GRADS 2006 Petr Krysl

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P. Krysl 04/08/06

Simulation:

To infinity and beyond.

Petr Krysl

http://Hogwarts.ucsd.edu/~pkrysl



P. Krysl 04/08/06

Simulation-based engng. science

Payoff: • Medicine

• Predictive Homeland Security • Energy and the Environment Materials • Industrial and Defense Applications Issues: • The Tyranny of Scales: The Challenge of Multiscale Modeling and Simulation• Verification, Validation, and Uncertainty Quantification• Dynamic Simulation Systems, Sensors, Measurements, and Heterogeneous Simulations • Big Data in Simulation and the Role of Visualization in SBES • Next-Generation Algorithms and Computational Performance

Payoff: • Medicine

• Predictive Homeland Security • Energy and the Environment Materials • Industrial and Defense Applications

Revolutionizing Engineering Science through SimulationFebruary 2006 Report of the National Science FoundationBlue Ribbon Panel on Simulation-Based Engineering Science



P. Krysl 04/08/06

Engineering Design

DesignDescription

PrototypeHardware

Function/ Behavior

Customer Preferences Technical Specifications

Design Synthesis

Modeling and Simulation

Fabrication Operation

Product

Manufacturing

Refinement



P. Krysl 04/08/06

Predictive?

Is this simulation capability predictive?

From: O’Brien et al. 1999

Experiment

Simulation

Not in this case: non-physical material properties had been used to make it

“look” right (computer graphics ;).



P. Krysl 04/08/06

Modeling

Physical problem

Mathematical idealization

Numerical approximation

Accurate solutionof mathematical model?

Agreement w/ physics of problem?

Equations,assumptions

Discretization(finite elements),algorithms (solvers)

Discretizationerrors

Conceptual errors

Transformationerrors



P. Krysl 04/08/06

Simulation Errors

Errors:Modeling Conceptual (omitted physics, range, …)

ApproximationDiscretization (space, time); and Transformation (finite-precisionarithmetics!)

Error control:Quantify (error estimation), and Minimize (adaptivity).



P. Krysl 04/08/06

Cost of Simulations

Asymptotic behaviour Example: linear statics Assembly of K: O(N),solution of Kx=f: O(N 2 ).

Total cost = aN 2 + bN + c Fixed budget (given grid)

Select modes as linear

combinations of hat functions

log(N) l o g

( E r r o r

) pCN e

−

≈

log(#modes) l o g

( E r r o r )

optimal



P. Krysl 04/08/06

RC Bridge under seismic loads

El Centro accelerogramIsotropic damage model



P. Krysl 04/08/06

RC Bridge: continued



P. Krysl 04/08/06

Monte Carlo Simulation

Statistics of theresponse due to

uncertainty?

Notched plate with uncertain material properties under low-cycle fatigue load

Displacement of theloaded face

Contour of plastic deformation at the end of the load cycling

Copper plate 24x20x2 mm.Finite element model of 1/8 of the plate: 415 hexahedra. J-2 elastoplastic material.Elastic and hardening modulus, yield stress areuncertain with standard deviation 0.025.

Evolution of theequivalent plastic strain at the notch



P. Krysl 04/08/06

Monte Carlo Simulation: cont

Plastic strain at the notch:mean value

Plastic strain at the notch:

standard deviation

Reduced dynamic model :3 Ritz modes yield accuracy of plastic strain better than 2%.

Full FE model: 3,250 CPU sec Reduced FE model: 170 CPU sec

Monte Carlo: Vary thematerial properties for eachrepeated run. Problem: may have to run thousands of simulations. Hence: use an

optimal (reduced) model .



P. Krysl 04/08/06

Bioacoustics

Forced vibration of the anatomical structures (neonate Z. Cavirostris).Planar acoustic waves in seawater of 3500 Hz and 180 dB re: 1µPa received level. Finite element model with 2 ½ million elements (resolution of 3.61 mm). Small displ., small strain kinematics. Almost incompressible elasticity, coupled with Newtonian viscosity (muscle,acoustic fats, connective tissues, and bone). Material properties heterogeneous -- mapped from Hounsfield units.

Horizontal slice.Pressuredistributionsnapshot.

Green:pterygoidsinuses; red:outline of thebones; purple:ear bones.

Vertical slices.Dissipated energy (heat).

GRADS 2006 Petr Krysl

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