OpenSees: modeling and performing static analysis
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This document provides steps for modeling and performing static analysis in OpenSees. It begins with general steps like defining nodes, elements, materials, boundary conditions, and analysis objects. Then it provides an example of coding for a cantilever beam problem in OpenSees. Key steps in the example include defining two nodes, fixing the first node, using an elastic beam column element, applying a point load, and running the analysis to obtain the deflection of the free end. The document also discusses considerations for choosing appropriate elements and defines terms used in finite element modeling like degrees of freedom.
OpenSees: modeling and performing static analysis
- 1. Modeling & Performing Static Analysis in OpenSees By Dhanaji S. Chavan, Assistant Professor, TKIET, Warananagar Dhanaji Chavan 1
- 2. General steps to be followed… i. Define ndm & ndf ii. Define nodes iii. Define element(s) iv. Define material(s) v. Define boundary conditions vi. Define matrix transformation vii. Apply load viii. Define recorders ix. Define analysis objects x. Run the analysis Dhanaji Chavan 2
- 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????? Dhanaji S. Chavan 3 3m 100kN
- 4. 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 4Dhanaji S. Chavan Tcl script for OpenSees starts now……… step 1: define ndm & ndf
- 5. • 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 5Dhanaji S. Chavan How to determine ndm & ndf……….
- 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 i. translation in x direction ii. Translation in y direction iii. Rotation In present case dof is 3 6Dhanaji S. Chavan ………..
- 7. node 1 0 0 node 2 3 0 7Dhanaji S. Chavan Step2: define nodes Command to define node Node number X coordinate of node Y coordinate of node
- 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 8Dhanaji S. Chavan ………… 1 2 (0,0) (3,0)
- 9. • If we assume origin at node 1, the coordinates for node 1 and 2 are as under: 1(0,0) & 2(3,0) 9Dhanaji S. Chavan ……….
- 10. fix 1 1 1 1 10Dhanaji S. Chavan Step 3: boundary conditions Command to define fixity Node number Constrain x-translation Constrain y-translation Constrain rotation
- 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 11Dhanaji S. Chavan …………………
- 12. element elasticBeamColumn 1 1 2 0.25 2.1e5 0.0052 1 12Dhanaji S. Chavan Step 4: define element command Type of element Element number Initial node Final node A E Iz Transformation tag ?
- 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 thinking…@ FEM…???????? 13Dhanaji S. Chavan ………………
- 14. 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. 14Dhanaji S. Chavan Three types of elements in finite element method
- 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. 15Dhanaji 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. 16Dhanaji 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……………….????????????? 17Dhanaji S. Chavan …………
- 18. 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 18Dhanaji 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…. 19Dhanaji S. Chavan ………
- 20. Different materials behave differently when subjected to load. This behavior is represented by stress-strain curves. e.g. 20Dhanaji S. Chavan Step 5: define material Elastic Spring Mild Steel F
- 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 21
- 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. Dhanaji Chavan 22 command type Number/Tag
- 23. Step 7: define recorders • Purpose: to get results of analysis as an output such as…….. i. Reaction ii. Displacement iii. Force iv. stiffness Dhanaji Chavan 23
- 24. To Record reactions at nodes….. recorder Node -file Rbase.out -time -node 1 2 -dof 1 2 reaction Dhanaji Chavan 24 command keyword keyword Name of the output file keyword keyword Node numbers keyword X- direction Y-direction keyword to get reactions as output
- 25. To Record displacements at nodes….. recorder Node -file Dbase.out -time -node 1 2 -dof 1 2 disp Dhanaji Chavan 25 Name of the output file keyword to get displacements as output
- 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 Dhanaji Chavan 26 Name of the output file keyword to get local force as output Name of the output file keyword to get local force as output
- 27. Step 8: application of load pattern Plain 1 "Constant" {load 2 0 -100.0 0.0} Dhanaji Chavan 27 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
- 28. Pattern…… • Defines the way time series, load & constraints are applied. E.g. i. pattern Plain: ordinary pattern ii. pattern UniformExcitation- transient analysis Dhanaji Chavan 28
- 29. Time series • Constant: load is constant throughout the analysis • Linear: load varies linearly with time • Sine : sinusoidal variation of load Dhanaji Chavan 29
- 30. 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 Dhanaji Chavan 30
- 31. ……………… • system UmfPack – solution procedure, how system of equations are solved Dhanaji Chavan 31 command Type of equation solver i.e. specific algorithm
- 32. ……………. constraints Transformation how it handles boundary conditions, enforce constraints e.g. fixity, equalDOF etc. Dhanaji Chavan 32 command type
- 33. ……………. test NormDispIncr 1.e-6 10 1 Sets criteria for the convergence at the end of an iteration step. Dhanaji Chavan 33 command type Convergence tolerance maximum number of iterations that will be performed before "failure to converge" is returned To print information on each step
- 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 Dhanaji Chavan 34 command type
- 35. ………. numberer RCM how degrees-of-freedom are numbered Dhanaji Chavan 35 command type
- 36. ………… integrator LoadControl $dLambda1 <$Jd $minLambda $maxLambda> $dLambda1: • – determine the predictive step for time t+dt – specify the tangent matrix at any iteration Dhanaji Chavan 36 type DOF Pseudo-time step Subsequent time increment
- 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 37
- 38. ………... analysis Static Dhanaji Chavan 38 command Type of analysis to be performed
- 39. ……… analyze 1 Dhanaji Chavan 39 Command to start analysis Number of analysis steps
- 40. Ex. 2: Quad element model BasicBuilder -ndm 2 -ndf 2 Dhanaji Chavan 40
- 41. Material has to be defined separately nDMaterial ElasticIsotropic $matTag $E $v Dhanaji Chavan 41
- 42. Assign material to element…….. element quad $eleTag $iNode $jNode $kNode $lNode $thick $type $matTag <$pressure $rho $b1 $b2 Dhanaji Chavan 42
- 43. Recorders… recorder Element -ele 3 -time -file stress1.out -dT 0.1 material 3 stress Dhanaji Chavan 43
- 44. ………. recorder Element -ele 3 -time -file strain1.out - dT 0.1 material 1 strain Dhanaji Chavan 44