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

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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

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Resonator (Cell Phone Chip Component)

Resonator (Cell Phone Chip Component)

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Resonator: Interaction Diagram

Resonator: Interaction Diagram

System entirely modeled in the frequency domainReduced Models useful

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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

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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)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures

StopStop

End of Part 2