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DEFLECION OF BEAMS WITH VARIABLE THICKNESS BY FINITE DIFFERENCE METHOD

Year 2014, Issue: 033, 9 - 24, 15.04.2014

Mustafa Haluk Saraçoğlu Mahmud Sami Döven Burak Kaymak

Abstract

Beams with variable thickness are commonly used in engineering fields such as civil, mechanical and aerospace engineering. In this study, relation between the deflection of beams with variable thickness and load is expressed as fourth order differential equations and calculated by finite difference method. Calculations were made by a developed computer program. Relationship between finite difference mesh number and deflection value at the specific point of beam with variable thickness were presented in tables and graphs as a result of the solutions of examples by developed computer program. Results have been compared with the ones obtained from the finite element analysis.

Keywords

Beams with varying cross section deflection elastic curve finite difference method

References

  • [1] S. Li, J. Hu, C. Zhai, L. Xie, “Static, vibration, and transient dynamic analyses by beam element with adaptive displacement interpolation functions”, Mathematical Problems in Engineering, 2012, 1 (2012).
  • [2] S. T. Wasti, “Prizmatik olmayan kiriş sonlu elemanları”, Yapı Mekaniği Semineri 2004, Eskişehir Osmangazi Üniversitesi Mühendislik-Mimarlık Fakültesi İnşaat Mühendisliği Bölümü, Eskişehir (2004).
  • [3] W.M.C. McKenzie, "Examples in Structural Analysis”, Taylor & Francis, NY, USA, 790 (2006).
  • [4] T. Tankut, “Kirişsiz döşeme yapıların hesabı için yeni bir yöntem”, İMO, 41 (1970).
  • [5] R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, "Concepts and Applications of Finite Element Analysis", John Wiley, New York, U.S.A., 784 (1989).
  • [6] Y. Xu, and D. Zhou, “Elasticity solution of multi-span beams with variable thickness under static loads”, Applied Mathematical Modelling, 33, 2951 (2009).
  • [7] Y. Xu, and D. Zhou, “Two-dimensional analysis of simply supported piezoelectric beams with variable thickness ”, Applied Mathematical Modelling, 35, 4458 (2011).
  • [8] F. Romano, and G. Zingone, “Deflection of beams with varying rectangular cross section”, Journal of Engineering Mechanics, 118(10), 2128 (1992).
  • [9] Z. Girgin, E. Demir, C. Kol, “Genelleştirilmiş diferansiyel quadrature metodunun kirişlerin serbest titreşim analizine uygulanması”, Pamukkale Üniversitesi Mühendislik Fakültesi Mühendislik Bilimleri Dergisi, 10(3), 347 (2004).
  • [10] A. K. Ashok, and S. B. Biggers, “Stiffness matrix for a non-prismatic beam-column element”, International Journal for Numerical Methods in Engineering, 10(5), 1125 (1976).
  • [11] H. Al-Gahtani, and M. Khan, “Exact Analysis of Nonprismatic Beams”, Journal of Engineering Mechanics, 124(11), 1290 (1998).
  • [12] T.J. Kotas, “A Numerical Solution for Non-Prismatic Beams with Arbitrary Transverse Loading and End Restraint Conditions”, The Structural Engineer, 47(11), (1969).
  • [13] R. Attarnejad, and A. Shahba, “Application of Differential Transform Method in Free Vibration Analysis of Rotating Non-Prismatic Beams”, World Applied Sciences Journal, 5(4), 441 (2008).
  • [14] M. Veiskarami, and S. Pourzeynali, “Green’s function for the deflection of non-prismatic simply supported beams by an analytical approach”, Estonian Journal of Engineering, 18(4), 336 (2012).
  • [15] M. Brojan, T. Videnic, F. Kosel, “Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law”, Meccanica, 44(6), 733 (2009).
  • [16] M. Brojan, M. Cebron, F. Kosel, “Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected ton non-uniform continuous load and a concentrated load at the free end”, Acta Mechanica Sinica, 28(3), 863 (2012).
  • [17] S.A. Hamoush, M.J. Terro, W.M. Mcginley, “Elastic and inelastic analysis of non-prismatic members using finite difference”, Kuwait Journal of Science, 29(2), 165 (2002).
  • [18] M. İnan, "Cisimlerin Mukavemeti”, İTÜ, İstanbul, Türkiye, 560 (1988).

