1. Modeling & Performing Static Analysis in OpenSeesBy
Dhanaji S. Chavan, Assistant Professor, TKIET, Warananagar
Dhanaji Chavan

2. General steps to be followed…
Define ndm & ndf
Define nodes
Define element(s)
Define material(s)
Define boundary conditions
Define matrix transformation
Apply load
Define recorders
Define analysis objects
Run the analysis
Dhanaji Chavan

3. 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?????
100kN 3m
Dhanaji S. Chavan

4. Tcl script for OpenSees starts now……… step 1: define ndm & ndf
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
Dhanaji S. Chavan

5. How to determine 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
Dhanaji S. Chavan

6. ……….. 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
translation in x direction
Translation in y direction
Rotation
In present case dof is 3
Dhanaji S. Chavan

7. Step2: define nodes node 1 0 0 node 2 3 0 Y coordinate of node
X coordinate of node
Command to define node
Node number
Dhanaji S. Chavan

8. …………
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 1 2
(0,0)
(3,0)
Dhanaji S. Chavan

9. ……….
If we assume origin at node 1, the coordinates for node 1 and 2 are as under:
1(0,0) & 2(3,0)
Dhanaji S. Chavan

10. Step 3: boundary conditions
fix
Constrain rotation
Constrain y-translation
Command to define fixity
Node number
Constrain x-translation
Dhanaji S. Chavan

11. ………………… In our case boundary condition is : node 1 is fixed i.e.
No translation in x direction
No translation in y direction
No rotation
Dhanaji S. Chavan

12. Step 4: define element
element elasticBeamColumn e Iz
Transformation tag E
Type of element
Element number A
Final node
command
Initial node
Dhanaji S. Chavan

13. ……………… 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 FEM…????????
Dhanaji S. Chavan

14. Three types of elements in finite element method
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 larger than its breadth and depth. i.e. x >>> y, z
In FEM such geometry is represented by just a line. When the element is created by connecting two nodes, software comes to know about only one out of 3 dimensions. Remaining two dimensions i.e. cross sectional area must be defined as additional input data & assigned to respective element.
Dhanaji S. Chavan

15. …….. 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.
Dhanaji S. Chavan

16. ……… 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.
Dhanaji S. Chavan

17. ………… 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……………….?????????????
Dhanaji S. Chavan

18. ……….. In present case, will be developed in the cantilever beam.
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
Dhanaji S. Chavan

19. ……… 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….
Dhanaji S. Chavan

20. Step 5: define material
Different materials behave differently when subjected to load.
This behavior is represented by stress-strain curves. e.g.
Elastic Spring
Mild Steel
Dhanaji S. Chavan

21. ……….
In present case material has been defined implicitly.(slide no:12)
However in many other cases we have to define material separately
Dhanaji Chavan

22. Step6:define geometric transformation
geomTransf Linear 1 Role : performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system.
Number/Tag
command
type
Dhanaji Chavan

23. Step 7: define recorders
Purpose: to get results of analysis as an output such as……..
Reaction
Displacement
Force
stiffness
Dhanaji Chavan

24. To Record reactions at nodes…..
keyword
Y-direction
recorder Node -file Rbase.out -time -node dof 1 2 reaction
keyword
keyword
X-direction
keyword
to get reactions as output
Name of the output file
keyword
command
Node numbers
keyword
Dhanaji Chavan

25. To Record displacements at nodes…..
recorder Node -file Dbase.out -time -node dof 1 2 disp
keyword
to get displacements as output
Name of the output file
Dhanaji Chavan

26. 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
Name of the output file
keyword
to get local force as output
Name of the output file
keyword
to get local force as output
Dhanaji Chavan

27. Step 8: application of load
pattern Plain 1 "Constant" {load }
Moment applied
Type of time series
command
command
Load in y-direction
Type of load pattern
Node number
Number/tag of load pattern
Load in x-direction
Dhanaji Chavan

28. Pattern……
Defines the way time series, load & constraints are applied. E.g.
pattern Plain: ordinary pattern
pattern UniformExcitation- transient analysis
Dhanaji Chavan

29. Time series Constant: load is constant throughout the analysis
Linear: load varies linearly with time
Sine : sinusoidal variation of load
Dhanaji Chavan

30. Step 9: defining analysis commands
system UmfPack constraints Transformation test NormDispIncr 1.e Algorithm Newton numberer RCM integrator LoadControl analysis Static analyze 1
Dhanaji Chavan

31. ………………
system UmfPack
solution procedure, how system of equations are solved
Type of equation solver i.e. specific algorithm
command
Dhanaji Chavan

32. ……………. constraints Transformation
how it handles boundary conditions, enforce constraints
e.g. fixity, equalDOF etc.
command
type
Dhanaji Chavan

33. ……………. test NormDispIncr 1.e-6 10 1
Sets criteria for the convergence at the end of an iteration step.
To print information on each step
command
type
maximum number of iterations that will be performed before "failure to converge" is returned
Convergence tolerance
Dhanaji Chavan

34. ………..
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
command
type
Dhanaji Chavan

35. ………. numberer RCM how degrees-of-freedom are numbered command type
Dhanaji Chavan

36. ………… determine the predictive step for time t+dt
integrator LoadControl $dLambda1 <$Jd $minLambda $maxLambda>
$dLambda1:
determine the predictive step for time t+dt
specify the tangent matrix at any iteration
Subsequent time increment
type
DOF
Pseudo-time step
Dhanaji Chavan

37. …………..
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

38. ………... analysis Static command Type of analysis to be performed
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39. ……… analyze 1 Number of analysis steps Command to start analysis
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40. Ex. 2: Quad element
model BasicBuilder -ndm 2 -ndf 2
Dhanaji Chavan

41. Material has to be defined separately
nDMaterial ElasticIsotropic $matTag $E $v
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42. Assign material to element……..
element quad $eleTag $iNode $jNode $kNode $lNode $thick $type $matTag <$pressure $rho $b1 $b2
Dhanaji Chavan

43. Recorders…
recorder Element -ele 3 -time -file stress1.out -dT 0.1 material 3 stress
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44. ……….
recorder Element -ele 3 -time -file strain1.out -dT 0.1 material 1 strain
Dhanaji Chavan