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MYSPEC: Educational Software for Structural Dynamics and Hysteretic Systems

MYSPEC: Educational Software for Structural Dynamics and Hysteretic Systems. Aristotelis Charalampakis and Vlasis Koumousis National Technical University of Athens Institute of Structural Analysis and Aseismic Research. National Technical University of Athens. Task.

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MYSPEC: Educational Software for Structural Dynamics and Hysteretic Systems

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  1. MYSPEC: Educational Software for Structural Dynamics and Hysteretic Systems Aristotelis Charalampakis and Vlasis Koumousis National Technical University of Athens Institute of Structural Analysis and Aseismic Research

  2. NationalTechnicalUniversity ofAthens Task Development of a user-friendly dynamic analysis tool for undergraduate and postgraduate students • User-friendly graphical interface • Visualization of the results • Dynamic analysis for SDOF or 2DOF systems with simple and advanced models: • Linear analysis • Response spectra • Non-linear analysis (bilinear model) • Hysteretic model (Bouc – Wen)

  3. NationalTechnicalUniversity ofAthens Motivation Lack of several features in existing educational software packages: • Arbitrary force excitation (ramp force, blast load etc) • Calculation of the response for free vibration after the excitation • Bouc – Wen hysteretic model for 2DOF systems with viscous damping • Robust computational techniques for non-linear models • Export of the results in ASCII files for further processing • 2D or 3D simulation of the response, including the motion of the ground • Various unit systems • Double-precision arithmetics

  4. NationalTechnicalUniversity ofAthens Excitation Earthquake library with stretching capabilities with respect to time or amplitude

  5. NationalTechnicalUniversity ofAthens Excitation Arbitrary force library defined by the user

  6. NationalTechnicalUniversity ofAthens Calculations • Newmark method (linear and bilinear model) Average acceleration Linear acceleration • Stiff ODE integrator based on “predictor-corrector” method (Bouc – Wen model)

  7. NationalTechnicalUniversity ofAthens Simulation 2D simulation of the response

  8. NationalTechnicalUniversity ofAthens Simulation 3D simulation of the response

  9. NationalTechnicalUniversity ofAthens Linear elastic analysis T = 0.667 s T = 1 s T = 2 s Zeta = 0% Zeta = 2%

  10. NationalTechnicalUniversity ofAthens Elastic response spectrum Elastic response spectrum for the following quantities: • Deformation • Pseudo-velocity • Pseudo-acceleration • Velocity • Acceleration Pseudo-velocity is related to peak strain energy stored: Pseudo-acceleration is related to peak base shear force:

  11. NationalTechnicalUniversity ofAthens Non-linear analysis (bilinear model) Based on Newmark method. Two sources or error: • Tangent stiffness instead of secant stiffness • Transitions from elastic to plastic state and vice versa lead to error accumulation These are addressed by: • Small time step • Variable time step when a transition is detected

  12. NationalTechnicalUniversity ofAthens Bouc – Wen model • Concise yet powerful smooth hysteretic model • Introduced by Bouc in 1967 • Extended by Wen in 1976 to produce a variety of hysteretic loops • Popular model, used in the fields of magnetism, electricity, materials and elasto‑plasticity of solids. • Examples include the response of R/C sections, steel sections, bolted connections, base isolators such as Lead Rubber Bearings (LRB), Friction Pendulum Systems (FPS) etc.

  13. NationalTechnicalUniversity ofAthens Bouc – Wen model (SDOF) Restoring force: Equation of motion: Hysteretic parameter:

  14. NationalTechnicalUniversity ofAthens Bouc – Wen model (SDOF) Restoring force: Equation of motion: Hysteretic parameter: • Fy : Yield force • Uy : Yield displacement • a : ratio of post-yield to pre-yield stiffness • c : viscous damping coefficient • n : controls the transition from elastic to plastic branch • A, beta, gamma : control the shape and size of the hysteretic loop

  15. NationalTechnicalUniversity ofAthens Bouc – Wen model (SDOF) In state-space form: The above system of three non-linear ODEs is solved following Livermore stiff ODE integrator based on “predictor-corrector” method

  16. NationalTechnicalUniversity ofAthens Bouc – Wen model (2DOF) In state-space form:

  17. NationalTechnicalUniversity ofAthens Bouc – Wen model Z parameter vs Time Spring force vs Displacement Relative displacement vs Time Athens, Sep 1999 El Centro, May 1940

  18. NationalTechnicalUniversity ofAthens Conclusions mySpec addresses the following issues: • Graphical interface, visualization of the results • Arbitrary force excitation (ramp force, blast load etc) • Calculation of the response for free vibration after the excitation • Bouc – Wen hysteretic model for 2DOF systems with viscous damping • Robust computational techniques for non-linear models • Export of the results in ASCII files for further processing • 2D or 3D simulation of the response, including the motion of the ground • Various unit systems • Double precision arithmetics

  19. NationalTechnicalUniversity ofAthens Conclusions mySpec is available at no cost from the following link: http://users.ntua.gr/vkoum

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