اثرهای معادلۀ ایستایی و تابع ترفتز بر پاسخ‌های جزء صفحۀ خمشی چهارپهلو

نوع مقاله : مقاله پژوهشی

نویسندگان

1 فردوسی مشهد

2 فردوسی

چکیده

در این پژوهش، ده جزء صفحۀ خمشی چهارپهلو کیرشهفی نو برپایۀ تابع تغییرمکان ترفتز و برقرارنمودن معادلۀ ایستایی پیشنهاد می‌شود. نخست، مناسب‌ترین چیدمان‌های درجه‌های آزادی و نیز گره‌های روی جزء برپایۀ پژوهش پیشینیان به‌دست می‌آیند. پس از آن، با بهره جستن از تقارن جمله‌ها، ده جزء‌ با تابع میدان متفاوت برای دو چیدمان برتر، معرفی خواهند شد. واکاوی‌های عددی آشکار می‌کنند که تابع‌ میدان برگرفته از تابع‌های ناقص ترفتز درصورت انتخاب درست جمله‌ها، با شمار درجۀ آزادی کمتر و مرتبۀ بالاتر نسبت به جزء‌های کامل، می‌توانند جزء‌های مفیدی را پدید آورند. چون تابع‌های ترفتز معادلۀ ایستایی را برقرار می‌سازند، پاسخ‌های نیرویی بیشتر جزء‌ها، دقت فزون‌تری نسبت به پاسخ‌های جابه‌جایی‌ها دارند.

کلیدواژه‌ها

عنوان مقاله [English]

The Effect of Equilibrium Equation and Trefftz Functions on the Responses of Quadrilateral Bending Plate

نویسندگان [English]

  • Mohammad Rezaiee Pazhand 1
  • M. Malekzadeh 2
  • N. Razbzadeh 2
1 Ferdowsi University of Mashhad
2 Ferdowsi
چکیده [English]

In this study, ten novel quadrilateral Kirchhoff’s bending plate elements based on the Trefftz displacement functions and satisfying equilibrium equation are suggested. First, the most suitable arrangement of degrees of freedom and nodes are achieved by benefiting from previous researches. Afterwards, using the symmetry of terms, ten elements with different interpolation functions for the two top arrangements will be introduced. Numerical tests reveal that the correct choice of the interpolation’s terms from the incomplete Trefftz functions leads to more efficient elements with lower degrees of freedom and higher order than the complete elements. Since the Trefftz functions meet the equilibrium conditions, the force responses of the most cases have a higher accuracy than the displacement responses.

.

کلیدواژه‌ها [English]

  • Thin bending plate
  • equilibrium equation
  • Analytical Solution
  • Trefftz function
  • quadrilateral bending element
  • incomplete interpolation function

