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Structural Engineering and Mechanics Volume 87, Number 4, August25 2023 , pages 363-373 DOI: https://doi.org/10.12989/sem.2023.87.4.363 |
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A stability factor for structure-dependent time integration methods |
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Shuenn-Yih Chang and Chiu-Li Huang
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| Abstract | ||
| Since the first family of structure-dependent methods can simultaneously integrate unconditional stability and explicit formulation in addition to second order accuracy, it is very computationally efficient for solving inertial problems except for adopting auto time-stepping techniques due to no nonlinear iterations. However, an unusual stability property is first found herein since its unconditional stability interval is drastically different for zero and nonzero damping. In fact, instability might occur for solving a damped stiffness hardening system while an accurate result can be obtained for the corresponding undamped stiffness hardening system. A technique of using a stability factor is applied to overcome this difficulty. It can be applied to magnify an unconditional stability interval. After introducing this stability factor, the formulation of this family of structuredependent methods is changed accordingly and thus its numerical properties must be re-evaluated. In summary, a large stability factor can result in a large unconditional stability interval but also lead to a large relative period error. As a consequence, a stability factor must be appropriately chosen to have a desired unconditional stability interval in addition to an acceptable period distortion. | ||
| Key Words | ||
| damped stiffness hardening systems; stability factor; stability property; structure-dependent method | ||
| Address | ||
| Shuenn-Yih Chang: Department of Civil Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, Republic of China Chiu-Li Huang: Fu Jen Catholic University, New Taipei City 242062, Taiwan, Republic of China | ||