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İnce Duvarlı Kirişlerin İzotropik ve Anizotropik Analizi İçin Kesit Değişim Modları Kullanılarak Bir Kiriş Elemanı Formülasyonu

Yıl 2025, Cilt: 15 Sayı: 1, 75 - 94, 22.04.2025

Yıldırım Serhat Erdoğan , Mehmet Ada

Öz

Bu makalede, kesit analizinden elde edilen yerdeğiştirme modları aracılığıyla ince cidarlı kirişlerin 3 boyutlu doğrusal statik analizini gerçekleştiren etkin bir sonlu elemanlar (SE) formülasyonu sunulmaktadır. Bu formülasyon, homojen izotropik ve/veya ince tabakalı kompozit malzemelerden yapılmış, gelişigüzel şekilli kesitlerin analizi için uygundur. Önerilen formülasyonda, kiriş elemanında yüksek dereceli etkiler oluşturan, düzensiz burulma ve kesme/eğilme kaynaklı tüm çarpılma ve şekil bozulma etkilerini dikkate alınmaktadır. Benzer yaklaşımlardan farklı olarak, bu yöntemde rijit modların belirlenmesi ya da bütün mod matrisinin kullanılmasına gerek bulunmamaktadır. İkinci dereceden özdeğer problemi çözümünden elde edilen kesit yer değiştirme modlarının genellikle karmaşık sayı olması rağmen, bu formülasyonda karmaşık sayılarla hesaplama yapılmasına da gerek yoktur. Birkaç durum için karşılaştırmalı olarak sunulan sayısal sonuçlar, sunulan kiriş elemanı formülasyonunun katı ve kabuk formülasyonlarına kıyasla doğruluğunu ve hesaplama verimliliğini göstermektedir.

Anahtar Kelimeler

İnce cidarlı kirişler katmanlı kompozit kirişler çarpılma etkileri kesitsel bozulma en kesit yerdeğiştirme modları.

