پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 161 |
| تعداد شمارهها | 6,532 |
| تعداد مقالات | 70,501 |
| تعداد مشاهده مقاله | 124,111,835 |
| تعداد دریافت فایل اصل مقاله | 97,215,436 |
Strongly stable multi-time stepping method with the option of controlling amplitude decay in responses | ||
| Journal of Computational Applied Mechanics | ||
| مقاله 13، دوره 49، شماره 1، شهریور 2018، صفحه 133-142 اصل مقاله (1.53 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2017.241371.183 | ||
| نویسندگان | ||
| Saeed Mohammadzadeh؛ Mehdi Ghassemieh* | ||
| School of Civil Engineering; University of Tehran; Tehran, Iran | ||
| چکیده | ||
| Recently, multi-time stepping methods have become very popular among scientist due to their high stability in problems with critical conditions. One important shortcoming of these methods backs to their high amount of uncontrolled amplitude decay. This study proposes a new multi-time stepping method in which the time step is split into two sub-steps. The first sub-step is solved using the well-known Newmark method and for the second sub-step an extended version of Newmark method is applied. In fact, similarity in basic formulas of the mentioned methods makes it available to control the amount of amplitude decay in responses obtained by the proposed method; in other words, the amplitude decay in the proposed method is controlled through constant parameters of the two methods applied on each sub-step. The precision assessment of the proposed method is performed using numerical approaches and revealed the minor period elongation error of the proposed method in comparison with other existing methods. In addition to this, the unconditional stability region of constant parameters is also determined through computation of spectral radius of the proposed method. Finally, practical assessment of the proposed method is performed through several numerical examples. | ||
| کلیدواژهها | ||
| time integration؛ multi-time stepping method؛ unconditional stability؛ period elongation | ||
| مراجع | ||
|
[1] M. Choulaie, A. Khademifar, Nonlinear Vibration and Stability Analysis of Beam on the Variable Viscoelastic Foundation, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 99-110, 2017. [2] R. Attarnejad, A. M. Ershadbakhsh, Analysis of Euler-Bernoulli nanobeams: A mechanical-based solution, Journal of Computational Applied Mechanics, Vol. 47, No. 2, pp. 159-180, 2016. [3] M. Zakeri, R. Attarnejad, Numerical free vibration analysis of higher-order shear deformable beams resting on two-parameter elastic foundation, Journal of Computational Applied Mechanics, Vol. 46, No. 2, pp. 117-131, 2015. [4] R. Fallahzadeh, M. Shariyat, Dynamic responses of poroelastic beams with attached mass-spring systems and time-dependent, non-ideal supports subjected to moving loads: An analytical approach, Journal of Computational Applied Mechanics, Vol. 46, No. 2, pp. 133-151, 2015. [5] K. J. Bathe, 2014, Finite element procedures, Prentice-Hall, NJ. [6] M. Rezaiee-Pajand, M. Hashemian, Time integration method based on discrete transfer function, International Journal of Structural Stability and Dynamics, Vol. 16, No. 05, pp. 1550009, 2016. [7] F. Tornabene, R. Dimitri, E. Viola, TRANSIENT DYNAMIC RESPONSE OF GENERALLY-SHAPED ARCHES BASED ON A GDQ-TIME-STEPPING METHOD, International Journal of Mechanical Sciences, 2016. [8] D. Soares, An implicit family of time marching procedures with adaptive dissipation control, Applied Mathematical Modelling, Vol. 40, No. 4, pp. 3325-3341, 2016. [9] S. Mohammadzadeh, M. Ghassemieh, Y. Park, Structure-dependent Improved Wilson-θ Method with Higher Order of Accuracy and Controllable Amplitude Decay, Applied Mathematical Modelling, 2017. [10] K.-J. Bathe, M. M. I. Baig, On a composite implicit time integration procedure for nonlinear dynamics, Computers & Structures, Vol. 83, No. 31, pp. 2513-2524, 2005. [11] K.-J. Bathe, G. Noh, Insight into an implicit time integration scheme for structural dynamics, Computers & Structures, Vol. 98, pp. 1-6, 2012. [12] S. S. Gautam, R. A. Sauer, A composite time integration scheme for dynamic adhesion and its application to gecko spatula peeling, International Journal of Computational Methods, Vol. 11, No. 05, pp. 1350104, 2014. [13] L. Zhang, T. Liu, Q. Li, A robust and efficient composite time integration algorithm for nonlinear structural dynamic analysis, Mathematical Problems in Engineering, Vol. 2015, 2015. [14] S. Kumar, S. S. Gautam, Analysis of A Composite Time Integration Scheme, 2015. [15] Y. Chandra, Y. Zhou, I. Stanciulescu, T. Eason, S. Spottswood, A robust composite time integration scheme for snap-through problems, Computational Mechanics, Vol. 55, No. 5, pp. 1041-1056, 2015. [16] J. Zhang, Y. Liu, D. Liu, Accuracy of a composite implicit time integration scheme for structural dynamics, International Journal for Numerical Methods in Engineering, Vol. 109, No. 3, pp. 368-406, 2017. [17] W. Wen, Y. Tao, S. Duan, J. Yan, K. Wei, D. Fang, A comparative study of three composite implicit schemes on structural dynamic and wave propagation analysis, Computers & Structures, Vol. 190, pp. 126-149, 2017. [18] W. Wen, K. Wei, H. Lei, S. Duan, D. Fang, A novel sub-step composite implicit time integration scheme for structural dynamics, Computers & Structures, Vol. 182, pp. 176-186, 2017. [19] A. A. Gholampour, M. Ghassemieh, New implicit method for analysis of problems in nonlinear structural dynamics, Applied and Computational Mechanics, Vol. 5, No. 1, pp. 15-20, 2011. [20] M. Shrikhande, 2014, Finite element method and computational structural dynamics, PHI Learning Pvt. Ltd., | ||
|
آمار تعداد مشاهده مقاله: 505 تعداد دریافت فایل اصل مقاله: 502 |
||