Structural and Multidisciplinary Optimization

, Volume 57, Issue 6, pp 2273–2289 | Cite as

Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear viscous dampers

  • Nicolò Pollini
  • Oren Lavan
  • Oded Amir


In this paper we discuss the adjoint sensitivity analysis and optimization of hysteretic systems equipped with nonlinear viscous dampers and subjected to transient excitation. The viscous dampers are modeled via the Maxwell model, considering at the same time the stiffening and the damping contribution of the dampers. The time-history analysis adopted for the evaluation of the response of the systems relies on the Newmark-β time integration scheme. In particular, the dynamic equilibrium in each time-step is achieved by means of the Newton-Raphson and the Runge-Kutta methods. The sensitivity of the system response is calculated with the adjoint variable method. In particular, the discretize-then-differentiate approach is adopted for calculating consistently the sensitivity of the system. The importance and the generality of the sensitivity analysis discussed herein is demonstrated in two numerical applications: the retrofitting of a structure subject to seismic excitation, and the design of a quarter-car suspension system. The MATLAB code for the sensitivity analysis considered in the first application is provided as “Supplementary Material”.


Adjoint sensitivity analysis Nonlinear dynamic systems Viscous dampers Gradient-based optimization 



The authors would like to thank the anonymous reviewers for their helpful comments. The research presented in this paper was founded by the Israeli Ministry of Science, Technology and Space. The authors gratefully acknowledge this financial support.

Supplementary material (1.3 mb)
(ZIP 1.25 MB)


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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringTechnion - Israel Institute of TechnologyTechnion CityIsrael

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