Kaynakça

  • Ádány, S., Schafer, BW. 2014. Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Primary modes, Thin-Walled Structures, 84: 150-169. doi: 10.1016/j.tws.2014.06.001
  • Addessi, D., Di Re, P., Cimarello, G. 2021. Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures. Thin-Walled Structures, 159:107259 doi:10.1016/j.tws.2020.107259
  • Barbero, EJ. 2018. Introduction to Composite Material Design. CRC Press.
  • Barsoum, RS., Gallagher, RH. 1970. Finite element analysis of torsional and torsional flexural stability problems. International Journal for Numerical Methods in Engineering, 2:335-352. doi: 10.1002/nme.1620020304
  • Bauld NR., Tzeng, LS. 1984. A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections. International Journal of Solids and Structures, 20(3):277–297. doi:10.1016/0020-7683(84)90039-8
  • Bažant, ZP., El Nimeri, M. 1973. Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames. Journal of the Engineering Mechanics Division, 99(6):1259-1281. doi: 10.1061/JMCEA3.0001837
  • Berdichevskii, VL. 1979. Variational-asymptotic method of constructing a theory of shells. Journal of Applied Mathematics and Mechanics, 43(4): 711-736. doi:10.1016/0021-8928(79)90157-6
  • Bianco, MJ., Könke, C., Habtemariam, A., Zabel, V. 2018. Exact finite element formulation in generalized beam theory. International Journal of Advanced Structural Engineering, 10:295-323. doi:10.1007/s40091-018-0199-8. Borri, M., Merlini, T. 1986. A large displacement formulation for anisotropic beam analysis. Meccanica, 21:30-37. doi:10.1007/BF01556314
  • Carrera, E., Giunta, G., Petrolo, M. 2011. Beam Structures: Classical and Advanced Theories. John Wiley & Sons, 2011.
  • Cesnik, .ES., Hodges, DH. 1997. VABS: A new concept for composite rotor blade cross-sectional modeling. Journal of the American Helicopter Society, 42(1): 27-38. doi:10.4050/JAHS.42.27
  • Davies, JM., Leach, P. 1994. First-order generalised beam theory. Journal of Constructional Steel Research, 31(2-3):187-220. doi:10.1016/0143-974X(94)90010-8.
  • Deo, A., Yu, W. 2020. Thin-walled composite beam cross-sectional analysis using the mechanics of structure genome. Thin-Walled Structures, 152:106663. doi:10.1016/j.tws.2020.106663.
  • Dhadwal, MK., Jung, SN. 2019. Multifield variational sectional analysis for accurate stress computation of multilayered composite beams. AIAA J., 54(4): 1702-1714. doi:10.2514/1.J057384
  • Dikaros, IC., Sapountzakis, EJ. 2014. Generalized warping analysis of composite beams of an arbitrary cross section by BEM. I: theoretical considerations and numerical implementation Journal of Engineering Mechanics, 140(9): (2014):04014062. doi:10.1061/(ASCE)EM.1943-7889.0000775
  • Erkmen, RE., Mohareb, M. 2006. Torsion analysis of thin-walled beams including shear deformation effects. Thin-Walled Structures, 44(10):1096-1108. doi:10.1016/j.tws.2006.10.012
  • Evseev, EG., Morozov, EV. 1997. Explicit finite difference method in the dynamic analysis of composite structures. Composite Structures 39(3-4): 215-221. doi:10.1016/S0263-8223(97)00115-3
  • Ferradi, MK., Cespedes, X. 2014. A new beam element with transversal and warping eigenmodes. Computers and Structures, 131:12-33 doi:10.1016/j.compstruc.2013.10.001
  • Gabbianelli, G. 2021. Applied element modelling of warping effects in thin-walled C-shaped steel sections. Buildings, 11(8):328. doi:10.3390/buildings11080328
  • Giavotto, V., Borri, M., Mantegazza, P., Ghiringhelli, G., Carmaschi, V., Maffioli, GC., Mussi, F. 1983. Anisotropic beam theory and applications. Computers and Structures, 16(1-4):403-413. doi:10.1016/0045-7949(83)90179-7
  • Hansen, AB., Jönsson, J. 2019a. A thin-walled beam element based on semi-analytical solution modes. Thin-Walled Structures, 144:106344. doi:10.1016/j.tws.2019.106344
