Dynamic Analysis of Civil

Engineering Structures

Jan Walczak

ADINA R&D, Inc., USA

www.adina.com Jan.Walczak@adina.com

Krynica 2012, Copyright ADINA R&D Inc. 2012

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

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)

The ADINA System

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

• 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

Strong robot picking up weight

ADINA in multibody dynamics

Weak robot picking up weight

Magnum Shock Absorber Analyzed using

ADINA

Courtesy of

Gabriel, India

FSI Analysis of Shock Absorber

Model created from Nastran input

Thermo-mechanical coupling, multi-layer shell

Thermo-fluid-structure interaction (TFSI)

TFSI – fluid velocity in a manifold

ADINA in biomedical applications -

Analysis of Carpal Tunnel Syndrome

Model used

Fluid response

Solid response

Fluid pressure and solid stress

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

Courtesy of Caltrans, Division of Structures

Analysis of the Bay Bridge

San Francisco

Oakland Bay

Bridge

West

Span

East

Span

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

Analysis of San Francisco Oakland Bay Bridge

East Span

San Francisco Oakland Bay Bridge

Damage caused by 1989 earthquake

• 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

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

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

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

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

A simple pendulum – implicit solutions

• Newmark method is unstable for large

deformation analysis over a long duration

Newmark Method

Pendulum under gravity load

Bathe Method

Pendulum under gravity load

Model problem: three degrees of

freedom spring system

7

1 2

1 2

10 ; 1

1; 1

k k

m m

Acceleration at node 2

Close-up of acceleration at node 2;

trapezoidal rule results of order 800

1D bar impact problem

1u

1E u t0u

0u

10L

0

Trapezoidal

rule

100 elements

Bathe

method

1u

1E u t0u

0u

10L

0 1D bar impact problem

100 elements

1D bar impact problem

Acceleration

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

•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

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

Wall pressure envelopes – horizontal and vertical ground motions,

potential-based fluid elements with Newmark method compared

With Navier-Stokes solutions

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

Reservoir – refined mesh for the Bathe method

Bathe method solution compared with Navier-Stokes solution

Solution times:

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

Schematic of the problem

Bathe method, solution accuracy of a pipe

breaking system - a simple problem

Courtesy of Onsala Ingenyorsbyra, Sweden

Large scale real application

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

Solution using standard Newmark method, spurious high

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

parasitic pressure distribution

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 )

Newmark method with Rayleigh damping, C=0.001K

Newmark method with numerical damping,

a0.3025 d0.6

Bathe method, no physical damping

Bathe method Newmark method,

without damping

Retrofit Seismic Analysis of

the AURORA bridge

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

Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 57

Aurora Avenue Bridge

• 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 %

• 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

Bridge layout

June 25, 2008 Analysis and Vulnerability Study

Layout

North Approach

June 25, 2008 Analysis and Vulnerability Study

Layout

South Approach

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

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

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

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

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

Moment-curvature relations - input into ADINA

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)

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)

Fundamental Transverse Mode, South Frame

Modal analysis using ADINA

Longitudinal Mode – North Approach, Tallest Frame

Fundamental Transverse Mode – North Approach

Fundamental Longitudinal Mode, South Approach

Pushover analysis using ADINA

•South Frame S7-S8

–Longitudinal

–Transverse

•North Frame N6-N9

–Longitudinal

–Transverse

Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 76

Overturning of Structure

ADINA time history model

Prescribed displacements at the North

main pillar

prescribed displacements at the South

main pillar

Modeling of friction pendulum bearings

Friction pendulum bearing, FE model

Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 82

Friction Pendulum Bearings

Workshop on Seismic Assessment and Retrofit Techniques for Freeway Bridges 83

Friction Pendulum Bearings

• Mechanically simple

• Mathematically complex

(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

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.

Normal reactions

Lateral reactions

Longitudinal reactions

Top of the bridge, longitudinal displacements

Top of the bridge, vertical displacements

Top of the bridge, lateral displacements

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

FRP Retrofit Testing

June 25, 2008 Analysis and Vulnerability Study

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

Amarube Railway Bridge (Japan)

• 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

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

BWR nuclear power plant schematic

Main steam line: 70 atm, 286 oC

1100 MW(e)

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.

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.

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.

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

Forsmark 3 reactor pressure

vessel model

Forsmark 3 reactor pressure

vessel model

• Model built in the AUI

(ADINA User

Interface)

• About 65000 nodes

• Shells, beams, fluid

elements

Forsmark 3 reactor pressure

vessel model

Cutaway of reactor pressure

vessel model Steam dryer

Core cover

Core grid

Steam separators

Core shroud, fuel

Core stand

Control rods

Core stand

Core shroud

Core grid

Core cover

Steam dryer

Steam separators

Modeling of water

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.

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

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.

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.

Loading - Pressure from steam

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”.

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

Forces applied to ends of pipe

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

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

Results

Results – detail near pipe break

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.

Example - dynamic membrane stresses

in core shroud

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.

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.

Validation of FSI solution

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

Dynamic analysis of a nuclear steel

container

Courtesy of GRS mbH, Germany

A complex FE model, including hatches, pipe penetrations,

and variation of wall thicknesses. 3000 steps of 0.00005s

Effective stress distribution at time 24ms

(view from outside)

Nuclear concrete dome subjected to an

impact loading – direct implicit solution

cracks on the external and internal surfaces

of the dome

Damaged areas of the concrete dome

vertical and horizontal reactions of the dome

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