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 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)

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

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

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

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)

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

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

Linear elastic analysis National Technical University of Athens Linear elastic analysis T = 0.667 s T = 1 s T = 2 s Zeta = 0% Zeta = 2%

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:

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

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.

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:

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

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

Bouc – Wen model (2DOF) In state-space form: National Technical University of Athens Bouc – Wen model (2DOF) In state-space form:

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

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

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: http://users.ntua.gr/vkoum