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Dynamic Analysis of Civil Engineering Structures Jan Walczak ADINA R&D, Inc., USA www.adina.com [email protected] Krynica 2012, Copyright ADINA R&D Inc. 2012

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Page 1: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Dynamic Analysis of Civil

Engineering Structures

Jan Walczak

ADINA R&D, Inc., USA

www.adina.com [email protected]

Krynica 2012, Copyright ADINA R&D Inc. 2012

Page 2: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Content of Presentation

•Philosophy in the development of the ADINA System

•Bathe method for implicit time integration

•Analysis of simple problems – stability and accuracy

of the Bathe method

•Analysis of civil engineering structures

•Concluding remarks

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Structures

CFD

Electromagnetics

Multi-Physics (TMC, FSI, TFSI, …)

The ADINA System

The ADINA System offers analysis capabilities in

in ONE system.

This makes the ADINA System unique in the market.

Note: ADINA is also the nonlinear solver for

NX Nastran (SOL 601)

Page 4: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

The ADINA System

Page 5: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

RELIABILTY is most important !

EFFICIENCY is also important !

We need to achieve both !

The ADINA System

for Structures, CFD and Multi-Physics

The philosophy of the ADINA development

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• What we believe to be important

The need for use of reliable finite element

methods

Using the state-of-the-art techniques

2d and 3d solids, shells,...

Plasticity, Contact,….

CFD, …

Multi-Physics,…

• Strong theoretical foundation is essential in the

development of reliable finite element program

• ADINA – from mechanical to biomedical applications

ADINA Development

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Strong robot picking up weight

ADINA in multibody dynamics

Page 8: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Weak robot picking up weight

Page 9: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Magnum Shock Absorber Analyzed using

ADINA

Courtesy of

Gabriel, India

Page 10: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

FSI Analysis of Shock Absorber

Model created from Nastran input

Page 11: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Thermo-mechanical coupling, multi-layer shell

Page 12: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Thermo-fluid-structure interaction (TFSI)

Page 13: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

TFSI – fluid velocity in a manifold

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ADINA in biomedical applications -

Analysis of Carpal Tunnel Syndrome

Page 15: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Model used

Page 16: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Fluid response

Page 17: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Solid response

Page 18: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Fluid pressure and solid stress

Page 19: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

ADINA in Civil Engineering

Applications

• Our involvement with civil engineering started

after the 1989 San Francisco earthquake

• All major codes were tested for reliability

• The ADINA program has been chosen by

CALTRANS as the main nonlinear analysis tool for

all California tall bridges

Page 20: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Courtesy of Caltrans, Division of Structures

Analysis of the Bay Bridge

San Francisco

Oakland Bay

Bridge

West

Span

East

Span

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San

Francisco

Oakland

West Span

East Span

Courtesy of Caltrans, Division of Structures

Analysis of San Francisco Oakland Bay Bridge

using ADINA

Total length – 23,556 ft (7,180m)

Height – 190 ft (58 m)

Construction started 1933, finished 1936

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Analysis of San Francisco Oakland Bay Bridge

East Span

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San Francisco Oakland Bay Bridge

Damage caused by 1989 earthquake

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Page 25: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

• Safety issues – tremendous responsibility

• Size of civil structures – modeling issues

• Lack of experimental data, reliability at most

important:

- Reliable finite elements

- Reliable and robust solution techniques

- Efficient and stable implicit time integration

method for long durations (Bathe method)

Civil engineering specific

requirements

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Bathe time integration method

Evaluating velocities in terms of

displacements and accelerations we have:

+t t t t t t t t M U C U R F

1 2 3

t t t t t t tc c c U U U U

1 2 3

t t t t t t tc c c U U U U

Page 27: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Where are displacement and velocity

solutions at time and:

,t t t t U U

t t

1

(1 )c

t

2

1

(1 )c

t

3

(2 )

(1 )c

t

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Using the above expressions, the equilibrium equation (1)

can be written at time t+dt in the following form:

( 1) ( )

3 3 3

( 1)

1 2

( 1)

3 1 3 2 3 3

( 1)

1 2 3

( _ )

(

)

