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MERCURY Optimized Software for Hybrid Simulation; from Pseudo-Dynamic to Hard Real Time V. Saouma D.H. Kang G. Haussmann University of Colorado, Boulder September 6, 2010 V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 1/37

Outline I Introduction 1 Global Context Background NRC/NEES Mercury Overview Analysis 2 Constitutive Models Elements Library State Determination Nonlinear Algorithms Hybrid 3 Matlab c++; General c++; Hybrid Element c++; Coordinate Transformation Improvements 4 RTHS on a Shared Memory Computer V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 2/37

Outline II RTHS on a Computer Cluster; Algorithm RTHS on a Computer Cluster; Results Scripting 5 Interface 6 Introduction Hybrid Pipe SCRAMNet Pipe Virtual Spring Pipe Environmental Variables Xtras 7 Documentation 8 Technical Manual User’s manuals Validation Manual Remarks 9 Current Development Graphical Post Processor Applications V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 3/37

Outline III Shake Table vs RTHS 10 Summary 11 Credit V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 4/37

Introduction Global Context Global Context Numerical simulation remains a major challenge to EQ engineering community. We can simulate the explosion of a nuclear bomb, but we can not (“exactly”) simulate seismic response of structures. Must rely on experiments of structural components, or systems to capture complex response. Finite element modeling capabilities are sophisticated, but not yet “perfect”. Many (hundreds of) laboratories Are equipped with digitally controlled actuators/load frames (and LabView), and continue to operate under load/strain/stroke control only. Could benefit from a full nonlinear finite element code which can be plugged in LabView/Simulink to drive their tests V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 5/37

Introduction Background Background Existing software not ideally suited for single site pseudo dynamic (PsD) and RTHS. Software may require support of a “facilitator” (such as OpenFresco or SIMCOR) to interact with hardware. Essential for distributed hybrid simulation, a handicap for single site HS. The literature provides very little evidence of RTHS of structures (complexity of the numerical substructure, validation with shake table tests). Boulder embarked in a project to Develop an optimized software for single site PsD and RTHS (not meant as an alternative to OpenSees, Sap2000, Midas, ...) Perform RTHS of a reinforced concrete frame previously tested on a shake table, and compare results. V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 6/37

Introduction NRC/NEES Preventing National Research Council Earthquake One of the primary goals of NEES Disasters is to foster a movement toward integrated computer simulation and THE GRAND CHALLENGE IN EARTHQUAKE ENGINEERING physical testing. A Research Agenda for the Network for Earthquake Engineering Simulation (NEES) Holy Grail: replace all testing by numerical simulation. How can we achieve it? Com m i t t ee t o Dev el op a L ong- Ter m Res ear c h Increase sophistication of real time 1 Agenda f or t he N et wor k f or Ear t hquake Engi neer i ng Si m ul at i on ( N EES) hybrid simulation (RTHS). Boar d on I nf r as t r uc t ur e and t he Cons t r uc t ed Env i r onm ent Di v i s i on on Engi neer i ng and Phys i c al Sc i enc es 2 Gradually replace/eliminate ST tests by RTHS. 3 Eliminate ST & RTHS V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 7/37

Introduction Mercury Overview Mercury Overview Two identical versions Matlab (used for prototyping, and pedagogical purposes) c++ for deployment Students found it much easier to start with the Matlab version, and then run the c++ version. Has most of the key features likely to be required in a comprehensive nonlinear RTHS of steel or reinforced concrete structures. Runs within LabView, Simulink/xPC, or real time Linux. Optimized for speed and performance. “Battle tested” c++ version with a complex RTHS simulation. Matlab version in a new course (Nonlinear Structural Analysis) Extensive documentation, and validation. Will be supported by Boulder if you decide to adopt it. V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 8/37