  • Hansen, AB., Jönsson, J. 2019b. Displacement modes of a thin-walled beam model with deformable cross sections. Thin-Walled Structures, 141:576-592. doi:10.1016/j.tws.2019.01.052
  • Hodges, DH. 2006. Nonlinear Composite Beam Theory. American Institute of Aeronautics and Astronautics, Reston, VA.
  • Islam, A., Sheikh, AH., Bennett, T., Thomsen, OT. 2021. An efficient model for laminated composite thin-walled beams of open or closed cross-section and with or without in-filled materials. Composites Structures, 256:112998. doi:10.1016/j.compstruct.2020.112998
  • Jang, GW., Kim, MJ., Kim, YY. 2012. Analysis of thin-walled straight beams with generally shaped closed sections using numerically determined sectional deformation functions. Journal of Structural Engineering, 138(12):1427-1435. doi:10.1061/(ASCE)ST.1943-541X.0000582
  • Jönsson, J. 1999. Distortional theory of thin-walled beams. Thin-Walled Structures, 33(4): 269–303. doi:10.1016/S0263-8231(98)00050-0.
  • Jönsson, J., Andreassen, MJ. 2011. Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams. Thin-Walled Structures, 49:691-707. doi:10.1016/j.tws.2010.12.009
  • Kashefi, K., Sheikh, A., Ali MM., Griffith, M. 2016. An efficient modelling approach based on a rigorous cross-sectional analysis for analysing box girder bridge superstructures. Advances in Structural Engineering, 19(3):513-528. doi:10.1177/1369433216630121
  • Kassab, MP., Campello, EMB., Pimenta, PM. 2023. Advances on kinematically exact rod models for thin-walled open-section members: Consistent warping function and nonlinear constitutive equation. Computer Methods in Applied Mechanics and Engineering, 407:115933. doi:10.1016/j.cma.2023.115933
  • Krajcinovic, D. 1969. A Consistent Discrete Elements Technique for Thinwalled Assemblages, International Journal of Solids and Structures 5(7):639-662, doi: 10.1016/0020-7683(69)90085-7
  • Lee, J., Lee, S. 2004. Flexural–torsional behavior of thin-walled composite beams. Thin-Walled Structures, 42(9): 1293-1305. doi:10.1016/j.tws.2004.03.015
  • Lee, J. 2005. Flexural analysis of thin-walled composite beams using shear-deformable beam theory. Composite Structures, 70(2): 212-222. doi:10.1016/j.compstruct.2004.08.023
  • Lezgy-Nazargah, M., Vidal, P., Polit, O. 2021. A quasi-3D finite element model for the analysis of thin-walled beams under axial-flexural-torsional loads. Thin-Walled Structures, 164:107811. doi:10.1016/j.tws.2021.107811
  • Liang, K., Mu, J., Li, Z. 2024. A novel reduced-order method using mixed nonlinear kinematics for geometrically nonlinear analysis of thin-walled structures. Computer Methods in Applied Mechanics and Engineering, 421:116756. doi:10.1016/j.cma.2024.116756
  • Liu, H., Wang, W., Deng, L., He, Y. 2023. Inelastic buckling analysis of cold-formed steel members with residual stresses based on CFSM. Structures, 56:104871. doi: 10.1016/j.istruc.2023.06.142 Mottram, JT. 1992. Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method. Composites Engineering, 2(2): 91-104. doi: 10.1016/0961-9526(92)90048-B
  • Naderian, HR., Ronagh, HR. 2015. Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method. Thin-Walled Structures, 90:74–83. doi:10.1016/j.tws.2015.01.008.
  • Osman, HS., Ozkan, I., Erkmen, R. 2024. Buckling analysis of thin-walled I-beams with web deformations. Structures, 69:107498. doi:10.1016/j.istruc.2024.107498
  • Palermo, L., Rachid, M., Venturini, WS. 1992. Analysis of thin walled structures using the boundary element method. Engineering Analysis with Boundary Elements, 9(4):359-363. doi: 10.1016/0955-7997(92)90021-X
  • Pavazza, R., Matoković, A., Vukasović, M. 2022. A theory of torsion of thin-walled beams of arbitrary open sections with influence of shear. Mechanics Based Design of Structures and Machines, 50(1): 206-241. doi:10.1080/15397734.2020.1714449
