Araştırma Makalesi
BibTex RIS Kaynak Göster

DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ

Yıl 2024, Cilt: 29 Sayı: 2, 393 - 412, 30.08.2024

Uğur Kafkas

https://doi.org/10.17482/uumfd.1459934

Öz

Üretim aşamasında çeşitli sorunlar sebebiyle gözenek oluşumu fonksiyonel derecelendirilmiş kirişlerde sıklıkla gözlemlenmektedir. Bu çalışmada gözenekli fonksiyonel derecelendirilmiş konsol nanokirişlerin değiştirilmiş gerilme çifti teorisi çerçevesinde sonlu elemanlar yöntemi kullanılarak statik yükler altında düşey yer değiştirmeleri incelenmiştir. Fonksiyonel derecelendirilmiş kirişlerin malzeme dağılımlarında kuvvet yasası teorisi, gözenek dağılımı içinse düzenli ve düzensiz dağılım olmak üzere iki model kullanılmıştır. Çalışma kapsamında gözeneksiz ve gözenekli fonksiyonel derecelendirilmiş konsol nano-kirişlerin düşey yer değiştirmelerinde, gözenek dağılım modellerinin, gözeneklilik parametresinin, değiştirilmiş gerilme çifti teorisinden gelen malzeme uzunluk ölçeği parametresinin ve kuvvet yasası parametresinin etkisi tablolar ve şekiller vasıtasıyla sunulmuştur. Çalışmada, malzeme uzunluk ölçeği parametresinin nano-kirişin rijitliğini arttırıcı etkisinin olduğu ve düzensiz gözenek dağılımına sahip nanokirişlerin, düzenli gözenek dağılımına sahip olanlara göre daha rijit davrandığı sonuçlarına ulaşılmıştır.

Anahtar Kelimeler

Fonksiyonel derecelendirilmiş malzeme Gözeneklilik Nano-kiriş Değiştirilmiş gerilme çifti teorisi Sonlu elemanlar yöntemi

