Post on 22-Dec-2015
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
CISM Lectures on
Computational Aspects of Structural
Acoustics and Vibration
Udine, June 19-23, 2006
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Presenter: Carlos A. FelippaDepartment of Aerospace Engineering Sciences
and Center for Aerospace StructuresUniversity of Colorado at Boulder
Boulder, CO 80309, USA
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
C. A. Felippa
Synthesis of Partitioned Analysis Synthesis of Partitioned Analysis ProceduresProcedures
Synthesis of Partitioned Analysis Synthesis of Partitioned Analysis ProceduresProcedures
CISM Lecture Series on Computational Methods inStructural Acoustics and Vibration - Part 2
Udine, June 19-23, 2006
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
General Comment on Lectures
General Comment on Lectures
Note that in an FSI simulation (say) I won’t talk on
how to do the structure how to do the fluid
I assume you know how to do each piece by itself,or to get existing software that do them.
My focus is how you may couple the pieces andsolve the coupled system.
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Lecture TopicsLecture Topics
1. Partitioned Analysis of Coupled Systems: OverviewPartitioned Analysis of Coupled Systems: Overview 2. Synthesis of Partitioned Methods 3. Mesh Coupling and Interface Treatment 4. Partitioned FSI by Localized Lagrange Multipliers
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Learning by RepetitionLearning by Repetition
Effective synthesis practice relies on recognizing some common features of coupled systems.
Important is to learn about:
software components types of interaction model systems
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Coupled System Examples
Coupled System Examples
Aeroelasticity
Underwater Shock
MEMS Resonator
Dam Under Seismic Action
Common Features favor Partitioned Analysis
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
AeroelasticityAeroelasticity
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Aeroelasticity: Interaction Diagram
Aeroelasticity: Interaction Diagram
QuickTime™ and a decompressor
are needed to see this picture.
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Lesson: Try Not to Reinvent
the Lesson: Try Not to Reinvent
the
Fluid modelbenefits from 50years of CFD
Structure modelbenefits from 50years of FEM
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Underwater Shock (UWS)- Early 70s
Underwater Shock (UWS)- Early 70s
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Resonator (Cell Phone Chip Component)
Resonator (Cell Phone Chip Component)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Resonator: Interaction Diagram
Resonator: Interaction Diagram
System entirely modeled in the frequency domainReduced Models useful
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Dam Under Seismic Action
Dam Under Seismic Action
Covered in Part 4
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Common Features of Examples (1)Common Features of Examples (1)
Dynamic, two-way interaction
Similar physical scales - these are not multiscale problems
Interfaces and partitions well defined, surface coupling only
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Common Features of Examples (2)Common Features of Examples (2)
Isolated components well understood
Software (commercial or public) for components often available
Treatment benefits from customization (different models & methods for different components)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Common Features of Examples (3)Common Features of Examples (3) In production projects, new modeling features
are often the result of customer requests; e.g.
What happens if “unnamed things” inside the submarine go nonlinear under a strong shock?
Can you simulate a fast fighter maneuver?
Can turbulence be the cause of a recent crash?
Often the request can be “localized”
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Common Features of Examples (4)Common Features of Examples (4)
Often the request can be “localized”. For instance when Lockheed was asked by the Navy:
What happens if “unnamed things” inside a N-sub go nonlinear under a strong shock?
The answer was to replace the linear structural analyzer (NASTRAN) by a nonlinear one (DYNA3D)The fluid and interaction software were not changed.
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Starting Project from Scratch with Limited Resources?
Starting Project from Scratch with Limited Resources?
Mine existing codes for software or data components (e.g, get stiffness/mass mtx from NASTRAN or ANSYS, read in Matlab)
Synthesize an interfacing method and a time marching scheme (following slides)
Use a higher order language (for example Matlab) as “driver-wrapper” and postprocessor
Try realistic problems from start and compare with validation codes.
Dont waste time on fancy features (e.g. parallel processing) before the “core stuff” works
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Partitioned Method SynthesisPartitioned Method Synthesis
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Some Experience So Far (1975-date)Some Experience So Far (1975-date)
Structure-structure, undamped / lightly damped: I-I, A-stable, 2nd-order accurate, single pass, schemes possible.
Control-structure interaction I-I, C-stable, 1st-order accurate, single pass schemes possible.
A-stable for light or moderate damping. 2nd order requires iteration
Underwater shock, no cavitation I-I, A-stable, 2nd-order accurate, single pass, schemes possible
only by augmentation of either fluid or structure
Underwater shock with cavitation I-E-I, C-stable, 2nd-order accurate, single pass, schemes possible
Fluid volume done explicitly. No augmentation required.
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
AugmentationAugmentation
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Important StepImportant Step
Construct a model equation test system
The system contains as many differential equations as coupled components
Goal: identify primary physics with minimal number of parameters
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Test System Example (Developed Later)
Test System Example (Developed Later)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
How Long Does It Take?How Long Does It Take?