  • Prokić, A. 1994. Material Nonlinear Analysis of Thin‐Walled Beams. Journal of Structural Engineering, 120(10):2840-2852. doi: 10.1061/(ASCE)0733-9445(1994)120:10(2840)
  • Prokić, A. 1996a. New Warping Function for Thin-Walled Beams. I: Theory. Journal of Structural Engineering, 122(12):1437-1442. doi:10.1061/(ASCE)0733-9445(1996)122:12(1437)
  • Prokić, A. 1996b. New Warping Function for Thin-Walled Beams. II: Finite Element Method and Applications. Journal of Structural Engineering, 122(12):1443-1452. doi: 10.1061/(ASCE)0733-9445(1996)122:12(1443).
  • Reddy, JN. 2004. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press.
  • Sheikh, AH., Thomsen, OT. 2008. An efficient beam element for the analysis of laminated composite beams of thin-walled open and closed cross sections. Composites Science and Technology, 68(10-11): 2273-2281. doi:10.1016/j.compscitech.2008.04.018
  • Shen, Z. 2024. Thin-walled composite beam elements via the absolute nodal coordinate formulation. Multibody System Dynamics, 62:107–135. Doi:10.1007/s11044-023-09956-y
  • Soltani, M, Asgarian, B. 2018. Determination of Lateral-Torsional Buckling Load of Simply Supported Prismatic Thin-Walled Beams with Mono-Symmetric Cross-Sections Using the Finite Difference Method. Amirkabir Journal of Civil Engineering, 50(1):23-26. doi: 10.22060/ceej.2017.11194.4986
  • Stoykov, S., Manoach, E., Margenov, S. 2016. An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations. Journal of Applied Mathematics and Mechanics, 96(7): 791–812. doi:10.1002/zamm.201400139
  • Van Erp, G., Menken, C. 1990. The spline finite-strip method in the buckling analyses of thin-walled structures Communications in Applied Numerical Methods, 6(6): 477-484. doi: 10.1002/cnm.1630060608
  • Vieira, RF., Virtuoso, FB., Pereira, EBR. 2014. A higher order model for thin-walled structures with deformable cross-sections. International Journal of Solids and Structures, 51(3-4): 575-598. doi:10.1016/j.ijsolstr.2013.10.023
  • Vlasov, VZ. 1961. Thin-Walled Elastic Beams, Second edition, Israel program for scientific translations, Jerusalem.
  • Vo, TP., Lee, J. 2008. Flexural–torsional behavior of thin-walled composite box beams using shear-deformable beam theory. Engineering Structures, 30(7): 1958-1968. doi:10.1016/j.engstruct.2007.12.003
  • Vo, TP., Lee, J. 2009. Flexural–torsional behavior of thin-walled composite space frames. International Journal of Mechanical Sciences, 51(11-12):837-845. doi:10.1016/j.ijmecsci.2009.09.019
  • Vojnić-Purčar, M., Prokić, A., Bešević, M. 2019. A numerical model for laminated composite thin-walled members with openings considering shear lag effect. Engineering Structures, 185: 392-399. doi:10.1016/j.engstruct.2019.01.142
  • Vukasović, M., Pavazza, R., Vlak, F. 2017. Analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear. The Journal of Strain Analysis for Engineering Design, 52(3): 190-203. doi:10.1177/0309324717697524
  • Wang, XF., Yang, QS., Law S-S. 2014. A shear locking-free spatial beam element with general thin-walled closed cross-section. Engineering Structures, 58:12–24. doi:10.1016/j.engstruct.2013.09.046
  • Yanlin, G., Shaofan, C. 1991. Postbuckling interaction analysis of cold-formed thin-walled channel sections by finite strip method. Thin-Walled Structures, 11(3): 277-289. doi:10.1016/0263-8231(91)90004-3
  • Yu, W., Hodges, D.H., Ho, J.C. 2012. Variational asymptotic beam sectional analysis - An updated version. International Journal of Engineering Science, 59: 40-64. doi:10.1016/j.ijengsci.2012.03.006
  • Zhang, YM., Gu, Y., Chen, JT. 2011. Boundary element analysis of 2D thin walled structures with high-order geometry elements using transformation. Engineering Analysis with Boundary Elements, 35(3):581-586. doi:10.1016/j.enganabound.2010.07.008

