Araştırma Makalesi
BibTex RIS Kaynak Göster

Nonlinear Behavior of Initially Imperfect Beams Subjected to Sinusoidal Load

Yıl 2020, Cilt: 9 Sayı: 1, 466 - 477, 13.03.2020
https://doi.org/10.17798/bitlisfen.592938

Öz

In
the present study, the buckling and post-buckling behaviors of beams having
small sinusoidal imperfection with pinned ends subjected to sinusoidal loading
are examined by using Euler-Bernoulli beam theory. The governing differential
equations of the geometrically nonlinear problem consisting of the equilibrium
equations, kinematical equations and the constitutive equations are converted
into algebraic equations via the finite differences and solved numerically by
using the Newton-Raphson method. The values of buckling loads and buckling
deflections are determined by drawing load-deflection curves. The effect of the
initial imperfection on the buckling values is investigated. Unlike previous
studies on the subject, the diagrams of the deformed shapes of the initially
sinusoidal curved beams as well as the diagrams of the internal forces at
various stages of the deformation including the prebuckling, buckling and
postbuckling states are presented. 

Kaynakça

  • Das K., Batra R.C. 2009. Symmetry Breaking, Snap-Through and Pull-In Instabilities under Dynamic Loading of Microelectromechanical Shallow Arches, Smart Materials and Structures, 18 (11): Article Number: 115008.
  • Gerson Y., Krylov S., Ilic B. 2010. Electrothermal Bistability Tuning in a Large Displacement Micro Actuator, J. Micromech. Microeng., 20 (11): Article Number: 112001.
  • Medina L., Gilat R., Ilic B., Krylov S. 2014. Experimental Investigation of the Snap-Through Buckling of Electrostatically Actuated Initially Curved Pre-Stressed Micro Beams, Sensors and Actuators A: Physical, 220 (1): 323–332.
  • Beharic J., Lucas T.M., Harnett C.K. 2014. Analysis of a Compressed Bistable Buckled Beam on a Flexible Support, Journal of Applied Mechanics-Transactions of the ASME, 81 (8): Article Number: 081011.
  • Chen X., Meguid S.A. 2015. Snap-Through Buckling of Initially Curved Microbeam Subject to an Electrostatic Force, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 471 (2177): Article Number: 20150072.
  • Bradford M.A., Uy. B., Pi Y.L. 2002. In-plane Elastic Stability of Arches under a Central Concentrated Load, Journal of Engineering Mechanics-ASCE, 128 (7): 710–719.
  • Chen J.S., Ro W.C., Lin J.S. 2009. Exact Static and Dynamic Critical Loads of a Sinusoidal Arch under a Point Force at the Midpoint, Int. J. Nonlin. Mech., 44 (1): 66-70.
  • Moon J., Yoon K.Y., Lee T.H., Lee H.E. 2007. In-plane Elastic Buckling of Pin-Ended Shallow Parabolic Arches, Eng. Struct., 29 (10): 2611–2617.
  • Hu C-F, Pi, Y-L, Li Li W.G. 2018. In-Plane Non-Linear Elastic Stability of Parabolic Arches with Different Rise-to Span Ratios, Thin-Walled Structures, 129: 74–84.
  • Fung Y.C., Kaplan A. 1952. Buckling of Low Arches or Curved Beams of Small curvature, NACA Technical Note, No: 2840.
  • Simitses G.J., Hodges D.H. 2006. Fundamentals of Structural Stability. Elsevier, Burlington, MA.
  • Luu A.T., Lee J. 2016. Non-Linear Buckling of Elliptical Curved Beams, International Journal of Non Linear Mechanics, 82: 132–143.
  • Liu N., Plucinsky P., Jeffers A.E. 2017. Combining Load-Controlled and Displacement-Controlled Algorithms to Model Thermal-Mechanical Snap-Through Instabilities in Structures, J. Eng. Mech., 143 (8): Article Number: 04017051.
  • Tsiatas G.C., Babouskos N.G. 2017. Linear and Geometrically Nonlinear Analysis of Non-Uniform Shallow Arches under a Central Concentrated Force, Int. J. Non-Linear Mech., 92: 92–101.
  • Mathews J.H. 1992. Numerical Methods for Mathematics, Science and Engineering. Prentice-Hall International Inc., USA.
  • Maron M.J., Lopez R.J. 1991. Numerical Analysis: A Practical Approach. Wadsworth Publishing Company, Belmont.
  • Altekin M., Yükseler R.F. 2008. A Parametric Study on Geometrically Nonlinear Analysis of Initially Imperfect Shallow Spherical Shells, Journal of Elastomers and Plastics 40 (1): 253-270.
  • Yıldırım B., Yükseler R.F. 2011. Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load, Journal of Elastomers and Plastics, 43 (2): 167-187.
  • Yıldırım B., Yükseler R.F. 2014. Combined Effect of Compressibility, Height and Thickness on the Nonlinear Behaviour of Polyurethane, Simply-Supported Spherical Shells under Apical Loads, Bitlis Eren Univ J Sci & Technol, 4 (1): 12-19.
  • Mortazavi P., Mirdamadi H.R., Shahidi A.R. 2018. Postbuckling, Limit Point, and Bifurcation Analyses of Shallow Nano-Arches by Generalized Displacement Control and Finite Difference Considering Small-Scale Effects, International Journal of Structural Stability and Dynamics, 18 (1): Article Number: 1850014.
  • Pflüger A. 1964. Stabilitats Probleme der Elastostatic. Springer Verlag, Berlin.