( )

t t i i

t t t t i t t t

t t t t t i

t t t t t i

c c c

c c

c c c c c c

c c c

K M C ΔU

R F M U U

U U U

C U U U

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Properties:

-- no parameter to adjust, simply the time

step has to be sufficiently small for accuracy

-- solves in nonlinear analysis when the TR fails

-- shows excellent accuracy/ dissipation

Effective in structural dynamics and

in wave propagations

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A simple pendulum – implicit solutions

• Newmark method is unstable for large

deformation analysis over a long duration

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Newmark Method

Pendulum under gravity load

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Bathe Method

Pendulum under gravity load

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Model problem: three degrees of

freedom spring system

7

1 2

1 2

10 ; 1

1; 1

k k

m m

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Acceleration at node 2

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Close-up of acceleration at node 2;

trapezoidal rule results of order 800

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1D bar impact problem

1u

1E u t0u

0u

10L

0

Trapezoidal

rule

100 elements

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Bathe

method

1u

1E u t0u

0u

10L

0 1D bar impact problem

100 elements

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1D bar impact problem

Acceleration

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Bathe method vs. trapezoidal method (TR)

• We have to distinguish between stability and

accuracy – loss of stability means huge error, totally

bad results

• The TR method is stable in linear analysis but not in

nonlinear

• The Bathe method is stable in linear and nonlinear

analysis

• The TR method has no amplitude decay

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•The Bathe method has a small amplitude decay

(which can be reduced by selecting a reasonable

small time step)

•For FE solutions, the Bathe method is much better

than TR and Newmark methods:

- always stable

- larger steps can be used

- better convergence in Newton iterations

- good accelerations, that means good reactions

Page 41: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Reservoir cross section, 471 ft long and 21.8 ft high Courtesy of Alexander Kozak, SC Solutions, USA

Bathe method vs Newmark method –

a sensitivity study

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Page 43: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Wall pressure envelopes – horizontal and vertical ground motions,

potential-based fluid elements with Newmark method compared

With Navier-Stokes solutions

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blue line – potential based fluid elements with Newmark method

red line – potential-based fluid elements with Bathe method

green line – CFD (Navier-Stokes fluids) solution

Page 45: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Reservoir – refined mesh for the Bathe method

Page 46: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Bathe method solution compared with Navier-Stokes solution

Solution times:

Bathe method -5.26 sec, Navier-Stokes – 158.36 sec

Page 47: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Schematic of the problem

Bathe method, solution accuracy of a pipe

breaking system - a simple problem

Courtesy of Onsala Ingenyorsbyra, Sweden

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Large scale real application

Page 49: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Checking Solution Accuracy

• test problem with the same features as

a nuclear container

• elastic shell fully clamped at its base, and

a fluid surrounding it

• MITC4 shell elements and potential-based fluid

elements were used

• the model is subjected to a sudden fluid flux

representing a pipe break

• solutions for Newmark and Bathe methods

are compared

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Solution using standard Newmark method, spurious high

frequency oscillations, non-smooth contact (on and off),

parasitic pressure distribution

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To overcome these problems, different

techniques can be used:

• Adding physical damping, e.g. Rayleigh damping,

to the structure only (difficult to predict how much

damping need to be added)

• Adding numerical damping to the Newmark method

(that reduces oscillations but also reduces response)

• Using Bathe time integration method

(no parameters needed to be adjust, the method is

second order and effectively damps out higher

frequencies )

Page 52: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Newmark method with Rayleigh damping, C=0.001K

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Newmark method with numerical damping,

a0.3025 d0.6

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Bathe method, no physical damping

Page 55: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Bathe method Newmark method,

without damping

Page 56: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Retrofit Seismic Analysis of

the AURORA bridge

Courtesy of Tim Ingham, T.Y. Lin International, USA

Page 57: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 57

Aurora Avenue Bridge

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• official name – George Washington Memorial

Bridge, Seattle, WA

• arch-truss bridge, constructed in 1929-1932

• 2,945 ft (898 m) long, 70 ft (21 m) wide,

167 ft (51 m) high (above water level)

