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Nonlinear dynamic analysis of hysteretic mechanical systems by combining a novel rate-independent model and an explicit time integration method

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Abstract

This paper presents a computational strategy that combines a novel rate-independent phenomenological model with an explicit time integration method to efficiently perform nonlinear dynamic analyses of non-stiffening hysteretic mechanical systems. The novel rate-independent model, developed by specializing a general class of uniaxial phenomenological models, has an algebraic nature, is based on a set of only three parameters having a clear mechanical significance, and can be easily implemented in a computer program. The adopted explicit structure-dependent time integration method, belonging to the Chang’s family of explicit methods, is unconditionally stable for all non-stiffening hysteretic mechanical systems, has a second-order accuracy, does not suffer from numerical damping, and displays a small relative period error for small time step. Furthermore, it does not require iterative procedures and, consequently, does not suffer from convergence issues. Numerical accuracy and computational efficiency of the proposed procedure are assessed by performing several nonlinear time history analyses on hysteretic mechanical systems and comparing the results with those obtained by employing a conventional strategy based on the celebrated Bouc–Wen model, or its modified version, and the widely used Newmark’s constant average acceleration method.

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Acknowledgements

The present research was supported by the Italian Government, ReLUIS 2017 Project [AQ DPC/ReLUIS 2014-2018, PR2, Task 2.3] and PRIN 2015 Grants [2015JW9NJT-PE8, WP2, Task 2.1], which is acknowledged by the authors.

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Correspondence to Nicolò Vaiana.

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Appendix: List of acronyms

Appendix: List of acronyms

AAM:

Average acceleration method

BWM:

Bouc–Wen model

CEM:

Chang’s explicit method

CFEMs:

Chang’s family of explicit methods

CHMs:

Class of hysteretic models

MBWM:

Modified Bouc–Wen model

MDOF:

Multi-degree-of-freedom

NLTHA:

Nonlinear time history analysis

ODEs:

Ordinary differential equations

PHM:

Proposed hysteretic model

System RdRiFn:

System with Rate-dependent and Rate-independent behavior (due to Friction) having n DOFs

System RdRiPn:

System with Rate-dependent and Rate-independent behavior (due to Plastic deformation mechanisms) having n DOFs

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Vaiana, N., Sessa, S., Marmo, F. et al. Nonlinear dynamic analysis of hysteretic mechanical systems by combining a novel rate-independent model and an explicit time integration method. Nonlinear Dyn 98, 2879–2901 (2019). https://doi.org/10.1007/s11071-019-05022-5

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