Nonlinear Behavior of Beams Having Initially Small Imperfection Subjected to Sinusoidal Load

Yıl 2020, Cilt: 9 Sayı: 1, 466 - 477, 13.03.2020
https://doi.org/10.17798/bitlisfen.592938

Öz

Bu
çalışmada, sinüzoidal yüke maruz, uçları sabit mesnetli sinüzoidal sığ
kemerlerin burkulma ve burkulma sonrası davranışları Euler-Bernoulli kiriş
teorisi kullanılarak incelenmiştir. Denge denklemleri, kinematik denklemler ve
bünye denklemlerini içeren, geometrik olarak doğrusal olmayan problemin
yönetici diferansiyel denklemleri, sonlu farklar yöntemi ile cebirsel
denklemlere dönüştürülmüş ve Newton-Raphson yöntemi kullanılarak sayısal olarak
çözülmüştür. Burkulma yüklerin ve burkulma çökmelerin değerleri, yük-çökme
eğrileri çizilerek belirlenmiştir. İlkel kusurun burkulma değerleri üzerindeki
etkisi incelenmiştir. Konuyla ilgili daha önceki çalışmalardan farklı olarak;
başlangıçta sinüzoidal kavisli olan kirişlerin, şekil değiştirmenin çeşitli
aşamalarındaki elastik eğri diyagramlarının yanı sıra; burkulma öncesindeki,
burkulma sırasındaki ve burkulma sonrasındaki durumlarına karşı gelen kesit
tesirlerinin diyagramları sunulmuştur.