• following the collapse of Minneapolis I-35 arch-truss

bridge in 2007 inspections have been ordered

• after inspections, the bridge has

been determined functionally obsolete with marginal

sufficiency rating of 55.2 %

Page 59: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

• The bridge consists of 2 V-shape cantilevers,

each 325 ft (99 m), balanced on large concrete

pilings on opposite site of the ship canal

• A 150 ft (46 m) long Warren truss suspended span

connects the two cantilevers in the middle

•Starting June 2011, the bridge has been undergoing

seismic retrofitting

• The bridge’s height and pedestrian access make it a

popular location for suicide jumpers

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Bridge layout

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June 25, 2008 Analysis and Vulnerability Study

Layout

North Approach

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June 25, 2008 Analysis and Vulnerability Study

Layout

South Approach

Page 63: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Geotechnical Investigations

•Field Investigations

–New borings at N-15, N-1, S-1, and S-5

–Sampling for geotech index properties

–Crosshole seismic testing

•Develop new ground motions

–Based on a 475-year Return Period

–Acceleration time histories at each pier

•Foundation Springs

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Evaluation Criteria - Standards

•AASHTO (American Association of State Highway and

Transportation Office) Seismic Guide Spec

•AASHTO LRFD (Load and Resistance Factor Design) 4th Ed

–Strength capacity calculations (except shear)

•FHWA (Federal Highway Administration) Seismic Retrofitting

Manual

–Shear provisions

•Priestley ( M.J.N. Priestley and F. Seible, Seismic Design and

Retrofit for Bridges, www.amazon.com)

–Detail checks and methods, consistent with Seismic Guide Spec and

Seismic Retrofitting Manual

Page 65: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Modeling

•New north and south approach models

•Inelastic M-C for columns, crossbeams/floorbeams

•Foundation stiffness and input based on Golder’s work

(Golder Associates, www.golder.com)

•Modal analysis

•Pushover (nonlinear) analysis

•Nonlinear dynamic, direct time integration analysis

Page 66: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Modal analysis using ADINA

• static dead load calculations of a full model with material

nonlinear models (moment-curvature relations for beams,

elasto-plastic material for shells,…)

• contact conditions are included in static and

frequency/modal solutions

• restart to frequency and mode superposition solutions

• frequencies calculated using Bathe’s Subspace iteration

method

Page 67: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Moment-curvature relations for

beam elements

• modeling of nonlinear elastic and elasto-plastic

beams with arbitrary cross sections

• small or large displacements

• bending moments vs. curvatures and torsional

moments vs. twists are functions of the axial forces

Page 68: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

Moment-curvature relations - input into ADINA

Page 69: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

0 1 103

2 103

3 103

4 103

0

5 103

1 104

1.5 104

Column

Splice

Curvature, /ft

Mom

ent, f

t-kip

0.000364

Moment-curvature relation used in the Aurora

N8 – splice at column base (longitudinal demands)

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0 1 103

2 103

3 103

4 103

0

5 103

1 104

1.5 104

Column

Splice

Curvature, /ft

Mom

ent, f

t-kip

0.000364

Moment curvature relation used in the Aurora

S8 – splice at column base (longitudinal demands)

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Fundamental Transverse Mode, South Frame

Modal analysis using ADINA

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Longitudinal Mode – North Approach, Tallest Frame

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Fundamental Transverse Mode – North Approach

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Fundamental Longitudinal Mode, South Approach

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Pushover analysis using ADINA

•South Frame S7-S8

–Longitudinal

–Transverse

•North Frame N6-N9

–Longitudinal

–Transverse

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Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 76

Overturning of Structure

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ADINA time history model

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Prescribed displacements at the North

main pillar

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prescribed displacements at the South

main pillar

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Modeling of friction pendulum bearings

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Friction pendulum bearing, FE model

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Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 82

Friction Pendulum Bearings

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Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 83

Friction Pendulum Bearings

• Mechanically simple

• Mathematically complex

Page 84: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

(sgn )N

F D N DR

F – lateral force,

N – vertical force acting on the bearing

(in practice it is the dead load supported by the

bearing),

R – radius of bearing surface curvature,

D – lateral displacement,

D(dot) - is a relative velocity between top an bottom

parts of the bearing

• implemented to ADINA as a user-supplied friction

Friction pendulum mathematical model

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Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 85

Contact Surface Model

Dish - Contact Surface

Slider - Contact Surface

Slider - Contact Point

Solid

Element

Rigid Link,

typ.