Kaynakça

  • Akbaş, Ş. D. (2017). Static, Vibration, and Buckling Analysis of Nanobeams. Nanomechanics. InTech. https://doi.org/10.5772/67973
  • Akbaş, Ş. D. (2018). Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  • Akgöz, B. ve Civalek, Ö. (2011). Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science, 49(11), 1268-1280. https://doi.org/10.1016/j.ijengsci.2010.12.009
  • Akgöz, B., ve Civalek, Ö. (2012). Investigation of Size Effects on Static Response of SingleWalled Carbon Nanotubes Based on Strain Gradient Elasticity. International Journal of Computational Methods, 09(02), 1240032. https://doi.org/10.1142/S0219876212400324
  • Akgöz, B. ve Civalek, Ö. (2015). Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Composite Structures, 134, 294-301. https://doi.org/10.1016/j.compstruct.2015.08.095
  • Alnujaie, A., Akbas, S. D., Eltaher, M. A. ve Assie, A. E. (2021). Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems, 27(4), 679-689. https://doi.org/https://doi.org/10.12989/sss.2021.27.4.669
  • Arefi, M., ve Amabili, M. (2021). A comprehensive electro-magneto-elastic buckling and bending analyses of three-layered doubly curved nanoshell, based on nonlocal threedimensional theory. Composite Structures, 257, 113100. https://doi.org/10.1016/j.compstruct.2020.113100
  • Arefi, M., Mohammad-Rezaei Bidgoli, E., Dimitri, R., Bacciocchi, M. ve Tornabene, F. (2019). Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets. Composites Part B: Engineering, 166, 1-12. https://doi.org/10.1016/j.compositesb.2018.11.092
  • Arshad, S. H., Naeem, M. N., ve Sultana, N. (2007). Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 221(12), 1483-1495. https://doi.org/10.1243/09544062JMES738
  • Askari, A. R. ve Tahani, M. (2015). Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory. Journal of Mechanical Science and Technology, 29(5), 2135-2145. https://doi.org/10.1007/s12206-015-0435-0
  • Avcar, M. (2019). Free vibration of imperfect sigmoid and power law functionally graded beams. Steel and Composite Structures, 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  • Chen, D., Gao, K., Yang, J. ve Zhang, L. (2023). Functionally graded porous structures: Analyses, performances, and applications – A Review. Thin-Walled Structures, 191, 111046. https://doi.org/10.1016/j.tws.2023.111046
  • Civalek, Ö., Ersoy, H., Uzun, B. ve Yaylı, M. Ö. (2023). Dynamics of a FG porous microbeam with metal foam under deformable boundaries. Acta Mechanica, 234(11), 5385-5404. https://doi.org/10.1007/s00707-023-03663-7
  • Civalek, Ö., Uzun, B., ve Yaylı, M. Ö. (2020). Frequency, bending and buckling loads of nanobeams with different cross sections. Advances in Nano Research, 9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091
  • Daghigh, H., Daghigh, V., Milani, A., Tannant, D., Lacy, T. E. ve Reddy, J. N. (2020). Nonlocal bending and buckling of agglomerated CNT-Reinforced composite nanoplates. Composites Part B: Engineering, 183, 107716. https://doi.org/10.1016/j.compositesb.2019.107716
  • Dastjerdi, S., ve Akgöz, B. (2019). On the statics of fullerene structures. International Journal of Engineering Science, 142, 125-144. https://doi.org/10.1016/j.ijengsci.2019.06.002
  • Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T. ve Eremeyev, V. A. (2022). On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. International Journal of Engineering Science, 170, 103604. https://doi.org/10.1016/j.ijengsci.2021.103604
  • Demir, Ç. ve Civalek, Ö. (2017). On the analysis of microbeams. International Journal of Engineering Science, 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016
  • Eltaher, M. A., Emam, S. A. ve Mahmoud, F. F. (2012). Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation, 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  • Eltaher, M. A., Khairy, A., Sadoun, A. M. ve Omar, F.-A. (2014). Static and buckling analysis of functionally graded Timoshenko nanobeams. Applied Mathematics and Computation, 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
  • Esen, I. ve Özmen, R. (2022). Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity. Composite Structures, 296, 115878. https://doi.org/10.1016/j.compstruct.2022.115878
  • Fouda, N., El-Midany, T. ve Sadoun, A. M. (2017). Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of applied and computational mechanics, 3(4), 274-282. https://doi.org/10.22055/JACM.2017.21924.1121
  • Güçlü, G., ve Artan, R. (2020). Large elastic deflections of bars based on nonlocal elasticity. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 100(4), e201900108. https://doi.org/10.1002/zamm.201900108
