Araştırma Makalesi
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Geometrik süreksizliğe sahip konsol kirişin Carrera birleşik formülasyonu ile statik analizi

Yıl 2022, Cilt: 24 Sayı: 2, 497 - 514, 08.07.2022

Öz

Bu çalışma, dikey tekil yük etkisinde ve kesitinde boyutları farklı olacak şekilde bir delik içeren dikdörtgen kesitli konsol bir kirişin statik analizi için sayısal bir çözüm sunmaktadır. N. mertebeden Taylor açılımı (TE) ve Lagrange açılımı (LE) uygulanarak Carrera Birleşik Formulasyonu (CUF) kullanılmıştır. Hem her iki geliştirilmiş kiriş teorisinin hem de farklı boyutlardaki deliğin, kesit üzerinde kalınlık boyunca gerilme bileşenleri üzerine etkisi incelenmiştir. İlk olarak, bir yakınsama ve kesin çözümden elde edilen sonuçlar ile bir karşılaştırma çalışması yapılmıştır. Daha sonra, tekil yük etkisinde ve kesitinde delik içermeyen dikdörtgen kesitli konsol kiriş ele alınmıştır. Son olarak da, aynı yük etkisi altında kesitte farklı yarıçaplara sahip delik olması durumu ele alınmıştır.

Kaynakça

  • Timoshenko, S.P., On the corrections for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine, 41, 744-746, (1921).
  • Cowper, G.R., The shear coefficient in Timoshenko’s beam theory, Journal of Applied Mechanics, 33,2, 335-340, (1966).
  • Pai, P.F. and Schulz, M.J., Shear correction factors and an energy consistent beam theory, International Journal of Solids and Structures, 36, 1523-1540, (1999).
  • Gruttmann, F., et al., Shear stresses in prismatic beams with arbitrary cross-sections, International Journal for Numerical Methods in Engineering, 45, 865-889, (1999).
  • Gruttmann, F., and Wagner, W., Shear correction factors in Tmoshenko’s beam theory for arbitrary shaped cross-section, Computational Mechanics, 27, 199-207, (2001).
  • Hutchinson, J.R., Transverse vibrations of beams, exact versus approximate solutions, Journal of Applied Mechanics-Transactions of the Asme, 48,4, 923-928, (1981).
  • Rychter, Z., On the shear coefficient in beam bending, Mechanics Research Communications, 14,5–6, 379–385, (1987).
  • Mechab, I., et al., Deformation of short composite beam using refined theories, Journal of Mathematical Analysis and Applications, 346, 468-479, (2008).
  • Dong, S.B., et al., Much ado about shear correction factors in Timoshenko beam theory, International Journal Of Solids And Structures, 47,13,, 1651-1665, (2010).
  • Mucichescu, D.T., Bounds for stiffness of prismatic beams, Journal of Structural Engineering, 110, 1410-1414, (1984).
  • Bekhadda, A., et al., Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory, Multidiscipline Modeling In Materials And Structures, 15,6, 1152-1169, (2019).
  • Rajagopal, A., Variational Asymptotic Based Shear Correction Factor for Isotropic Circular Tubes, AIAA Journal, 57,10, 4125-4131, (2019).
  • Wagner, W., and Gruttmann, F., A displacement method for the analysis of flexural shear stresses in thin-walled isotropic composite beams, Computers & Structures, 80,24, 1843-1851, (2002).
  • Cai, J., and Moen, C.D., Elastic buckling analysis of thin-walled structural members with rectangular holes using generalized beam theory, Thin-Walled Structures, 107, 274-286, (2016).
  • Taig, G., and Ranzi, G., Generalised Beam Theory (GBT) for composite beams with partial shear interaction, Engineering Structures, 99, 582-602, (2015).
  • Carrera, E., Pagani, A., Petrolo, M., et al., Recent developments on refined theories for beams with applications, Mechanical Engineering Reviews, 2,2, (2015).
  • Liu, L., and Lu, N., Variational formulations, instabilities and critical loadings of space curved beams, International Journal Of Solids And Structures, 87, 48-60, (2016).
  • Pagani, A., and Carrera, E., Unified formulation of geometrically nonlinear refined beam theories, Mechanics Of Advanced Materials And Structures, 25,1, 15-31, (2018).
  • Carrera, E., de Miguel, A. G., and Pagani, A., Extension of MITC to higher-order beam models and shear locking analysis for compact, thin-walled, and composite structures, International Journal For Numerical Methods In Engineering, 112,13, 1889-1908, (2017).
  • Carrera, E., and Zappino, E., One-dimensional finite element formulation with node-dependent kinematics, Computers & Structures, 192, 114-125, (2017).
  • Richard, S., Generalized Beam Theory-an adequate method for coupled stability problems, Thin-Walled Strcut, 19,2-4, 161-80, (1994).
  • Carrera, E., and Giunta, G., Refined beam theories based on a unified formulation, International Journal of Applied Mechanics, 2,1, 117-143, (2010).
  • Carrera, E., Giunta, G., and Petrolo, M., Beam Structures Classical and Advanced Theories, A John Wiley & Sons, Ltd., Publication, (2011).
  • Karataş, E.E., Filippi, M., and Carrera, E., Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements, European Journal of Mechanics/A Solids, 88, (2021).
  • Carrera, E., and Demirbas, D.M.,Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regimewith CUF, Composite Structures, 275,(2021).
  • Carrera, E., Demirbaş, M.D., and Augello, R., Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions, Applied Scıences-Basel, 11(22), (2021).
  • Demirbaş, M.D., Çalışkan, U., Xu, X., and Filippi, M., Evaluation of the bending response of compact and thin-walled FG beams with CUF, MECHANICS OF Advanced Materials And Structures, 28(17), (2021).
  • Reddy, J.N., Mechanics of laminated composite plates and shells: theory and analysis, Boca Raton, FL: CRC Press, (2004).
  • Bathe, K., Finite element procedure, Prentice Hall, Englewood Cliffs, NJ, (1996).
  • Carrera, E., Petrolo, M., and Zappino, E., Performance of CUF Approach to Analyze the Structural Behavior of Slender Bodies, Journal of Structural Engineering, 138,2, 284-296, (2012).
  • Timoshenko, S.P., and Goodier, J.N., Theory of elasticity, McGraw-Hill; (1970).
  • Carrera, E., et al., Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons Ltd, (2014).

Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation

Yıl 2022, Cilt: 24 Sayı: 2, 497 - 514, 08.07.2022

Öz

This paper presents a numerical solution for static analysis of a rectangular cantilever beam with different sizes of a hole on its cross-section subjected to vertical concentrated load. Carrera Unified Formulation (CUF) is used by employing both N-OrderTaylor type expansion (TE) and Lagrange type expansion (LE). The influence of both these different refined beam models and the different sizes of hole on the evaluation of the stress components on the cross-section along the thickness is examined. First, with the convergence study, a comparison is performed with the results obtained from the exact solution. Then, a rectangular cantilever beam with compact cross-section subjected to vertical concentrated load is considered. Finally, the presence of a hole with different radius sizes on its cross-section subjected to the same loading is discussed.

Kaynakça

  • Timoshenko, S.P., On the corrections for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine, 41, 744-746, (1921).
  • Cowper, G.R., The shear coefficient in Timoshenko’s beam theory, Journal of Applied Mechanics, 33,2, 335-340, (1966).
  • Pai, P.F. and Schulz, M.J., Shear correction factors and an energy consistent beam theory, International Journal of Solids and Structures, 36, 1523-1540, (1999).
  • Gruttmann, F., et al., Shear stresses in prismatic beams with arbitrary cross-sections, International Journal for Numerical Methods in Engineering, 45, 865-889, (1999).
  • Gruttmann, F., and Wagner, W., Shear correction factors in Tmoshenko’s beam theory for arbitrary shaped cross-section, Computational Mechanics, 27, 199-207, (2001).
  • Hutchinson, J.R., Transverse vibrations of beams, exact versus approximate solutions, Journal of Applied Mechanics-Transactions of the Asme, 48,4, 923-928, (1981).
  • Rychter, Z., On the shear coefficient in beam bending, Mechanics Research Communications, 14,5–6, 379–385, (1987).
  • Mechab, I., et al., Deformation of short composite beam using refined theories, Journal of Mathematical Analysis and Applications, 346, 468-479, (2008).
  • Dong, S.B., et al., Much ado about shear correction factors in Timoshenko beam theory, International Journal Of Solids And Structures, 47,13,, 1651-1665, (2010).
  • Mucichescu, D.T., Bounds for stiffness of prismatic beams, Journal of Structural Engineering, 110, 1410-1414, (1984).
  • Bekhadda, A., et al., Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory, Multidiscipline Modeling In Materials And Structures, 15,6, 1152-1169, (2019).
  • Rajagopal, A., Variational Asymptotic Based Shear Correction Factor for Isotropic Circular Tubes, AIAA Journal, 57,10, 4125-4131, (2019).
  • Wagner, W., and Gruttmann, F., A displacement method for the analysis of flexural shear stresses in thin-walled isotropic composite beams, Computers & Structures, 80,24, 1843-1851, (2002).
  • Cai, J., and Moen, C.D., Elastic buckling analysis of thin-walled structural members with rectangular holes using generalized beam theory, Thin-Walled Structures, 107, 274-286, (2016).
  • Taig, G., and Ranzi, G., Generalised Beam Theory (GBT) for composite beams with partial shear interaction, Engineering Structures, 99, 582-602, (2015).
  • Carrera, E., Pagani, A., Petrolo, M., et al., Recent developments on refined theories for beams with applications, Mechanical Engineering Reviews, 2,2, (2015).
  • Liu, L., and Lu, N., Variational formulations, instabilities and critical loadings of space curved beams, International Journal Of Solids And Structures, 87, 48-60, (2016).
  • Pagani, A., and Carrera, E., Unified formulation of geometrically nonlinear refined beam theories, Mechanics Of Advanced Materials And Structures, 25,1, 15-31, (2018).