A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes

Yıl 2025, Cilt: 15 Sayı: 1, 75 - 94, 22.04.2025

Yıldırım Serhat Erdoğan , Mehmet Ada

Öz

This paper presents an efficient finite element (FE) formulation for the 3D linear static analysis of thin-walled beams through displacement modes obtained from cross-sectional analysis. The formulation is suitable for the analysis of cross-sections made of homogeneous isotropic and/or laminated composite materials with arbitrary shapes. The FE formulation concerns all the warping and the distortional effects arise from the non-uniform torsion and the shear/bending, which leads to a higher order beam element. Unlike similar approaches, the method does not require the determination of rigid modes and the utilization of a full modal matrix. Although the cross-section displacement modes obtained from the solution of a quadratic eigenvalue problem are generally complex, the formulation itself does not have to deal with calculations involving complex numbers. The numerical results presented comparatively for several cases, demonstrate the accuracy and the computational efficiency of the presented beam element formulation compared to solid and shell formulations.

Anahtar Kelimeler

cross section displacement modes. cross-section distortion laminated composite beams Thin-walled beams warping effects

Kaynakça

  • Ádány, S., Schafer, BW. 2014. Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Primary modes, Thin-Walled Structures, 84: 150-169. doi: 10.1016/j.tws.2014.06.001
  • Addessi, D., Di Re, P., Cimarello, G. 2021. Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures. Thin-Walled Structures, 159:107259 doi:10.1016/j.tws.2020.107259
  • Barbero, EJ. 2018. Introduction to Composite Material Design. CRC Press.
  • Barsoum, RS., Gallagher, RH. 1970. Finite element analysis of torsional and torsional flexural stability problems. International Journal for Numerical Methods in Engineering, 2:335-352. doi: 10.1002/nme.1620020304
  • Bauld NR., Tzeng, LS. 1984. A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections. International Journal of Solids and Structures, 20(3):277–297. doi:10.1016/0020-7683(84)90039-8
  • Bažant, ZP., El Nimeri, M. 1973. Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames. Journal of the Engineering Mechanics Division, 99(6):1259-1281. doi: 10.1061/JMCEA3.0001837
  • Berdichevskii, VL. 1979. Variational-asymptotic method of constructing a theory of shells. Journal of Applied Mathematics and Mechanics, 43(4): 711-736. doi:10.1016/0021-8928(79)90157-6
  • Bianco, MJ., Könke, C., Habtemariam, A., Zabel, V. 2018. Exact finite element formulation in generalized beam theory. International Journal of Advanced Structural Engineering, 10:295-323. doi:10.1007/s40091-018-0199-8. Borri, M., Merlini, T. 1986. A large displacement formulation for anisotropic beam analysis. Meccanica, 21:30-37. doi:10.1007/BF01556314
  • Carrera, E., Giunta, G., Petrolo, M. 2011. Beam Structures: Classical and Advanced Theories. John Wiley & Sons, 2011.
  • Cesnik, .ES., Hodges, DH. 1997. VABS: A new concept for composite rotor blade cross-sectional modeling. Journal of the American Helicopter Society, 42(1): 27-38. doi:10.4050/JAHS.42.27
  • Davies, JM., Leach, P. 1994. First-order generalised beam theory. Journal of Constructional Steel Research, 31(2-3):187-220. doi:10.1016/0143-974X(94)90010-8.
  • Deo, A., Yu, W. 2020. Thin-walled composite beam cross-sectional analysis using the mechanics of structure genome. Thin-Walled Structures, 152:106663. doi:10.1016/j.tws.2020.106663.
  • Dhadwal, MK., Jung, SN. 2019. Multifield variational sectional analysis for accurate stress computation of multilayered composite beams. AIAA J., 54(4): 1702-1714. doi:10.2514/1.J057384
  • Dikaros, IC., Sapountzakis, EJ. 2014. Generalized warping analysis of composite beams of an arbitrary cross section by BEM. I: theoretical considerations and numerical implementation Journal of Engineering Mechanics, 140(9): (2014):04014062. doi:10.1061/(ASCE)EM.1943-7889.0000775
  • Erkmen, RE., Mohareb, M. 2006. Torsion analysis of thin-walled beams including shear deformation effects. Thin-Walled Structures, 44(10):1096-1108. doi:10.1016/j.tws.2006.10.012
