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. National Technical University of Athens
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. National Technical University of Athens
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. National Technical University of Athens
Excitation
Earthquake library with stretching capabilities with respect to time or amplitude

5. Excitation Arbitrary force library defined by the user
National Technical University of Athens
Excitation
Arbitrary force library defined by the user

6. Calculations Newmark method (linear and bilinear model)
National Technical University of Athens
Calculations
Newmark method (linear and bilinear model)
Average acceleration
Linear acceleration
Stiff ODE integrator based on “predictor-corrector” method (Bouc – Wen model)

7. Simulation 2D simulation of the response
National Technical University of Athens
Simulation
2D simulation of the response

8. Simulation 3D simulation of the response
National Technical University of Athens
Simulation
3D simulation of the response

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

10. Elastic response spectrum
National Technical University of Athens
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. Non-linear analysis (bilinear model)
National Technical University of Athens
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. Bouc – Wen model Concise yet powerful smooth hysteretic model
National Technical University of Athens
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. Bouc – Wen model (SDOF) Restoring force: Equation of motion:
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Bouc – Wen model (SDOF)
Restoring force:
Equation of motion:
Hysteretic parameter:

14. Bouc – Wen model (SDOF) Restoring force: Equation of motion:
National Technical University of Athens
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. Bouc – Wen model (SDOF) In state-space form:
National Technical University of Athens
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. Bouc – Wen model (2DOF) In state-space form:
National Technical University of Athens
Bouc – Wen model (2DOF)
In state-space form:

17. Bouc – Wen model Spring force vs Displacement
National Technical University of Athens
Bouc – Wen model
Spring force vs Displacement
Relative displacement vs Time
Z parameter vs Time
Athens, Sep 1999
El Centro, May 1940

18. Conclusions mySpec addresses the following issues:
National Technical University of Athens
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. mySpec is available at no cost from the following link:
National Technical University of Athens
Conclusions
mySpec is available at no cost from the following link: