Dynamic Analysis

ByDhanaji S. Chavan ,

Assistant Professor, TKIET, Warananagar

Problem-1

4 m

-6.00E-01-4.00E-01-2.00E-010.00E+002.00E-014.00E-016.00E-01

0 1 2 3 4 5

acce

lera

tio

n

time

E= 2.1e8 kPa

C/s: 0.3mx0.3m

Input motion is given

500 kN

……………..

• Objectives: to determine………

– Displacement at fee end & fixed end

– Reactions at free end & fixed end

– Local & global forces in the column

– Plot displacement time history at free end for first

2 second

Coding starts……….

model basic -ndm 2 -ndf 3

node 1 0 0

node 2 0 4

fix 1 1 1 1

To define mass

• In dynamic analysis it is must to define nodal or elemental mass

– Beacause Transient(earthquake) motion develops inertial force which is

f=m .a

Inertial force mass

Acceleration to which mass is subjected

……..

mass $nodeTag (ndf $MassValues)

Node number at which mass to be defined

command

Mass for specific degree of motion

…………

mass 2 50 00 0

command

Node number

Mass in x-direction

Mass in y direction

Mass in the direction of rotation

……….

• while defining mass we have to be very careful.

• In present case earthquake motion is in x-direction, so we have to define mass in that direction

• If we defined mass in any other direction that will be

ineffective in analysis

………….

geomTransf Linear 1

element elasticBeamColumn 1 1 2 .09 2.1e8 0.000675 1

recorder Node -file Rbase.out -time -node 1 -dof 1 2 reaction

recorder Node -file RFree.out -time -node 2 -dof 1 2 reaction

recorder Node -file Dbase.out -time -node 1 -dof 1 2 disp

recorder Node -file Dfree.out -time -node 2 -dof 1 2 disp

recorder Element -file ele_Lfor.out -time -ele 1 localForce

recorder Element -file ele_Gfor.out -time -ele 1 globalForce

…………

pattern Plain 1 Constant {

load 2 000 -500.0 0.0}

– Remember that self weight of the super structure

has to be applied separately as a force. It won’t be

calculated automatically form mass .

.............

system UmfPack

constraints Plain

test NormDispIncr 1.0e-5 10 0

algorithm Newton

numberer RCM

integrator LoadControl 1

analysis Static

analyze 10

Quick review of integrator LoadControl

integrator LoadControl $dLambda1 <$Jd$minLambda $maxLambda>

$dLambda1:- first load-increment factor (pseudo-time step)

- Usually same is followed further

<$Jd: - must be integer

-factor relating load increment at subsequent time steps

minLambda, maxLambda:-decides minimum &maximum time increment bound

- optional, default: $dLambda1 for both

Dhanaji Chavan 12

……….

loadConst -time 00.00

– This command is used to restart the time for the transient analysis

command keywordStart time

……….

wipeAnalysis

– This command clears previously-defined analysis

parameters. i.e. parameters defined for static

analysis

To define the input motion..

set accelSeries "Series -dt 0.01 -filePath INPUT_accl.dat -factor 1“

Set: command

accelSeries: variable name to which acceleration time history is to be assigned

• Portion in the box is a time Time Series

Time Series

• Types of time series are :

i. Constant Time Series

ii. Linear Time Series

iii. Rectangular Time Series

iv. Sine Time Series

v. Path Time Series

• For the first four time series the load variation follows fixed pattern.

………..

• When load pattern does not follow a fixedpattern i.e. earthquake load, we have to go forPath Time Series

Ways to define Path Time Series

where the values are specified in a list included in the command & at constant time interval

Series -dt $dt -filePath $fileName <-factor $cFactor>

– In our case we have used this series

keyword

File name which contains the values e.g. accl, vel,load etc

keywordConstant time interval e.g 0.01

keyword

Load factor coefficient.Default value is 1

………….

