Modeling & Performing Static Analysis in OpenSees

ByDhanaji S. Chavan, Assistant Professor, TKIET, Warananagar

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General steps to be followed…

i. Define ndm & ndfii. Define nodesiii. Define element(s)iv. Define material(s)v. Define boundary conditions

vi. Define matrix transformationvii. Apply loadviii. Define recordersix. Define analysis objectsx. Run the analysis

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Example 1- Cantilever Beam

• What is the deflection of the free end of a 3 m

cantilever beam subjected to a point load of 100 kN?

(E =2*1005 kN/m2 ,c/s:0.3mx0.3m)

How to do coding for this problem in OpenSees?????

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3m

100kN

wipe

model basic -ndm 2 -ndf 3

• wipe :clears the previous coding present in OpenSees memory, if any

• model basic :key word to start the definition of model

• ndm :defines number of dimensions of the problem

• ndf :defines the degrees of freedom at a node in a model

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Tcl script for OpenSees starts now………step 1: define ndm & ndf

• ndm: number of dimensions

we have to specify whether problem is 2-dimensional or

3-dimensional.

How to determine whether problem is 2-D or 3-D:

If to specify the geometry of the problem only two coordinates x

and y are required , it is 2-D problem

If to specify the geometry of the problem three coordinates x,y

and z are required , it is 3-D problem

In present case ndm is 2

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How to determine ndm & ndf……….

• We have to specify degree of freedom at a node

What is degree of freedom?

The number unknowns ,to be determined, at a node is called as

degree of freedom

In present case: three unknowns are there at each node

i. translation in x direction

ii. Translation in y direction

iii. Rotation

In present case dof is 3

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………..

node 1 0 0

node 2 3 0

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Step2: define nodes

Command to define node

Node number

X coordinate of node

Y coordinate of node

In finite element method we discretize the given domain(geometry) into certain number of finite elements.

in our case 3 m long beam is the domain

in present case let’s use only one element for sake of simplicity.

The ends of an element in finite element method are called as nodes

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…………

1 2(0,0) (3,0)

• If we assume origin at node 1, the coordinates

for node 1 and 2 are as under:

1(0,0) & 2(3,0)

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……….

fix 1 1 1 1

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Step 3: boundary conditions

Command to define fixity

Node numberConstrain x-translation

Constrain y-translation

Constrain rotation

• In our case boundary condition is : node 1 is

fixed i.e.

No translation in x direction

No translation in y direction

No rotation

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…………………

element elasticBeamColumn 1 1 2 0.25 2.1e5 0.0052 1

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Step 4: define element

command

Type of element Element number

Initial node

Final node

A

E

Iz

Transformation tag

?

• Which finite element to use to model the behavior of

beam? Why?

• OpenSees has wide range of elements in its library

• Is it fine if we use any element from it?

• Or we have to choose certain element only

• How to decide which element to use ?

…………..Needs some thinking…@ FEM…????????

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………………

1-d element :

Used for geometries for which one of the dimensions is quite larger than rest two.

E.g. beam : in case of beam its length is considerably largerthan its breadth and depth. i.e. x >>> y, z

In FEM such geometry is represented by just a line. Whenthe element is created by connecting two nodes, softwarecomes to know about only one out of 3 dimensions.Remaining two dimensions i.e. cross sectional area must bedefined as additional input data & assigned to respectiveelement.

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Three types of elements in finite element method

2-d element:

Two dimensions are quite larger than third one

E.g. metal plate: length & width are considerably

larger than thickness. i.e. x, y >>> z

The third dimension i.e. thickness has to be

provided as additional input in coding by user &

assigned to respective element.

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……..

3-d element:

All three dimensions are comparable

E.g. brick: x~y~z

No additional dimension to be defined. While

meshing itself all three dimensions are

included.

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………

• In our case, we understood that we have to use 1-d element.

• Which 1-d element should we use?

Should we use spring element?

Or bar/truss element?

Or beam element

Think……………….?????????????

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…………

In present case,

– Shear force &

– Bending moment

will be developed in the cantilever beam.

We have to choose 1-d finite element in such a way

that it will take both shear force & bending moment

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………..

We can not use spring or bar element because

Spring element models axial load only

Bar elements model axial load and axial stress

However beam element takes axial, shear &

bending stresses. Hence….

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………

Different materials behave differently when subjected to load.

This behavior is represented by stress-strain curves. e.g.

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Step 5: define material

Elastic Spring

Mild Steel

F

……….

• In present case material has been defined implicitly.(slide no:12)

• However in many other cases we have to define material separately

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Step6:define geometric transformation

geomTransf Linear 1

Role : performs a linear geometric transformationof beam stiffness and resisting force from thebasic system to the global-coordinate system.

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commandtype

Number/Tag

Step 7: define recorders

• Purpose: to get results of analysis as an output such as……..

i. Reaction

ii. Displacement

iii. Force

iv. stiffness

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To Record reactions at nodes…..

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

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command

keyword

keywordName of the output file

keyword

keyword

Node numbers

keyword

X-direction

Y-direction

keywordto get reactions as output

To Record displacements at nodes…..

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

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Name of the output file

keywordto get displacements as output

To Record force in element…..

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

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

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Name of the output file

keywordto get local force as output

Name of the output file

keywordto get local force as output

Step 8: application of load

pattern Plain 1 "Constant" {load 2 0 -100.0 0.0}

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command

Type of load pattern

Number/tag of load pattern

Type of time series

command

Node number

Load in x-direction

Load in y-direction

Moment applied

Pattern……

• Defines the way time series, load & constraintsare applied. E.g.

i. pattern Plain: ordinary pattern

ii. pattern UniformExcitation- transient analysis

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Time series

• Constant: load is constant throughout the analysis

• Linear: load varies linearly with time

• Sine : sinusoidal variation of load

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Step 9: defining analysis commands

system UmfPack

constraints Transformation

test NormDispIncr 1.e-6 200 1

Algorithm Newton

numberer RCM

integrator LoadControl 1 1 1 1

analysis Static

analyze 1

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………………

• system UmfPack

– solution procedure, how system of equations are solved

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command Type of equation solver i.e. specific algorithm

…………….

constraints Transformation

how it handles boundary conditions, enforce constraints

e.g. fixity, equalDOF etc.

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command type

…………….

test NormDispIncr 1.e-6 10 1

Sets criteria for the convergence at the end of an iteration step.

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command

type

Convergence tolerance

maximum number of iterations that will be performed before "failure to converge" is returned

To print information on each step

………..

Algorithm Newton

uses the Newton-Raphson method to advance to the next time step.

The tangent is updated at each iteration

Recommendation: numerical methods for engineers by Chapra

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command type

……….

numberer RCM

how degrees-of-freedom are numbered

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command type

…………

integrator LoadControl $dLambda1 <$Jd $minLambda

$maxLambda> $dLambda1:

•

– determine the predictive step for time t+dt

– specify the tangent matrix at any iteration

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type

DOFPseudo-time step

Subsequent time increment

…………..

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

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………...

analysis Static

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commandType of analysis to be performed

………

analyze 1

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Command to start analysis

Number of analysis steps

Ex. 2: Quad element

model BasicBuilder -ndm 2 -ndf 2

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Material has to be defined separately

nDMaterial ElasticIsotropic $matTag $E $v

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Assign material to element……..

element quad $eleTag $iNode $jNode $kNode $lNode $thick $type $matTag <$pressure $rho $b1 $b2

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Recorders…

recorder Element -ele 3 -time -file stress1.out -dT 0.1 material 3 stress

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……….

recorder Element -ele 3 -time -file strain1.out -dT 0.1 material 1 strain

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