathematics description
• Validation
• Next steps and summary
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Challenge 1: Capturing model information
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Problem of encoding one model Ambiguity
Ref: Ansys capabilities overview
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The method: decomposition and reuse
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Start with the definition of finite element mathematics
PHYSICS
GEOMETRY
MATHEMATICS
Finite Element
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Challenge 2: Describing finite element mathematics
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Difficult to create an ontology
Literature names are not descriptive
Logg A. et Al., Automated solution of differential equation by the finite element method, 2012, SpringerLogg A., Arnold D., periodic table of finite elements, 2014, Siam News
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Removing ambiguity?
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1 finite element Many Names 1 Reference
Linear simplexLinear triangleLinear Lagrange element…
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FE mathematics description
• Validation
• Next steps and summary
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Ciarlet’s definition of FE mathematics
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New FE mathematics description:
Assigning requirements to the geometry
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Tetrahedron
Name: Element XY• Tetrahedron• 𝐶1 Ω = 𝑃𝐸; 1• 𝐶0 Ω = 𝑃𝐸; 1• Polynomial ref.
𝐶0 Ω = 𝑃𝐸; 1 𝐶1 Ω = 𝑃𝐸; 1
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Polynomial basis dictionary
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Pascal triangle of 2-dimensional monomials
Monomials can be ordered in a dictionary
Graded Lexicographic ordering
1 < 𝑦 < 𝑥 < 𝑦2 < 𝑥𝑦 < 𝑥2 < 𝑦3 < 𝑥2𝑦…
0 1 2 3 4 5 6 7
A polynomial is composed of monomials
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Encoding FE mathematics
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PG3-RC0PE1C1PE1-PFD2-0-1-2-3-4-5
GeometryFunctional requirements
Polynomial
This specification provides non ambiguous information for code implementation
Custom code
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Reusing the new FE description for physics
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• line• 𝐶0 Ω = 𝑃𝐸; 1• D1-0-1
• Temperature• Type: Scalar
• Displacement• Type: Vector
• line• 𝐶0 Ω = 𝑃𝐸; 1• D1-0-1
• line• 𝐶0 Ω = 𝑃𝐸; 1• D1-0-1
REUSE
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Reusing the new FE specification for geometry
description
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REUSE
• Line• 𝐶1 Ω = 𝑃𝐸; 1• 𝐶0 Ω = 𝑃𝐸; 1• D1-1-2-3
In a Cartesian coord. system
• Line• 𝐶1 Ω = 𝑃𝐸; 1• 𝐶0 Ω = 𝑃𝐸; 1• D1-1-2-3
• Dimension: 2• Type: Cartesian
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Merging information to describe parametric finite
elements
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• Line• 𝐶1 Ω = 𝑃𝐸; 1• 𝐶0 Ω = 𝑃𝐸; 1• D1-1-2-3
• Dimension: 2• Type: Cartesian
• Temperature• Type: Scalar
• line• 𝐶0 Ω = 𝑃𝐸; 1• D1-0-1
GEOMETRY
PHYSICS
MERGE
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Next step of our work:
Specifying the FEA model
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Use the same principle:Decomposition for reusability
Many physics use the same computational model…to be continued…
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Unifying assembly process
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Assembler
Ax=b
Solver
Solution
Ref: M. S. Alnæs, A. Logg, K.-A. Mardal, O. Skavhaug, and H. P. Langtangen (2008) ‘Unified Framework for Finite Element Assembly’.
Numerical model description
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Problem classification
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Numerical model 1 Numerical model 2
1D Thermal conduction
1D Electrostatics
1D Magnetostatics
2D Electrostatics
2D Thermal conduction
…….
model input knowledge
1D bar element
Model reuse
Associating numerical model to physics
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Using SysML for model description:
Example of domain sub-classing
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Example domain sub-classing by material properties
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Remove ambiguity of software specific vocabulary
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Example of Dirichletboundary conditions for axial elastostaticproblems
Reconcile vocabulary of input deck files
1D problem – vector is a scalar 2 combinationsu=0 (fixed, pin, wall) or u=free
2D problem – vector has 2 components.4 combinationsux=0 and uy=0 (vocab: fixed, pin, wall…)ux=free and uy=0 (vocab: roller, guide…)ux=0 and uy=free (vocab: roller, guide…)ux=free and uy=free (vocab: planar…)
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Model reuse and connectivity
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1D Thermal conduction
1D bar element
FEA model
Inputs Outputs
Parameters
Parameters
Parameters
Interface ?
Midterm goal: block based description of FEA problem using SysML
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FE mathematics description
• Validation
• Next steps and summary
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Python code to validate FE mathematics spec
• Model FEA specification in SysML
• FEA code to test the new proposed FEA spec
• FEA implemented in Python using object oriented
concepts
• Using symbolic equations for interoperability
• integration with open source FreeCAD
• Code available on GitHub:
https://github.com/koneksys/KFE/
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Translating FE description into SysML
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New FE-description
SysML model
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Code interoperability
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Code uses symbolic equation for interoperability
Symbolic equation program (i.e. Sympy)
HTML specification MathML info
Text
Equation image
Plot image
Code generator
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Information aggregation
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Aggregation of finite element information in a single python object
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Outline
• Introduction and motivation
• Challenges in FEA standardization
• New proposed FEA description
• Validation
• Summary
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Summary
• Benefits of new FE mathematics specification based on algebraic topology:
– Covering FE mathematics
– Understandable to engineers who are not mathematicians
– Simple and precise definition of a finite element
– Covering information for implementing FE mathematics in FEA code
– Can describe more FE elements than with descriptions based on
Ciarlet/periodic table
• New FE mathematics specification will benefit integration between systems
engineering and FEA
– Traceability
– Consistency/Synchronization
– Reuse
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Thank You!
Koneksys
Jerome Szarazi
t: +44(0)7736732512
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