  • Hamed, M. A., Sadoun, A. M. ve Eltaher, M. A. (2019). Effects of porosity models on static behavior of size dependent functionally graded beam. Structural Engineering and Mechanics, An Int’l Journal, 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089
  • Ike, C. C. (2019). Point Collocation Method for the Analysis of Euler-Bernoulli Beam on Winkler Foundation. International Journal of Darshan Institute on Engineering Research and Emerging Technologies, 7(2), 1. https://doi.org/10.32692/IJDI-ERET/7.2.2018.1801
  • Jalaei, M. H. ve Civalek, Ӧ. (2019). On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. International Journal of Engineering Science, 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013
  • Jia, X. L., Ke, L. L., Zhong, X. L., Sun, Y., Yang, J. ve Kitipornchai, S. (2018). Thermalmechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory. Composite Structures, 202, 625-634. https://doi.org/10.1016/j.compstruct.2018.03.025
  • Kafkas, U., Uzun, B., Yaylı, M. Ö., ve Güçlü, G. (2023). Thermal vibration of perforated nanobeams with deformable boundary conditions via nonlocal strain gradient theory. Zeitschrift für Naturforschung A, 78(8). https://doi.org/10.1515/zna-2023-0088
  • Kafkas, U., Ünal, Y., Yaylı, M. Ö., ve Uzun, B. (2023). Buckling analysis of perforated nano/microbeams with deformable boundary conditions via nonlocal strain gradient elasticity. Advances in Nano Research, 15(4), 339-353. https://doi.org/10.12989/anr.2023.15.4.339
  • Kahya, V. ve Turan, M. (2018). Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering, 146, 198- 212. https://doi.org/10.1016/j.compositesb.2018.04.011
  • Karamanli, A., ve Vo, T. P. (2022). Finite element model for free vibration analysis of curved zigzag nanobeams. Composite Structures, 282, 115097. https://doi.org/10.1016/J.COMPSTRUCT.2021.115097
  • Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. ve Tong, P. (2003). Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  • Li, Y. S. ve Pan, E. (2015). Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory. International Journal of Engineering Science, 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009
  • Logan, D. L. (2011). A first course in the finite element method (4. bs). Thomson.
  • Ma, H., Gao, X. ve Reddy, J. (2008). A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. Journal of the Mechanics and Physics of Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  • Ma, H. M., Gao, X.-L. ve Reddy, J. N. (2011). A non-classical Mindlin plate model based on a modified couple stress theory. Acta Mechanica, 220(1-4), 217-235. https://doi.org/10.1007/s00707-011-0480-4
  • Mercan, K., Numanoglu, H. M., Akgöz, B., Demir, C. ve Civalek, Ö. (2017). Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 87(11), 1797-1814. https://doi.org/10.1007/s00419- 017-1288-z
  • Mollamahmutoğlu, Ç., ve Mercan, A. (2019). A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory. Composite Structures, 223, 110950. https://doi.org/10.1016/j.compstruct.2019.110950
  • Murmu, T., ve Pradhan, S. C. (2009). Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E: Low-dimensional Systems and Nanostructures, 41(7), 1232- 1239. https://doi.org/10.1016/J.PHYSE.2009.02.004
  • Najafzadeh, M., Adeli, M. M., Zarezadeh, E. ve Hadi, A. (2020). Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field. Mechanics Based Design of Structures and Machines. https://doi.org/10.1080/15397734.2020.1733602
  • Numanoğlu, H. M. (2021). Examination of How Size-Effect Modifies the Stiffness and Mass Matrices of Nanotrusses/Nanoframes. International Journal of Engineering and Applied Sciences, 13(4), 155-165. https://doi.org/10.24107/ijeas.1036574
  • Numanoğlu, H. M., Akgöz, B. ve Civalek, Ö. (2018). On dynamic analysis of nanorods. International Journal of Engineering Science, 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001
  • Park, S. K. ve Gao, X.-L. (2006). Bernoulli–Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16(11), 2355-2359. https://doi.org/10.1088/0960-1317/16/11/015
  • Polat, S. C. ve Bağdatlı, S. M. (2023). Investigation of stepped microbeam vibration motions according to modified couple stress theory. Zeitschrift für Naturforschung A, 78(5), 379-393. https://doi.org/10.1515/zna-2022-0286
  • Reddy, J. N. (2007). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2-8), 288-307. https://doi.org/10.1016/J.IJENGSCI.2007.04.004