مراجع

1. کارکن، محمد، «واکاوی خطی و ناخطی هندسی صفحه‌ها برپایۀ پاسخ تحلیلی»، پایان‌نامۀ دکترای تخصصی عمران (سازه)، دانشکدۀ مهندسی، دانشگاه فردوسی مشهد، (1393).
2. Soh, A.K., Cen, S., Long, Y.Q. and Long, Z.F., "A new twelve DOF quadrilateral element for analysis of thick and thin plates", European Journal of Mechanics-A/Solids, Vol. 20(2), pp. 299-326, (2001).
3. Sheikh, A.H., Haldar, S. and Sengupta, D., "A high precision shear deformable element for the analysis of laminated composite plates of different shapes", Composite Structures, Vol. 55(3), pp. 329-336, (2002).
4. Prathap, G. and Viswanath, S., "An optimally integrated four‐node quadrilateral plate bending element", International Journal for Numerical Methods in Engineering, Vol. 19(6), pp. 831-840, (1983).
5. Somashekar, B.R., Prathap, G. and Babu, C.R., "A field-consistent, four-noded, laminated, anisotropic plate/shell element", Computers & structures, Vol. 25(3), pp. 345-353, (1987).
6. Sheikh, A.H., Haldar, S. and Sengupta, D., "A high precision shear deformable element for the analysis of laminated composite plates of different shapes", Composite Structures, Vol. 55(3), pp. 329-336, (2002).
7. Rezaiee-Pajand, M. and Mohamadzade, H., "A finite element template for four-sided kirchhoff plate bending element", J. Civil Environ. Eng., Vol. 40, pp. 25–38, (2010), (in Persian).
8. Batoz, J.L. and Katili, I., "On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints", International Journal for Numerical Methods in Engineering, Vol. 35(8), pp. 1603-1632, (1992).
9. Razaqpur, A.G., Nofal, M. and Vasilescu, A., "An improved quadrilateral finite element for analysis of thin plates", Finite elements in analysis and design, Vol. 40(1), pp. 1-23, (2003).
10. Batoz, J.L. and Tahar, M.B., "Evaluation of a new quadrilateral thin plate bending element", International Journal for Numerical Methods in Engineering, Vol. 18(11), pp. 1655-1677, (1982).
11. Jirousek, J. and Wroblewski, A., "T-elements: state of the art and future trends", Archives of Computational Methods in Engineering, Vol. 3(4), pp. 323-434, (1996).
12. Jirousek, J. and Leon, N., "A powerful finite element for plate bending", Computer Methods in Applied Mechanics and Engineering, Vol. 12(1), pp. 77-96, (1977).
13. Pian, T.H. and Wu, C.C., "A rational approach for choosing stress terms for hybrid finite element formulations", International Journal for Numerical Methods in Engineering, Vol. 26(10), pp. 2331-2343, (1988).
14. De Miranda, S. and Ubertini, F., "A simple hybrid stress element for shear deformable plates", International Journal for Numerical Methods in Engineering, Vol. 65(6), pp. 808-833, (2006).
15. Spilker, R.L. and Munir, N.I., "The hybrid‐stress model for thin plates", International Journal for Numerical Methods in Engineering, Vol. 15(8), pp. 1239-1260, (1980).
16. Cen, S., Long, Y. and Yao, Z., "A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates", Computers & structures, Vol. 80(9), pp. 819-833, (2002).
17. Jirousek, J., "Hybrid‐Trefftz plate bending elements with p‐method capabilities", International journal for numerical methods in engineering, Vol. 24(7), pp. 1367-1393, (1987).
18. Jirousek, J., Wroblewski, A. and Szybinski, B., "Alternative displacement frame formulations in hybrid-Trefftz Kirchhoff plate p-elements", Computer Assisted Mechanics and Engineering Sciences, Vol. 4, pp. 417-452, (1997).
19. Jirouseka, J. and Guex, L., "The hybrid‐Trefftz finite element model and its application to plate bending", International Journal for Numerical Methods in Engineering, Vol. 23(4), pp. 651-693, (1986).
20. Qin, Q.H., "Trefftz finite element method and its applications", Applied Mechanics Reviews, Vol. 58(5), pp. 316-337, (2005).
21. Petrolito, J., "Analytical formulation of hybrid-Trefftz thick plate elements", Computer Assisted Mechanics and Engineering Sciences, Vol. 10(4), pp. 575-586, (2003).
22. Dhananjaya, H.R., Pandey, P.C. and Nagabhushanam, J., "New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method", Structural engineering and mechanics, Vol. 33(4), pp. 485-502, (2009).
23. Rezaiee-Pajand, M. and Karkon, M., "Two higher order hybrid-Trefftz elements for thin plate bending analysis", Finite Elements in Analysis and Design, Vol. 85, pp. 73-86, (2014).
24. Rezaiee-Pajand, M., Yaghoobi, M. and Karkon, M., "Hybrid trefftz formulation for thin plate analysis", International Journal of Computational Methods, Vol. 9(04), pp. 1250053(1-29), (2012).
25. Herrera, I., "Boundary methods: an algebraic theory", Pitman Advanced Pub. Program, (1984).
26. اختری، محمدرضا، «اثر محل گره و نوع درجۀ آزادی در جزء مثلثی صفحۀ خمشی»، پایان‌نامۀ کارشناسی ارشد مهندسی عمران (سازه)، دانشکدۀ مهندسی، دانشگاه فردوسی مشهد، (1375).
27. Timoshenko, S.P. and Woinowsky-Krieger, S., "Theory of plates and shells", McGraw-hill, New York, (1959).
28. Wanji, C. and Cheung, Y.K., "Refined quadrilateral discrete Kirchhoff thin plate bending element", International Journal for Numerical Methods in Engineering, Vol. 40(21), pp. 3937-3953, (1997).
29. Soh, A.K., Long, Z.F. and Cen, S., "A new nine DOF triangular element for analysis of thick and thin plates", Computational Mechanics, Vol. 24(5), pp. 408-417, (1999).
30. Yu-qiu, L. and Ke-gui, X., "Generalized conforming element for bending and buckling analysis of plates", Finite Elements in Analysis and Design, Vol. 5(1), pp. 15-30, (1989).
31. Rezaiee-Pajand, M. and Akhtary, M.R., "A family of 13-node plate bending triangular elements", Communications in numerical methods in engineering, Vol. 14(6), pp. 529-537, (1998).
32. Zeinkiewicz, O.C. and Taylor, R.L., "The Finite Element Method", 4th Edition, Volume 2, McGraw-Hill, London, (1991).
33. Cheung, Y.K. and Chan, H.C., "A family of rectangular bending elements", Computers & Structures, Vol. 10(4), pp. 613-619, (1979).
ارسال نظر در مورد این مقاله
CAPTCHA Image

فایل ها

هم رسانی

ارجاع به این مقاله

آمار