Going through a test system synthesis loop can be time consuming, even for an experienced engineer or scientist.
The amount of work strongly depends on many design variables are carried along. This is problem dependent (next slide)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Design Parameters in Test SystemDesign Parameters in Test System
Structure-structure, undamped 4
Structure-structure, Rayleigh damped 7
Control-structure interaction 7
Underwater shock, no cavitation 5
Underwater shock with cavitation 6
Aeroelasticity with dynamic mesh 7-8
Flexible ship hydrodynamics 6-7
Electrothermomechanics 7-9
Counts are for minimum # of partitions
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Recommendations to Save WorkRecommendations to Save Work
Try to reduce number of physical parameters by looking at the essential physics & by forming dimensionless combinations
Try to reduce the number of integration & predictor parameters by using theory if available
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Your Computer Can Help Your Computer Can Help
Synthesis loop may take weeks or months if done by hand (or by “potshot” computations)
The use of Computer Algebra Systems (CAS) such as Mathematica o Maple can reduce the time to days or hours. Examples in notes
Why the gain? Faster algebra, reduction of human errors & integrated graphics facilities
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Recent Research: Partition Localization
Recent Research: Partition Localization
Basic goal: maximally isolate software modules doing component computations so they communicate only by interface forces
akaLagrange Multipliers
Four Possibilities, with last one covered in Part 4: Distributed Global Lagrange Multipliers Distributed Local Lagrange Multipliers Collocated Global Lagrange Multipliers Collocated Local Lagrange Multipliers
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Localization GoalsLocalization Goals
Software reuse, including extrating equations from commercial codes
Nonmatching meshes
Multilevel parallelization
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
How Long Does It Take?How Long Does It Take?
Going through a test system synthesis loop can be time consuming, even for an experienced engineer or scientist.
The amount of work strongly depends on many design variables are carried along. This is problem dependent. Some examples follow.
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Test System Example (Developed Later)
Test System Example (Developed Later)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Design Variables in Test System (1)Design Variables in Test System (1)
Structure-structure interaction, undamped: 2 subsystem frequencies 1 frequency coupling parameter 1 stepsize
Total: 4 physical parameters + integrator & predictor parameters
With Rayleigh damping: add 3
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Recommendations to Save WorkRecommendations to Save Work
Try to reduce number of physical parameters by looking at the essential physics & by forming dimensionless combinations
Try to reduce the number of integration & predictor parameters by using theory if available
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Getting Computer Help Getting Computer Help
Synthesis loop may take weeks or months if done by hand (or by sample computations)
The use of Computer Algebra Systems (CAS) such as Mathematica o Maple can reduce the time to days or hours
Why the gain? Faster algebra, reduction of human errors & integrated graphics facilities
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Auxiliary Mathematica Modules Auxiliary Mathematica Modules
Provided in notes to help with
Stability Analysis
Derivation of characteristic equation
Polynomial stability (Routh criterion, etc.)
Accuracy Analysis
Derivation of Modified Equation
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
A WarningA Warning For second order coupled systems,
stability depends on the computational path
The path dictates how auxiliary variables such as velocities and momenta are computed
Consequence: a tiny change in the guts of a program may suddenly affect stability
Good news: changes in computational path can be compensated by predictor changes (details in article)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Stability Analysis Example:
Structure-Structure Interaction
Stability Analysis Example:
Structure-Structure Interaction
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
SSI: Staggered PartitionSSI: Staggered Partition
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
SSI: Test System (1)SSI: Test System (1)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
SSI: Test System (2)SSI: Test System (2)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
SSI: Test System (2)SSI: Test System (2)
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Theoretical ResultTheoretical Result
Result obtained by Park (1980)
If both structures are treated by the Trapezoidal Rule, and an optimal predictor used (adjusted for the computational path) then
The staggered solution method is unconditionally stable and has second order accuracy
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Verified by Mathematica 24 Years Later
Verified by Mathematica 24 Years Later
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Stable PredictorsStable Predictors
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Mathematica Code Mathematica Code
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
SummarySummary
For undamped structure-structure interaction, optimal staggered methods are known, which do not hinder stability or accuracy
If the coupled system is Rayleigh damped, the same methods are recommended
For generally damped coupled systems, or control-structure interaction, no general theory is available. Problems must be done case by case
University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures
Lecture SourcesLecture Sources
Parts 1 and 2: Material of recent FSI course (Spr 2003) posted at
http://caswww.colorado.edu/courses.d/FSI.d/Home.html
contains posted student projects and references to journal papers, includingthose in CISM brochure:(Felippa-Park-Farhat - CMAME 2001)(Park-Ohayon-Felippa - CMAME 2002)Will add these slides sets on return to Boulder
Part 3: a potpourri of bits and pieces, mostly unpublishedPart 4: two CMAME papers under preparation (Ross’ Thesis)