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Normal reactions

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Lateral reactions

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Longitudinal reactions

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Top of the bridge, longitudinal displacements

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Top of the bridge, vertical displacements

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Top of the bridge, lateral displacements

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June 25, 2008 Analysis and Vulnerability Study

Proposed Retrofit Scheme –

North Approach

• Retrofit columns N9-N15 using FRP

(fiber reinforced plastic)

• Split column modification N6, N9, N11, N14; and

wrap with FRP

• Longitudinal girder strengthening

• Confinement of N6-N9 crossbeams

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FRP Retrofit Testing

June 25, 2008 Analysis and Vulnerability Study

Page 97: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

June 25, 2008 Analysis and Vulnerability Study

Proposed Retrofit Scheme –

South Approach

• Strengthen deficient elements in 75’ truss spans

• Strengthen bracing in steel bent S4 / S5

• Retrofit S6 bearing / Retrofit S6 backwall for shear

with concrete or FRP

• Steel casings at split columns S7, S8 (eliminate

split) and S9

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Amarube Railway Bridge (Japan)

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• old steel bridge replaced in 2010 by a pre-stressed

concrete bridge

• 93-meter concrete girder moved with slow sliding to be

adjusted to the tunel entrance

• ADINA has been used for the analysis

courtesy of Kozo Keikaku, Japan

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Page 101: Dynamic Analysis of Civil Engineering · PDF fileNX Nastran (SOL 601) ... • Our involvement with civil engineering started ... • restart to frequency and mode superposition solutions

FSI analysis in nuclear power plant

assessments

• Forsmarks Kraftsgrupp operates three nuclear power plants in Sweden, all boiling water reactors.

Courtesy of A. Thorsson, B. Olsson, J, Sundqvist – Forsmark Kraftsgrup

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BWR nuclear power plant schematic

Main steam line: 70 atm, 286 oC

1100 MW(e)

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Safety issues • Forsmark is responsible for the safe operation of

the plants.

• The plants must operate safely under normal operating conditions.

• The plants must be shut down safely when an emergency occurs:

– Turbine trip

– Earthquake

– LOCA (loss of coolant accident)

– Blowdown

• The plants are being upgraded during the next several years. The plants must operate safely,

and be shut down safely, after the upgrades.

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Numerical modeling at Forsmark

• Forsmark creates numerical models of the

reactor pressure vessels, piping systems,

containment buildings, etc.

• These models are routinely used to analyze the

plants.

– Analysis corresponding to normal operation,

and to anticipated emergencies, to show

authorities that the plants are safe.

– Analysis after emergency, to determine if the

plant can be safely restarted.

• These models are continually maintained and

upgraded, as the plants are upgraded.

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Need for FSI analysis • Many of the plant components contain water and steam,

which must be considered in the analyses.

• Decoupled fluid analysis: approximately include fluid

effects in structural analysis, e.g., include added mass of

water as extra density in structural analysis.

• Decoupled fluid analysis gives in most cases an

overconservative design, but also sometimes a

nonconservative assessment.

• FSI-based models are more accurate than decoupled

fluid models, because FSI effects such as reduced speed

of sound, wave propagation in fluid, etc. are directly

included.

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FSI vs without FSI

Measured

FSI

w/o FSI

from

Andersson

et. al.,

“Numerical

simulation

of the HDR

blowdown

experiment

V31.1

at

Karlsruhe”,

2002

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Forsmark 3 reactor pressure

vessel model

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Forsmark 3 reactor pressure

vessel model

• Model built in the AUI

(ADINA User

Interface)

• About 65000 nodes

• Shells, beams, fluid

elements

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Forsmark 3 reactor pressure

vessel model

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Cutaway of reactor pressure

vessel model Steam dryer

Core cover

Core grid

Steam separators

Core shroud, fuel

Core stand

Control rods

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Core stand

Core shroud

Core grid

Core cover

Steam dryer

Steam separators

Modeling of water

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FSI solution procedure • Potential-based fluid

elements

– Unknown is the velocity potential (one DOF per fluid node)

– Inviscid irrotational fluid with constant density and bulk modulus

– Fluid velocities can be subsonic (nonlinear element) or small (linear element)

– Structural boundary motions are coupled to fluid.