  • Evseev, EG., Morozov, EV. 1997. Explicit finite difference method in the dynamic analysis of composite structures. Composite Structures 39(3-4): 215-221. doi:10.1016/S0263-8223(97)00115-3
  • Ferradi, MK., Cespedes, X. 2014. A new beam element with transversal and warping eigenmodes. Computers and Structures, 131:12-33 doi:10.1016/j.compstruc.2013.10.001
  • Gabbianelli, G. 2021. Applied element modelling of warping effects in thin-walled C-shaped steel sections. Buildings, 11(8):328. doi:10.3390/buildings11080328
  • Giavotto, V., Borri, M., Mantegazza, P., Ghiringhelli, G., Carmaschi, V., Maffioli, GC., Mussi, F. 1983. Anisotropic beam theory and applications. Computers and Structures, 16(1-4):403-413. doi:10.1016/0045-7949(83)90179-7
  • Hansen, AB., Jönsson, J. 2019a. A thin-walled beam element based on semi-analytical solution modes. Thin-Walled Structures, 144:106344. doi:10.1016/j.tws.2019.106344
  • Hansen, AB., Jönsson, J. 2019b. Displacement modes of a thin-walled beam model with deformable cross sections. Thin-Walled Structures, 141:576-592. doi:10.1016/j.tws.2019.01.052
  • Hodges, DH. 2006. Nonlinear Composite Beam Theory. American Institute of Aeronautics and Astronautics, Reston, VA.
  • Islam, A., Sheikh, AH., Bennett, T., Thomsen, OT. 2021. An efficient model for laminated composite thin-walled beams of open or closed cross-section and with or without in-filled materials. Composites Structures, 256:112998. doi:10.1016/j.compstruct.2020.112998
  • Jang, GW., Kim, MJ., Kim, YY. 2012. Analysis of thin-walled straight beams with generally shaped closed sections using numerically determined sectional deformation functions. Journal of Structural Engineering, 138(12):1427-1435. doi:10.1061/(ASCE)ST.1943-541X.0000582
  • Jönsson, J. 1999. Distortional theory of thin-walled beams. Thin-Walled Structures, 33(4): 269–303. doi:10.1016/S0263-8231(98)00050-0.
  • Jönsson, J., Andreassen, MJ. 2011. Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams. Thin-Walled Structures, 49:691-707. doi:10.1016/j.tws.2010.12.009
  • Kashefi, K., Sheikh, A., Ali MM., Griffith, M. 2016. An efficient modelling approach based on a rigorous cross-sectional analysis for analysing box girder bridge superstructures. Advances in Structural Engineering, 19(3):513-528. doi:10.1177/1369433216630121
  • Kassab, MP., Campello, EMB., Pimenta, PM. 2023. Advances on kinematically exact rod models for thin-walled open-section members: Consistent warping function and nonlinear constitutive equation. Computer Methods in Applied Mechanics and Engineering, 407:115933. doi:10.1016/j.cma.2023.115933
  • Krajcinovic, D. 1969. A Consistent Discrete Elements Technique for Thinwalled Assemblages, International Journal of Solids and Structures 5(7):639-662, doi: 10.1016/0020-7683(69)90085-7
  • Lee, J., Lee, S. 2004. Flexural–torsional behavior of thin-walled composite beams. Thin-Walled Structures, 42(9): 1293-1305. doi:10.1016/j.tws.2004.03.015
  • Lee, J. 2005. Flexural analysis of thin-walled composite beams using shear-deformable beam theory. Composite Structures, 70(2): 212-222. doi:10.1016/j.compstruct.2004.08.023
  • Lezgy-Nazargah, M., Vidal, P., Polit, O. 2021. A quasi-3D finite element model for the analysis of thin-walled beams under axial-flexural-torsional loads. Thin-Walled Structures, 164:107811. doi:10.1016/j.tws.2021.107811
  • Liang, K., Mu, J., Li, Z. 2024. A novel reduced-order method using mixed nonlinear kinematics for geometrically nonlinear analysis of thin-walled structures. Computer Methods in Applied Mechanics and Engineering, 421:116756. doi:10.1016/j.cma.2024.116756
  • Liu, H., Wang, W., Deng, L., He, Y. 2023. Inelastic buckling analysis of cold-formed steel members with residual stresses based on CFSM. Structures, 56:104871. doi: 10.1016/j.istruc.2023.06.142 Mottram, JT. 1992. Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method. Composites Engineering, 2(2): 91-104. doi: 10.1016/0961-9526(92)90048-B
  • Naderian, HR., Ronagh, HR. 2015. Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method. Thin-Walled Structures, 90:74–83. doi:10.1016/j.tws.2015.01.008.
  • Osman, HS., Ozkan, I., Erkmen, R. 2024. Buckling analysis of thin-walled I-beams with web deformations. Structures, 69:107498. doi:10.1016/j.istruc.2024.107498
