OpenSees Tutorial

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OpenSees Tutorial

for SE 207: Nonlinear Structural Analysis

by

Quan Gu, Andre Barbosa, and Joel Conte

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Introduction to OpenSees§ OpenSees (Open System for Earthquake Engineering

Simulation) is an open source software framework used to model structural and geotechnical systems and simulate their earthquake response.

§ This framework has been under development by the Pacific Earthquake Engineering Research Center (PEER) since 1997.

§ OpenSees has been recently adopted as a NEESgridsimulation component.

§ Website: http://opensees.berkeley.edu


http://opensees.berkeley.edu


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OpenSees is an Object-Oriented Software

§ An object is a bundle of variables and related methods.

§ A method is an operation which can modify an object’s behavior. In other words, it changes an object by manipulating its variables.

§ Only an object's methods should modify its variables.

§ A class is a blueprint for an object (i.e., it is a data structure, but not the memory allocated for the object)

§ Instantiation: process of allocating the memory to implement a class.

§ Inheritance. A subclass is a class definition which derives functionality from another class definition.

Concepts of Object-Oriented Programming (OOP):



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class Material {public:

Material() { };virtual ~Material( ) { };

void setE (double passedE) {E=passedE;}void setStrain (double pStrain) { strain = pStrain;}double getStrain (void) {return strain;}double getStress (void) {

stress = strain*E; return stress;}

double getTangent (void) { return E; }

private:

double E; double strain;double stress;

};

E, σ, ε

Set value of E

Set value of εGet value of σGet value of εGet Tangent

Material object

Private members

Public methods



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int main (int argc, char* argv[]){

Material theMat; //create an object and allocate the memory for this object

theMat.setE(2.1e11); //call the object’s method to modify its variable

theMat.setStrain(0.001); //call the object’s method to modify its variable

double stress = theMat.getStress(); //call the object’s method

printf("stress is: %f \n", stress);

return 0;}

Output:stress is: 210000000.000000

Matlab: theMat.E = 2.1E11;

In Matlab: getStress( 0.001);



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OpenSees Framework -- Object Oriented Programming (OOP)

§ OpenSees is a C++ based FE software

class DirectIntegrationAnalysis:public TransientAnalysis{public:

int analyze( );int domainChanged( );…

private:TransientIntegrator * theIntegrator;

EquiSolnAlgo * theAlgorithm;…

};

Class DirectIntegrationAnalysis

How to analyze a structural model by using DirectIntegrationAnalysis

Pointer

DirectIntegrationAnalysis::analyze( intnumSteps, double dT) {

for (int i=0; i<numSteps; i++) {

this -> domainChanged();

theIntegrator ->newStep(dT);

theAlgorithm ->solveCurrentStep();

theIntegrator ->commit();

} // end for} // end program



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OpenSees Framework– NR Iteration Procedure

theAlgorithm->solveCurrentStep();I. AnalysisModel * theAnaModel = this->getAnalysisModelPtr();

IncrementalIntegrator *theIntegrator = this->getIncrementalIntegratorPtr();LinearSOE *theSOE = this->getLinearSOEptr();

II. theIntegrator->formUnbalance(..);III. theTest->setEquiSolnAlgo(*this);

int result = theTest->start()Do {

IV. theIntegrator->formTangent(tangent)V. theSOE->solve(); VI. theIntegrator->update (theSOE->getX();VII. theIntegrator->formUnbalance()VIII. result = theTest->test(); // refer right side IX. this->record(count++);

} while (result == -1) // i.e., while not converged;

Newton Raphson iteration algorithmnu 1

n 1+u 2n 1+u 3

n 1+u

n1n+

1nδu 2

nδu 3nδu

1( )

n 1

0dynT

+

− K

n =Ψ 0

0n+1 =Ψ 0

0n+1−Ψ

1n∆u

2n∆u

3n∆u

Ψ

u

1n+1−Ψ 2

n+1−Ψ



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OpenSees Framework Data structure (2)class Node : public DomainComponent {

