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

Adjoint sensitivity analysis and optimization of hysteretic dynamic systems with nonlinear... 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”. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Structural and Multidisciplinary Optimization Springer Journals

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

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Computational Mathematics and Numerical Analysis; Engineering Design
ISSN
1615-147X
eISSN
1615-1488
D.O.I.
10.1007/s00158-017-1858-2
Publisher site
See Article on Publisher Site

Abstract

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”.

Journal

Structural and Multidisciplinary OptimizationSpringer Journals

Published: Nov 21, 2017

References

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