Generating Force-Displacement Curves for the Bouc-Wen Model Using Identified Parameters

In structural dynamics, the Bouc-Wen model is a widely used mathematical framework for characterizing hysteretic behavior in materials and structural systems. This model employs a set of nonlinear differential equations to simulate complex force-displacement relationships, particularly suited for systems exhibiting hysteresis properties.

To generate force-displacement curves for the Bouc-Wen model, it is essential to first accurately identify key model parameters. These parameters typically include: shape parameters governing curve smoothness, amplitude parameters determining hysteresis loop size, and parameters influencing stiffness degradation. Parameter identification can be achieved through experimental data fitting or optimization algorithms such as least-squares minimization or genetic algorithms implemented in MATLAB/Python.

The curve generation process involves three primary steps: First, configure the model equations using identified parameters (commonly implemented through ode45 in MATLAB or solve_ivp in SciPy). Second, select appropriate numerical integration methods (e.g., fourth-order Runge-Kutta method) to solve the differential equations. Finally, plot the force-displacement relationship by pairing computed displacement values with corresponding force values, typically using visualization libraries like matplotlib or MATLAB's plot function.

Notably, Bouc-Wen model force-displacement curves exhibit characteristic hysteresis phenomena including stiffness degradation, strength deterioration, and pinch effects. The specific curve morphology varies with loading history, loading rates, and parameter configurations, which can be programmed through time-varying input signals in simulation code.

In practical applications, tuning model parameters enables close alignment between simulation results and experimental force-displacement data, providing crucial analytical tools for seismic analysis, isolation design, and other engineering domains. Code implementation often involves parameter sensitivity analysis loops to optimize model fidelity.