رابطه‌سازی نوین برای جرم ساختگی در روش رهایی پویای لزج

نوع مقاله : پژوهشی

نویسندگان

• ایمان زردی
• جواد علامتیان

دانشگاه آزاد اسلامی مشهد

10.22067/civil.v31i1.53685

چکیده

در این مقاله رابطه‌سازی نوینی برای جرم ساختگی در روش رهایی پویای لزج پیشنهاد می‌گردد. نخست معادله‌های خطا برای تکرارهای رهایی پویا ارائه می‌شود. سپس، بااستفاده از نگرۀ گرشگورین بهبود یافته، کران‌های جدیدی برای کمیت جرم ساختگی به ‌دست می‌آید. رابطه‌سازی پیشنهادی به الگوریتم جدیدی برای روش رهایی پویای لزج منجر می‌گردد. برای سنجش کارایی عددی فرایند پیشنهادی، سازه‌های مختلفی مانند خرپا و قاب‌های دو بعدی و سه‌بعدی، با رفتارهای خطی و غیرخطی هندسی تحلیل می‌شوند. نتایج این تحلیل‌ها نشان می‌دهد که استفاده از الگوریتم ارائه‌شده و رابطۀ نوین پیشنهادی برای جرم ساختگی، نرخ همگرایی روش رهایی پویای لزج را بهبود می‌دهد، به گونه‌ای که همگرایی با تعداد کمتری تکرار انجام می‌پذیرد.

کلیدواژه‌ها

• روش رهایی پویا
• میرایی لزج
• جرم ساختگی
• رفتارغیرخطی
• نیروی نامیزان
• نرخ همگرایی

---

عنوان مقاله [English]

A New Formulation for Fictitious Mass in the Viscous Dynamic Relaxation Method

نویسندگان [English]

• Iman Zardi
• javad alamatian

Islamic Azad University of Mashhad

چکیده [English]

In this paper, new algorithm is proposed for fictitious mass of Dynamic Relaxation (DR) method with viscous damping. First, the incremental equations are derived for DR procedure. By using the transformed Gershgörin theory, new boundaries are achieved for fictitious mass. This formulation leads to a new algorithm for viscous DR method. For evaluating the efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed by elastic linear and geometrically nonlinear behaviors. Results show that the proposed scheme for fictitious mass improves the convergence rate of DR method so that the suggested algorithm presents the structural response with less iteration in comparison with other common DR techniques.

کلیدواژه‌ها [English]

• Dynamic Relaxation method
• Viscous Damping
• Fictitious Mass,
• Nonlinear Behavior
• Residual Energy
• Convergence Rate

مراجع

1. Alamatian, J., "A New Formulation for Fictitious Mass of the Dynamic Relaxation Method with Kinetic Damping", Computers & Structures, Vol. 90-91, pp. 42–54, (2012).

2. Otter, J.R.H., "Dynamic Relaxation", Proceedings of the Institution of Civil Engineers, Vol. 35, pp. 633–656, (1966).

3. Day, A.S., "An Introduction to Dynamic Relaxation", The Engineer, Vol. 219, pp. 218–221, (1965).

4. Otter, J.R.H., "Computation for Prestressed Concrete Reactor Pressure Vessels Using Dynamic Relaxation", Nuclear Structural Engineering, Vol. 1, pp. 61-75, (1965).

5. Brew, J.S. and Brotton, M., "Non-linear Structural Analysis by Dynamic Relaxation Method", International Journal for Numerical Methods in Engineering, Vol. 3, pp. 463–483, (1971).

6. Lewis, W.J., Jones, M.S. and Lewis, G., "Cladding-network Interaction in Pretensioned Cable Roofs, Studied by Dynamic Relaxation", Computers & Structures, Vol. 19, pp. 885-897, (1984).

7. Kmet, S. and Mojdis, M., "Time-dependent Analysis of Cable Domes Using a Modified Dynamic Relaxation Method and Creep Theory", Computers & Structures, Vol. 125, pp. 11–22, (11–22).

8. Rushton, K.R., "Dynamic Relaxation Solutions of Elastic Plate Problems", Journal of Strain Analysis for Engineering Design, Vol. 3, pp. 23–32, (1968).