  • Carrera, E., de Miguel, A. G., and Pagani, A., Extension of MITC to higher-order beam models and shear locking analysis for compact, thin-walled, and composite structures, International Journal For Numerical Methods In Engineering, 112,13, 1889-1908, (2017).
  • Carrera, E., and Zappino, E., One-dimensional finite element formulation with node-dependent kinematics, Computers & Structures, 192, 114-125, (2017).
  • Richard, S., Generalized Beam Theory-an adequate method for coupled stability problems, Thin-Walled Strcut, 19,2-4, 161-80, (1994).
  • Carrera, E., and Giunta, G., Refined beam theories based on a unified formulation, International Journal of Applied Mechanics, 2,1, 117-143, (2010).
  • Carrera, E., Giunta, G., and Petrolo, M., Beam Structures Classical and Advanced Theories, A John Wiley & Sons, Ltd., Publication, (2011).
  • Karataş, E.E., Filippi, M., and Carrera, E., Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements, European Journal of Mechanics/A Solids, 88, (2021).
  • Carrera, E., and Demirbas, D.M.,Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regimewith CUF, Composite Structures, 275,(2021).
  • Carrera, E., Demirbaş, M.D., and Augello, R., Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions, Applied Scıences-Basel, 11(22), (2021).
  • Demirbaş, M.D., Çalışkan, U., Xu, X., and Filippi, M., Evaluation of the bending response of compact and thin-walled FG beams with CUF, MECHANICS OF Advanced Materials And Structures, 28(17), (2021).
  • Reddy, J.N., Mechanics of laminated composite plates and shells: theory and analysis, Boca Raton, FL: CRC Press, (2004).
  • Bathe, K., Finite element procedure, Prentice Hall, Englewood Cliffs, NJ, (1996).
  • Carrera, E., Petrolo, M., and Zappino, E., Performance of CUF Approach to Analyze the Structural Behavior of Slender Bodies, Journal of Structural Engineering, 138,2, 284-296, (2012).
  • Timoshenko, S.P., and Goodier, J.N., Theory of elasticity, McGraw-Hill; (1970).
  • Carrera, E., et al., Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons Ltd, (2014).
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Esra Eylem Karataş 0000-0003-1396-2463

Yayımlanma Tarihi 8 Temmuz 2022
Gönderilme Tarihi 16 Eylül 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 24 Sayı: 2

Kaynak Göster

APA Karataş, E. E. (2022). Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24(2), 497-514.
AMA Karataş EE. Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation. BAUN Fen. Bil. Enst. Dergisi. Temmuz 2022;24(2):497-514.
Chicago Karataş, Esra Eylem. “Static Analysis of Cantilever Beam With Geometrical Discontinuity by Carrera Unified Formulation”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24, sy. 2 (Temmuz 2022): 497-514.
EndNote Karataş EE (01 Temmuz 2022) Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 2 497–514.
IEEE E. E. Karataş, “Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation”, BAUN Fen. Bil. Enst. Dergisi, c. 24, sy. 2, ss. 497–514, 2022.
ISNAD Karataş, Esra Eylem. “Static Analysis of Cantilever Beam With Geometrical Discontinuity by Carrera Unified Formulation”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24/2 (Temmuz 2022), 497-514.
JAMA Karataş EE. Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation. BAUN Fen. Bil. Enst. Dergisi. 2022;24:497–514.
MLA Karataş, Esra Eylem. “Static Analysis of Cantilever Beam With Geometrical Discontinuity by Carrera Unified Formulation”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 24, sy. 2, 2022, ss. 497-14.
Vancouver Karataş EE. Static analysis of cantilever beam with geometrical discontinuity by Carrera Unified Formulation. BAUN Fen. Bil. Enst. Dergisi. 2022;24(2):497-514.