DEĞİŞKEN KESİTLİ KİRİŞLERDE ELASTİK EĞRİNİN SONLU FARKLAR YÖNTEMİ İLE HESABI

Year 2014, Issue: 033, 9 - 24, 15.04.2014

Mustafa Haluk Saraçoğlu Mahmud Sami Döven Burak Kaymak

Abstract

Değişken kesitli kirişler, inşaat, makine, havacılık ve uzay gibi mühendislik alanlarında yaygın olarak kullanılmaktadır. Bu çalışmada, değişken kesitli kirişlerde çökmeler ile buna sebep olan dış yükler arasında kurulan dördüncü dereceden diferansiyel denklemler sonlu farklar yöntemi ile çözümlenmiştir. Bu amaçla bir bilgisayar programı geliştirilmiştir. Literatürde konu ile ilgili yer alan örneklerin geliştirilen bilgisayar programı ile çözümü sonucunda sonlu fark bölüm sayısı ile değişken kesitli kirişin belirli noktasındaki çökme değeri arasındaki ilişkiler tablo ve grafikler şeklinde sunulmuştur. Bu sonuçlar sonlu elemanlar yöntemi ile elde edilen sonuçlarla karşılaştırılmıştır.

Keywords

Değişken kesitli kiriş çökme elastik eğri sonlu farklar yöntemi

References

  • [1] S. Li, J. Hu, C. Zhai, L. Xie, “Static, vibration, and transient dynamic analyses by beam element with adaptive displacement interpolation functions”, Mathematical Problems in Engineering, 2012, 1 (2012).
  • [2] S. T. Wasti, “Prizmatik olmayan kiriş sonlu elemanları”, Yapı Mekaniği Semineri 2004, Eskişehir Osmangazi Üniversitesi Mühendislik-Mimarlık Fakültesi İnşaat Mühendisliği Bölümü, Eskişehir (2004).
  • [3] W.M.C. McKenzie, "Examples in Structural Analysis”, Taylor & Francis, NY, USA, 790 (2006).
  • [4] T. Tankut, “Kirişsiz döşeme yapıların hesabı için yeni bir yöntem”, İMO, 41 (1970).
  • [5] R. D. Cook, D. S. Malkus, M. E. Plesha, R. J. Witt, "Concepts and Applications of Finite Element Analysis", John Wiley, New York, U.S.A., 784 (1989).
  • [6] Y. Xu, and D. Zhou, “Elasticity solution of multi-span beams with variable thickness under static loads”, Applied Mathematical Modelling, 33, 2951 (2009).
  • [7] Y. Xu, and D. Zhou, “Two-dimensional analysis of simply supported piezoelectric beams with variable thickness ”, Applied Mathematical Modelling, 35, 4458 (2011).
  • [8] F. Romano, and G. Zingone, “Deflection of beams with varying rectangular cross section”, Journal of Engineering Mechanics, 118(10), 2128 (1992).
  • [9] Z. Girgin, E. Demir, C. Kol, “Genelleştirilmiş diferansiyel quadrature metodunun kirişlerin serbest titreşim analizine uygulanması”, Pamukkale Üniversitesi Mühendislik Fakültesi Mühendislik Bilimleri Dergisi, 10(3), 347 (2004).
  • [10] A. K. Ashok, and S. B. Biggers, “Stiffness matrix for a non-prismatic beam-column element”, International Journal for Numerical Methods in Engineering, 10(5), 1125 (1976).
  • [11] H. Al-Gahtani, and M. Khan, “Exact Analysis of Nonprismatic Beams”, Journal of Engineering Mechanics, 124(11), 1290 (1998).
  • [12] T.J. Kotas, “A Numerical Solution for Non-Prismatic Beams with Arbitrary Transverse Loading and End Restraint Conditions”, The Structural Engineer, 47(11), (1969).
  • [13] R. Attarnejad, and A. Shahba, “Application of Differential Transform Method in Free Vibration Analysis of Rotating Non-Prismatic Beams”, World Applied Sciences Journal, 5(4), 441 (2008).
  • [14] M. Veiskarami, and S. Pourzeynali, “Green’s function for the deflection of non-prismatic simply supported beams by an analytical approach”, Estonian Journal of Engineering, 18(4), 336 (2012).
  • [15] M. Brojan, T. Videnic, F. Kosel, “Large deflections of nonlinearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law”, Meccanica, 44(6), 733 (2009).
  • [16] M. Brojan, M. Cebron, F. Kosel, “Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected ton non-uniform continuous load and a concentrated load at the free end”, Acta Mechanica Sinica, 28(3), 863 (2012).
  • [17] S.A. Hamoush, M.J. Terro, W.M. Mcginley, “Elastic and inelastic analysis of non-prismatic members using finite difference”, Kuwait Journal of Science, 29(2), 165 (2002).
  • [18] M. İnan, "Cisimlerin Mukavemeti”, İTÜ, İstanbul, Türkiye, 560 (1988).
There are 18 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Mustafa Haluk Saraçoğlu

Mahmud Sami Döven This is me

Burak Kaymak

Publication Date April 15, 2014
Published in Issue Year 2014 Issue: 033

Cite

APA Saraçoğlu, M. H., Döven, M. S., & Kaymak, B. (2014). DEĞİŞKEN KESİTLİ KİRİŞLERDE ELASTİK EĞRİNİN SONLU FARKLAR YÖNTEMİ İLE HESABI. Journal of Science and Technology of Dumlupınar University(033), 9-24.
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