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Modeling & Performing Static Analysis in OpenSees
ByDhanaji S. Chavan, Assistant Professor, TKIET, Warananagar
Dhanaji Chavan 1
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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
Dhanaji Chavan 2
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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?????
Dhanaji S. Chavan 3
3m
100kN
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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
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• 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……….
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• 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
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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)
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• 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
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• 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
?
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• 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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………………
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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
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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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……..
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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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………..
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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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………
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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
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……….
• 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
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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
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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
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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
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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
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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
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…………….
constraints Transformation
how it handles boundary conditions, enforce constraints
e.g. fixity, equalDOF etc.
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command type
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…………….
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
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………..
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
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……….
numberer RCM
how degrees-of-freedom are numbered
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command type
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…………
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
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…………..
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
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………
analyze 1
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Command to start analysis
Number of analysis steps
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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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