Kaynakça

  • Das K., Batra R.C. 2009. Symmetry Breaking, Snap-Through and Pull-In Instabilities under Dynamic Loading of Microelectromechanical Shallow Arches, Smart Materials and Structures, 18 (11): Article Number: 115008.
  • Gerson Y., Krylov S., Ilic B. 2010. Electrothermal Bistability Tuning in a Large Displacement Micro Actuator, J. Micromech. Microeng., 20 (11): Article Number: 112001.
  • Medina L., Gilat R., Ilic B., Krylov S. 2014. Experimental Investigation of the Snap-Through Buckling of Electrostatically Actuated Initially Curved Pre-Stressed Micro Beams, Sensors and Actuators A: Physical, 220 (1): 323–332.
  • Beharic J., Lucas T.M., Harnett C.K. 2014. Analysis of a Compressed Bistable Buckled Beam on a Flexible Support, Journal of Applied Mechanics-Transactions of the ASME, 81 (8): Article Number: 081011.
  • Chen X., Meguid S.A. 2015. Snap-Through Buckling of Initially Curved Microbeam Subject to an Electrostatic Force, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 471 (2177): Article Number: 20150072.
  • Bradford M.A., Uy. B., Pi Y.L. 2002. In-plane Elastic Stability of Arches under a Central Concentrated Load, Journal of Engineering Mechanics-ASCE, 128 (7): 710–719.
  • Chen J.S., Ro W.C., Lin J.S. 2009. Exact Static and Dynamic Critical Loads of a Sinusoidal Arch under a Point Force at the Midpoint, Int. J. Nonlin. Mech., 44 (1): 66-70.
  • Moon J., Yoon K.Y., Lee T.H., Lee H.E. 2007. In-plane Elastic Buckling of Pin-Ended Shallow Parabolic Arches, Eng. Struct., 29 (10): 2611–2617.
  • Hu C-F, Pi, Y-L, Li Li W.G. 2018. In-Plane Non-Linear Elastic Stability of Parabolic Arches with Different Rise-to Span Ratios, Thin-Walled Structures, 129: 74–84.
  • Fung Y.C., Kaplan A. 1952. Buckling of Low Arches or Curved Beams of Small curvature, NACA Technical Note, No: 2840.
  • Simitses G.J., Hodges D.H. 2006. Fundamentals of Structural Stability. Elsevier, Burlington, MA.
  • Luu A.T., Lee J. 2016. Non-Linear Buckling of Elliptical Curved Beams, International Journal of Non Linear Mechanics, 82: 132–143.
  • Liu N., Plucinsky P., Jeffers A.E. 2017. Combining Load-Controlled and Displacement-Controlled Algorithms to Model Thermal-Mechanical Snap-Through Instabilities in Structures, J. Eng. Mech., 143 (8): Article Number: 04017051.
  • Tsiatas G.C., Babouskos N.G. 2017. Linear and Geometrically Nonlinear Analysis of Non-Uniform Shallow Arches under a Central Concentrated Force, Int. J. Non-Linear Mech., 92: 92–101.
  • Mathews J.H. 1992. Numerical Methods for Mathematics, Science and Engineering. Prentice-Hall International Inc., USA.
  • Maron M.J., Lopez R.J. 1991. Numerical Analysis: A Practical Approach. Wadsworth Publishing Company, Belmont.
  • Altekin M., Yükseler R.F. 2008. A Parametric Study on Geometrically Nonlinear Analysis of Initially Imperfect Shallow Spherical Shells, Journal of Elastomers and Plastics 40 (1): 253-270.
  • Yıldırım B., Yükseler R.F. 2011. Effect of Compressibility on Nonlinear Buckling of Simply Supported Polyurethane Spherical Shells Subjected to an Apical Load, Journal of Elastomers and Plastics, 43 (2): 167-187.
  • Yıldırım B., Yükseler R.F. 2014. Combined Effect of Compressibility, Height and Thickness on the Nonlinear Behaviour of Polyurethane, Simply-Supported Spherical Shells under Apical Loads, Bitlis Eren Univ J Sci & Technol, 4 (1): 12-19.
  • Mortazavi P., Mirdamadi H.R., Shahidi A.R. 2018. Postbuckling, Limit Point, and Bifurcation Analyses of Shallow Nano-Arches by Generalized Displacement Control and Finite Difference Considering Small-Scale Effects, International Journal of Structural Stability and Dynamics, 18 (1): Article Number: 1850014.
  • Pflüger A. 1964. Stabilitats Probleme der Elastostatic. Springer Verlag, Berlin.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Ayfer Tekin Atacan 0000-0001-8161-1345

Receb Faruk Yükseler 0000-0002-2733-580X

Yayımlanma Tarihi 13 Mart 2020
Gönderilme Tarihi 17 Temmuz 2019
Kabul Tarihi 18 Ekim 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 9 Sayı: 1

Kaynak Göster

IEEE A. Tekin Atacan ve R. F. Yükseler, “Nonlinear Behavior of Initially Imperfect Beams Subjected to Sinusoidal Load”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 9, sy. 1, ss. 466–477, 2020, doi: 10.17798/bitlisfen.592938.



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