Analysis Constitutive Models Constitutive Models; fiber elements Concrete Modified Kent and Park Steel σ c A Models with isotropic and kinematic hardening D( ε 1 , σ 1 ) m m Bilinear with isotropic hardening G E c B C E I( ε 2 , σ 2 ) m m F Modified Giuffre-Pinto E 0.5 ⋅ E 1 c H R 0.5 ⋅ E 2 ε R ε 1 ε 2 c t 2 t E E 20 R 1 E R R( ε , σ ) C ( ε 1 , σ 1 ) R R rev rev B ( ε 2 , σ 2 ) (b) E tan 2000 0 0 Anisotropic damage model E (LMT/Cachan) 1000 Stress [Mpa] (a) 0 ε Strain-Strain Curve y 1.0 0.5 -1000 0.0 -0.5 Stress [kN/mm 2 ] -1.0 ( ε 1 , σ 1 ) -2000 -1.5 0 0 A ( ε 2 , σ 2 ) -2.0 rev rev -0.04 -0.02 0 0.02 0.04 0.06 0.08 -2.5 Strain [mm/mm] -3.0 -3.5 -4.0 -0.010 -0.008 -0.006 -0.004 -0.002 0.000 0.002 Strain [mm/mm] V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 9/37

Analysis Constitutive Models Constitutive Models; Lumped Plasticity Model of Ibarra, Medina and Krawinkler (2005) F F 2 ! 1 F K ! y ! 0 ! F ! F K 8 ref ,0 1 1 ! 2 F ref ,1 1 F ! 8 y 7 K K " " 0 1 0 7 3 ! ! " " 0 3 0 1 0 1 6 ! ! 1 0 K re ,1 4 " " F 6 K 1 5 F " 1 " 4 y K " F F " y ref ,1 5 0 " F Original Envelope ref ,0 Original Envelope Basic strength deterioration Post capping strength deterioration F F # ! s ,1 8 2 2 9 ! 1 ! 1 F F 7 y y K 7 Interruption re ,1 (Disregard stiffness deterioration) K 1 K K K " 0 3 0 0 ! 6 6 3 0 K 2 4 4 F " F " y y # " 5 Original Envelope 5 s ,1 Original Envelope Unloading stiffness deterioration Accelerated reloading stiffness deterioration V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 10/37

Analysis Elements Element Library 2D truss and beam-columns Layered (fiber) sections y y z Stiffness Based ifib y Flexibility Based (with or without ifib z x element iterations) z y w , ( ) x e y N ɶ , u Zero length elements and sections ɶ x 2 x 2 x , ( ) w x , θ ɶ , θ M ɶ e x M ɶ ɶ 1 1 2 2 z z z z z L e w , ( ) x e y ( ), ( ) N x ε x x z , ( ) , w x M ɶ θ ɶ M x ( ), φ ( ) x 1 1 e x z z z z x V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 11/37

Analysis Elements State Determination a) Structure level; , u P b) Element level; , d f ? int ext 8 P P t n , t n , 3 Element Nodal d 2 Displacements e n , Analysis 1 P u tn , tn , Displacements Element Nodal Structure Nodal 7 int Element Nodal P intint ,, , ff Forces tn , Forces enen Structure Tangent tan K 7 d Stiffness Matrix S e n , Element Tangent tan tan , k k Stiffness Matrix e n , e n , 6 6 Forces Nodal Element ? int 5 d d f e n , e n , e n , c) Section level; Section # Forces s e n , , 4 Section int Section sen ,, sen ,, Forces Deformations Constitutive Model # $ $ f % ! &$ " ! D V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 12/37

Analysis Nonlinear Algorithms Nonlinear Analysis Solution Algorithms Linear static Eigenvalue analysis Initial stiffness Newton-Raphson Modified Newton-Raphson Mixed User can specify automatic change of solution algorithm if convergence fails Convergence Criteria Displacement norm Force norm Energy norm Integrators Static Load control Displacement control Arc length † Transient Newmark β Hilber-Hughes-Taylor α Shing (IS, NR, or MNR) V. Saouma et al. ; Univ. of Colorado Mercury; Optimized Software for Hybrid Simulation 13/37