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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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:
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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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DOI: https://doi.org/10.1007/s11071-019-05022-5