  • Palermo, L., Rachid, M., Venturini, WS. 1992. Analysis of thin walled structures using the boundary element method. Engineering Analysis with Boundary Elements, 9(4):359-363. doi: 10.1016/0955-7997(92)90021-X
  • Pavazza, R., Matoković, A., Vukasović, M. 2022. A theory of torsion of thin-walled beams of arbitrary open sections with influence of shear. Mechanics Based Design of Structures and Machines, 50(1): 206-241. doi:10.1080/15397734.2020.1714449
  • Prokić, A. 1994. Material Nonlinear Analysis of Thin‐Walled Beams. Journal of Structural Engineering, 120(10):2840-2852. doi: 10.1061/(ASCE)0733-9445(1994)120:10(2840)
  • Prokić, A. 1996a. New Warping Function for Thin-Walled Beams. I: Theory. Journal of Structural Engineering, 122(12):1437-1442. doi:10.1061/(ASCE)0733-9445(1996)122:12(1437)
  • Prokić, A. 1996b. New Warping Function for Thin-Walled Beams. II: Finite Element Method and Applications. Journal of Structural Engineering, 122(12):1443-1452. doi: 10.1061/(ASCE)0733-9445(1996)122:12(1443).
  • Reddy, JN. 2004. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press.
  • Sheikh, AH., Thomsen, OT. 2008. An efficient beam element for the analysis of laminated composite beams of thin-walled open and closed cross sections. Composites Science and Technology, 68(10-11): 2273-2281. doi:10.1016/j.compscitech.2008.04.018
  • Shen, Z. 2024. Thin-walled composite beam elements via the absolute nodal coordinate formulation. Multibody System Dynamics, 62:107–135. Doi:10.1007/s11044-023-09956-y
  • Soltani, M, Asgarian, B. 2018. Determination of Lateral-Torsional Buckling Load of Simply Supported Prismatic Thin-Walled Beams with Mono-Symmetric Cross-Sections Using the Finite Difference Method. Amirkabir Journal of Civil Engineering, 50(1):23-26. doi: 10.22060/ceej.2017.11194.4986
  • Stoykov, S., Manoach, E., Margenov, S. 2016. An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations. Journal of Applied Mathematics and Mechanics, 96(7): 791–812. doi:10.1002/zamm.201400139
  • Van Erp, G., Menken, C. 1990. The spline finite-strip method in the buckling analyses of thin-walled structures Communications in Applied Numerical Methods, 6(6): 477-484. doi: 10.1002/cnm.1630060608
  • Vieira, RF., Virtuoso, FB., Pereira, EBR. 2014. A higher order model for thin-walled structures with deformable cross-sections. International Journal of Solids and Structures, 51(3-4): 575-598. doi:10.1016/j.ijsolstr.2013.10.023
  • Vlasov, VZ. 1961. Thin-Walled Elastic Beams, Second edition, Israel program for scientific translations, Jerusalem.
  • Vo, TP., Lee, J. 2008. Flexural–torsional behavior of thin-walled composite box beams using shear-deformable beam theory. Engineering Structures, 30(7): 1958-1968. doi:10.1016/j.engstruct.2007.12.003
  • Vo, TP., Lee, J. 2009. Flexural–torsional behavior of thin-walled composite space frames. International Journal of Mechanical Sciences, 51(11-12):837-845. doi:10.1016/j.ijmecsci.2009.09.019
  • Vojnić-Purčar, M., Prokić, A., Bešević, M. 2019. A numerical model for laminated composite thin-walled members with openings considering shear lag effect. Engineering Structures, 185: 392-399. doi:10.1016/j.engstruct.2019.01.142
  • Vukasović, M., Pavazza, R., Vlak, F. 2017. Analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear. The Journal of Strain Analysis for Engineering Design, 52(3): 190-203. doi:10.1177/0309324717697524
  • Wang, XF., Yang, QS., Law S-S. 2014. A shear locking-free spatial beam element with general thin-walled closed cross-section. Engineering Structures, 58:12–24. doi:10.1016/j.engstruct.2013.09.046
  • Yanlin, G., Shaofan, C. 1991. Postbuckling interaction analysis of cold-formed thin-walled channel sections by finite strip method. Thin-Walled Structures, 11(3): 277-289. doi:10.1016/0263-8231(91)90004-3
  • Yu, W., Hodges, D.H., Ho, J.C. 2012. Variational asymptotic beam sectional analysis - An updated version. International Journal of Engineering Science, 59: 40-64. doi:10.1016/j.ijengsci.2012.03.006
  • Zhang, YM., Gu, Y., Chen, JT. 2011. Boundary element analysis of 2D thin walled structures with high-order geometry elements using transformation. Engineering Analysis with Boundary Elements, 35(3):581-586. doi:10.1016/j.enganabound.2010.07.008
Toplam 57 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İnşaat Mühendisliğinde Sayısal Modelleme
Bölüm Research Article
Yazarlar