9. Alwar, R.S. and Ramachandra-Rao, N., "Large Elastic Deformations of Clamped Skewed Plates by Dynamic Relaxation", Computers & Structures, Vol. 4, pp. 381-398, (1974).

10. Ramesh, G. and Krishnamoorthy, C.S., "Geometrically Non-linear Analysis of Plates and Shallow Shells by Dynamic Relaxation", Computer Methods in Applied Mechanics and Engineering, Vol. 123, pp. 15–32, (1995).

11. Barnes, M.R., "Form Finding and Analysis of Tension Structures by Dynamic Relaxation", International Journal of Space Structures, Vol. 14, pp. 89–104, (1999).

12. Ramesh, G. and Krishnamoorthy, C.S., "Inelastic Post-buckling Analysis of Truss Structures by Dynamic Relaxation Method", International Journal for Numerical Methods in Engineering, Vol. 37, pp. 3633-3657, (1994).

13. Kadkhodayan, M., Zhang, L.C. and Sowerby, R., "Analysis of Wrinkling and Buckling of Elastic Plates by DXDR Method", Computers & Structures, Vol. 65, pp. 561–574, (1997).

14. Lee, K.S., Han, S.E. and Park, T., "A Simple Explicit Arc-length Method Using the Dynamic Relaxation Method with Kinetic dDamping", Computers & Structures, Vol. 89, pp. 216–233, (2011).

15. Bunce, J.W., "A Note on Estimation of Critical Damping in Dynamic Relaxation", International Journal for Numerical Methods in Engineering, Vol. 4, pp. 301–304, (1972).

16. Cassell, A.C. and Hobbs, R.E., "Numerical Stability of Dynamic Relaxation Analysis of Non-linear Structures", International Journal for Numerical Methods in Engineering, Vol. 10, pp. 1407–1410, (1976).

17. Papadrakakis, M., "A Method for the Automatic Evaluation of the Dynamic Relaxation Parameters", Computer Methods in Applied Mechanics and Engineering, Vol. 25, pp. 35–48, (1981).

18. Rezaiee-Pajand, M. and Taghavian-Hakkak, M., "Nonlinear Analysis of Truss Structures Using Dynamic Relaxation", International Journal of Engineering, Vol. 19, pp. 11–22, (2006).

19. Kadkhodayan, M., Alamatian, J. and Turvey, G.J., "A New Fictitious Time for the Dynamic Relaxation (DXDR) mMethod", International Journal for Numerical Methods in Engineering, Vol. 74, pp. 996–1018, (2008).

20. Rezaiee-Pajand, M. and Alamatian, J., "The dDynamic Relaxation Method Using New Formulation for Fictitious Mass and Damping", Journal of Engineering Mechanics, Vol. 34, pp. 109–133, (2010).

21. Rezaiee-Pajand, M. and Sarafrazi, S.R., "Nonlinear Dynamic Structural Analysis Using Dynamic Relaxation with Zero Damping", Computers & Structures, Vol. 89, pp. 1274–1285, (2011).

22. Rezaiee-Pajand, M., Kadkhodayan, M., Alamatian, J. and Zhang, L.C., "A New Method of Fictitious Viscous Damping Determination for the Dynamic Relaxation", Computers & Structures, Vol. 89, pp. 783–794, (2011).

23. Rezaiee-Pajand, M., Kadkhodayan, M. and Alamatian, J., "Timestep Selection for Dynamic Relaxation Method", Mechanics Based Design of Structures and Machines, Vol. 40, pp. 42–72, (2012).

24. Felippa, C.A., "Nonlinear Finite Element Methods (ASEN 5017)", Chapter 11, Course Material, (1999).

25. Underwood, P., "Dynamic Relaxation", Computational Method for Transient Analysis, Chapter 5, Vol. 1, pp. 245–265, (1983).

26. Guo, X., Bai, W. and Zhang, W., "Confidence Extremal Structural Response Analysis of Truss Structures under Static Load Uncertainty Via SDP Relaxation", Computers & Structures, Vol. 87, pp. 246–253, (2009).