Public:Node( …) ; ~Node(..)virtual const Vector &getDisp(void);virtual int setTrialDisp(const Vector &); virtual int setTrialVel(const Vector &); virtual const Vector &getUnbalancedLoad(void); virtual int commitState();virtual const Matrix &getMass(void);…private:int createDisp(void);int createVel(void);int createAccel(void); …int numberDOF; Vector *Crd; // original nodal coordsVector *commitDisp, *commitVel, *commitAccel;Vector *trialDisp, *trialVel, *trialAccel; Vector *unbalLoad; Matrix *mass; // pointer to mass….}

Public methods may be called by other objects

Private methods are called only by themselves

Private data are managed only by themselves



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OpenSees and Tcl§ Tcl (Tool Command Language) is a string-based scripting

language and interpreter, first developed by John Ousterhout. § TCL was designed for easy learning, but it provides all the

powerful functions the expert programmer wants. § OpenSees.exe is an extension of the Tcl interpreter for finite

element analysis using OpenSees.

TCL

DOS, Windows or Unix OS

OpenSees

C:\>dir C:\>

% set a 0.250.25% set b [expr $a+1]1.25%

OpenSees > model BasicBuilder -ndm 3 -ndf 6OpenSees > node 1 0.0 0.0 0.1OpenSees >



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Using Tcl



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Using Tcl

set a(1) 1set a(2) 2parray aset b $a(1)



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Tcl Commands for OpenSees



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Building a FE model in OpenSees using Tcl



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Building a FE model in OpenSees using TCL

x

y

# A simple 2D truss problems ( unit: kips, inch, s)

2 –ndf 2



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• Perform the analysis



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RC section behavior under Combined Bending and Axial Load



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RC section behavior under Combined RC section behavior under Combined Bending and Axial LoadBending and Axial Load

Concrete crushes before steel yields

Steel yields before concrete crushes

Moment

Axia

lLoa

d, P

Failure Criterion: εcu = 0.003

Interaction Diagram

( Failure Envelope )



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General ProcedureGeneral Procedure– For various levels of axial load, increase curvature

of the section until a concrete strain of 0.003 is reached.

– Files used:• Mp.tcl• model.tcl

– Output:• mp.out

Moment = f(χ)

Axia

lLoa

d,

PP

M



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Zero Length Section ElementZero Length Section Elementfor RC Section Analysisfor RC Section Analysis

y

z

y

x

1Lu u

L

L

ε

θχ θ

≡∆

= = ∆

∆= = ∆

Zero-Length Section



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Concrete01

Initial stiffness:2*$fpc/$epsc0

$fpc$fpcu

$epsU $eps0

strain

stre

ss

Steel01

$E0

$b*E0$Fy

strain

stre

ss$Fy

$b*E0

As1 = 4 No. 8 bars

As2 = 4 No. 8 bars

y

zy1

-y1

-z1z1

cover

Fiber sectionFiber section



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Interaction Diagram Interaction Diagram

c si1=

= + ∑n

ni

P C F

( )c si12 =

= − + −

∑n

n ii

aM C y F y d

Reinforced Concrete: Mechanics and Design (4th Edition) by James G. MacGregor, James K. Wight

1 11

0.003 ; where = 0.003

ε εε

= −

s ys

c d Z

= 0.003ε−

isi

c dc

= ; ε ≤si si s si yf E f f

1 = 1.05 0.051000

β′

−

cfpsi

( ) ( ) 1 = 0.85 ; β′ =c cC f ab a c

= (positive in compression)si si siF f A

( ) = 0.85 ′−si si c siF f f A

if < ia d

else

for symmetric sections2

=hy



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Interaction DiagramInteraction Diagram

0 100 200 300 4000

200

400

600

800

1000

1200

1400

1600

Moment [kips-ft]

Axi

al L

oad

[kip

s]Column Interaction Diagram

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