The load factor to be applied to the loads in the LoadPattern object is :

– load factor = $cFactor*(user-defined series)

Ways to define Path Time Series

For a load path where the values are specified at constant time intervals:

Series -dt $dt -values {list_of_values} <-factor $cFactor>

keyword

Constant time interval e.g 0.01

keyword

List of values e.g. accl, vel, load etc

keyword

Load factor coefficient.Default value is 1

…………

• For a load path where the values are specified at non-constant time intervals:

Series -time {list_of_times} -values {list_of_values} <-factor $cFactor>

• where both time and values are specified in a list included in the command:

Series -fileTime $fileName1 -filePath $fileName2 <-factor $cFactor>

To define load pattern

pattern UniformExcitation $patternTag $dir -accel(TimeSeriesType arguments) <-vel0 $ver0>

• Pattern: command

• UniformExcitation: name/type of load pattern

• $patternTag: unit pattern tag/ number

• $dir: direction of excitation (1, 2, or 3) used in formulating the inertial loads for the transient analysis

• -accel: keyword to define acceleration history

• -vel0: keyword to define initial velocity $ver0 whose default value is zero

……………

In our case…….

pattern UniformExcitation 2 1 -accel $accelSeries

Unique pattern tagDirection of excitation X-direction

A uniform acceleration history is imposed at all nodes constrained in the x-direction i.e. in our case node 1 only

Defining Dynamic analysis commands………………

system ProfileSPD

test NormDispIncr 1.e-6 50 0

algorithm KrylovNewton

constraints Transformation

To define integrator

• We can not use the integrator defined for static analysis

• We have to define the following integrator

integrator Newmark $gamma $beta

command

Name of the integrator

Newmarkparameter

Newmarkparameter

…………

Integrator Newmark 0.5 0.25

numberer RCM

analysis Transient

analyze 4000 0.01

Thank u……………………………………

Assignment -1.

1. Perform both static & dynamic analysis for given problem discretizing into one element only

2. Don’t define nodal mass & see what happens

3. Define the mass in y direction & see the results

4. Apply both vertical & lateral static loads at free end & perform the analysis

5. Don’t use the loadConst -time 00.00 & see what happens

Assignment -2

• Discretize above model in 4 elements & perform the complete analysis

Problem- 2

1(0,0) 2(1,0)

3(1,1)4(0,1)

E= 2.1e8 kPa, mass density = 1.6 ton/m3

input motion: sinusoidal acceleration at base

3.0

………

Wipe

model basic -ndm 2 -ndf 2

nDMaterial ElasticIsotropic 1 2.1e8 0.3

node 1 0.000 0.000

node 2 1.000 0.000

node 3 1.000 1.000

node 4 0.000 1.000

…………

element quad 1 1 2 3 4 1.0 "PlaneStrain" 1 0.0 0.0 0 -16

Surface pressure

Mass density

Body force in x direction

Body force in y direction

………

fix 1 1 1

fix 2 1 1

system ProfileSPD

test NormDispIncr 1.e-12 25 0

constraints Transformation

integrator LoadControl 1 1 1 1

algorithm Newton

numberer RCM

analysis Static

………………..

analyze 1

loadConst -time 0.000

wipeAnalysis

Application of earthquake motion

pattern UniformExcitation 1 1 -accel "Sine 0 1000

1 -factor 10"

Sinusoidal variation

Start time

End timePeriod of sine wave

Load factor coefficient

……………….

constraints Transformation; test NormDispIncr 1.e-12 25 0algorithm Newton numberer RCMsystem ProfileSPDintegrator Newmark 0.5 0.25 analysis Transient recorder Node -file disp.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 disprecorder Node -file acce.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 accelrecorder Element -ele 1 -time -file stress1.out -dT 0.01 material 1 stress recorder Element -ele 1 -time -file strain1.out -dT 0.01 material 1 strain recorder Element -ele 1 -time -file stress3.out -dT 0.01 material 3 stress recorder Element -ele 1 -time -file strain3.out -dT 0.01 material 3 strain analyze 2000 0.01

……………

recorder Node -file disp.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 disp

recorder Node -file acce.out -time -node 1 2 3 4 -dof 1 2 -dT 0.01 accel

recorder Element -ele 1 -time -file stress1.out -dT 0.01 material 1 stress

recorder Element -ele 1 -time -file strain1.out -dT 0.01 material 1 strain

recorder Element -ele 1 -time -file stress3.out -dT 0.01 material 3 stress

recorder Element -ele 1 -time -file strain3.out -dT 0.01 material 3 strain

analyze 2000 0.01

Assignment-3

1. Perform both static & dynamic analysis for given problem &………

Plot displacement time history plot for node 3 & 4

Plot acceleration time history plot for node 3 & 4

Assignment-4

• Discretize domain in 4 elements & perform the complete analysis

Assignment- 5

• Apply equal dof for node 3 & 4 , perform dynamic analysis and

Plot displacement time history plot for node 3 & 4

Plot acceleration time history plot for node 3 & 4

………

equalDOF 3 4 1 2

Thank u............