Yıldırım Serhat Erdoğan 0000-0001-9206-5474

Mehmet Ada 0000-0002-7099-590X

Yayımlanma Tarihi 22 Nisan 2025
Gönderilme Tarihi 2 Eylül 2024
Kabul Tarihi 16 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 15 Sayı: 1

Kaynak Göster

APA Erdoğan, Y. S., & Ada, M. (2025). A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes. Karaelmas Fen Ve Mühendislik Dergisi, 15(1), 75-94. https://doi.org/10.7212/karaelmasfen.1542278
AMA Erdoğan YS, Ada M. A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes. Karaelmas Fen ve Mühendislik Dergisi. Nisan 2025;15(1):75-94. doi:10.7212/karaelmasfen.1542278
Chicago Erdoğan, Yıldırım Serhat, ve Mehmet Ada. “A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes”. Karaelmas Fen Ve Mühendislik Dergisi 15, sy. 1 (Nisan 2025): 75-94. https://doi.org/10.7212/karaelmasfen.1542278.
EndNote Erdoğan YS, Ada M (01 Nisan 2025) A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes. Karaelmas Fen ve Mühendislik Dergisi 15 1 75–94.
IEEE Y. S. Erdoğan ve M. Ada, “A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes”, Karaelmas Fen ve Mühendislik Dergisi, c. 15, sy. 1, ss. 75–94, 2025, doi: 10.7212/karaelmasfen.1542278.
ISNAD Erdoğan, Yıldırım Serhat - Ada, Mehmet. “A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes”. Karaelmas Fen ve Mühendislik Dergisi 15/1 (Nisan 2025), 75-94. https://doi.org/10.7212/karaelmasfen.1542278.
JAMA Erdoğan YS, Ada M. A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes. Karaelmas Fen ve Mühendislik Dergisi. 2025;15:75–94.
MLA Erdoğan, Yıldırım Serhat ve Mehmet Ada. “A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes”. Karaelmas Fen Ve Mühendislik Dergisi, c. 15, sy. 1, 2025, ss. 75-94, doi:10.7212/karaelmasfen.1542278.
Vancouver Erdoğan YS, Ada M. A Beam Element Formulation for the Analysis of Isotropic and Anisotropic Thin-Walled Beams Using Cross Section Displacement Modes. Karaelmas Fen ve Mühendislik Dergisi. 2025;15(1):75-94.
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