– Small structural boundary motions.

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FSI solution procedure • System matrices are symmetric and sparse.

• Frequency analysis, harmonic/random/response spectrum analysis are possible.

• Results from potential-based elements are comparable to results from Navier-Stokes based CFD elements (when the same modeling assumptions are used).

• Primary reason to use potential-based elements: speed with reasonable accuracy.

TUUU UUUU FU

FF FFFU

RM 0 K 0u u uC C

R0 M 0 KC 0

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Division of water into element

groups • The water is divided into

7 element groups.

• Each element group has different physical properties (bulk modulus and density).

• Physical properties based on analysis of steam/water mixture under normal operating temperatures and pressures using RELAP5.

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Modeling of water - detail

• The water is separated by structural elements.

• The adjacent water groups are connected with fluid-fluid interfaces (need continuity of pressure between adjacent groups).

• Pressure is applied on the free surfaces, corresponding to the pressure in the steam.

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Loading - Pressure from steam

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Initial conditions • Solved for in one static

load step.

• Loads include gravity, pressures from steam, pressure from recirculation pump

• Effect of fluid flow during normal operation is neglected; water is modeled “at rest”.

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Pipe break analysis

Low pressure coolant

injection inlet

Prescribed mass flux, calculated

from RELAP5 analysis:

0

200

400

600

800

1000

1200

1400

1600

9.999 10.049 10.099 10.149 10.199

Time (sec)

Ma

ss

flu

x (

kg

/s)

Assume pipe break opening

time approx. 16 ms

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Forces applied to ends of pipe

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Solution procedure

• Implicit dynamic analysis, Bathe method, time step size 10-5 sec.

– Step size chosen to accurately integrate the highest frequency of interest in the structure.

• 15000 time steps.

• Linear analysis. Linear structural elements, linear

potential-based fluid elements (neglect

effect).

21v

2

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Justification for using linear potential-based elements

• In the linear potential-based elements, we compute the pressure using

and neglect the nonlinear term .

• Analysis show that is significant only close to the

pipe break, when the outflow velocity is developed.

• Linear potential-based elements can be used only because

the mass flux is prescribed at the pipe break. If the pressure

had been prescribed instead, then the term cannot

be neglected.

21v

2

p

21v

2

21v

2

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Results

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Results – detail near pipe break

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Use of model results • Results are used

– to verify that the stresses/forces are less than allowable values

– to generate loads for more detailed analyses of reactor internals, e.g. new core shroud lid to be installed during uprate.

– to generate floor response spectra (acceleration response spectra), used as loadings for more detailed analyses.

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Example - dynamic membrane stresses

in core shroud

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Pipe break analysis - summary

• The pipe break analysis is one of many similar

analyses routinely performed at Forsmark.

• This model is also used for

– earthquake analysis

– blowdown analysis, for different configurations of safety

relief valves

• This model can be locally refined as necessary to

perform a more detailed analysis.

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Validation of FSI solution

procedure • HDR blowdown experiment V31.1

– Experiments performed in late 1970s to provide data for

verification of numerical codes used in reactor pressure

vessel analysis.

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Validation of FSI solution

procedure • Typical results for strains on outside of core barrel:

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Dynamic analysis of a nuclear steel

container

Courtesy of GRS mbH, Germany

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A complex FE model, including hatches, pipe penetrations,

and variation of wall thicknesses. 3000 steps of 0.00005s

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Effective stress distribution at time 24ms

(view from outside)

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Nuclear concrete dome subjected to an

impact loading – direct implicit solution

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cracks on the external and internal surfaces

of the dome

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Damaged areas of the concrete dome

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vertical and horizontal reactions of the dome

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Conclusions

and a look into the future

• Very powerful capabilities are now available to perform finite element analyses of civil engineering structures

• Any “new” development should be measured against the already existing techniques

• Further significant challenges are still before us and major advances must still be expected