  • Reddy, J. N. (2022). Theories and Analyses of Beams and Axisymmetric Circular Plates. Boca Raton: CRC Press. https://doi.org/10.1201/9781003240846
  • Saraçoğlu, M. H., Güçlü, G. ve Uslu, F. (2022). Deflection analysis of functionally graded equal strength beams. European Mechanical Science, 6(2), 119-128. https://doi.org/10.26701/ems.1015629
  • Soltani, M., Atoufi, F., Mohri, F., Dimitri, R. ve Tornabene, F. (2021). Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials. Thin-Walled Structures, 159, 107268. https://doi.org/10.1016/j.tws.2020.107268
  • Tadi Beni, Y., Mehralian, F. ve Zeighampour, H. (2016). The modified couple stress functionally graded cylindrical thin shell formulation. Mechanics of Advanced Materials and Structures, 23(7), 791-801. https://doi.org/10.1080/15376494.2015.1029167
  • Talha, M. ve Singh, B. N. (2010). Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling, 34(12), 3991- 4011. https://doi.org/10.1016/j.apm.2010.03.034
  • Togun, N. ve Bağdatli, S. M. (2016). Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255-262. https://doi.org/10.1016/j.compositesb.2016.04.074
  • Tran, T. T. ve Le, P. B. (2023). Nonlocal dynamic response analysis of functionally graded porous L-shape nanoplates resting on elastic foundation using finite element formulation. Engineering with Computers, 39(1), 809-825. https://doi.org/10.1007/s00366-022-01679-6
  • Tsiatas, G. C. (2009). A new Kirchhoff plate model based on a modified couple stress theory. International Journal of Solids and Structures, 46(13), 2757-2764. https://doi.org/10.1016/j.ijsolstr.2009.03.004
  • Turan, M. (2022). Fonksiyonel Derecelendirilmiş Gözenekli Kirişlerin Sonlu Elemanlar Yöntemiyle Statik Analizi. Mühendislik Bilimleri ve Tasarım Dergisi, 10(4), 1362-1374. https://doi.org/10.21923/jesd.1134356
  • Turan, M., ve Kahya, V. (2018). Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119-130. https://doi.org/10.31466/kfbd.453833
  • Turan, M., ve Kahya, V. (2021). Fonksiyonel derecelendirilmiş sandviç kirişlerin Navier yöntemiyle serbest titreşim ve burkulma analizi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 36(2), 743-758. https://doi.org/10.17341/gazimmfd.599928
  • Uzun, B., Kafkas, U., Deliktaş, B. ve Yaylı, M. Ö. (2022). Size-Dependent Vibration of Porous Bishop Nanorod with Arbitrary Boundary Conditions and Nonlocal Elasticity Effects. Journal of Vibration Engineering & Technologies. https://doi.org/10.1007/s42417-022- 00610-z
  • Uzun, B., Kafkas, U. ve Yaylı, M. Ö. (2020). Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 100(12), e202000039. https://doi.org/10.1002/ZAMM.202000039
  • Uzun, B., Kafkas, U. ve Yaylı, M. Ö. (2021). Free vibration analysis of nanotube based sensors including rotary inertia based on the Rayleigh beam and modified couple stress theories. Microsystem Technologies, 27(5), 1913-1923. https://doi.org/10.1007/s00542-020- 04961-z
  • Uzun, B. ve Yaylı, M. Ö. (2022a). Porosity dependent torsional vibrations of restrained FG nanotubes using modified couple stress theory. Materials Today Communications, 32, 103969. https://doi.org/10.1016/J.MTCOMM.2022.103969
  • Uzun, B. ve Yaylı, M. Ö. (2022b). A Finite Element Solution for Bending Analysis of a Nanoframe using Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences, 14(1), 1-14. https://doi.org/10.24107/ijeas.1064690
  • Uzun, B. ve Yayli, M. Ö. (2024). Rotary inertia effect on dynamic analysis of embedded FG porous nanobeams under deformable boundary conditions with the effect of neutral axis. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(2), 111. https://doi.org/10.1007/s40430-023-04605-z
  • Wang, L. (2010). Size-dependent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 26(4), 675-684. https://doi.org/10.1016/j.jfluidstructs.2010.02.005
  • Wang, Y. Q. ve Zu, J. W. (2017). Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerospace Science and Technology, 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023
  • Wattanasakulpong, N. ve Ungbhakorn, V. (2014). Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  • Xia, W., Wang, L. ve Yin, L. (2010). Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. International Journal of Engineering Science, 48(12), 2044-2053. https://doi.org/10.1016/j.ijengsci.2010.04.010
  • Yang, F., Chong, A. C. M., Lam, D. C. C. ve Tong, P. (2002). Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10), 2731- 2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  • Yayli, M. Ö. (2018). Torsional vibrations of restrained nanotubes using modified couple stress theory. Microsystem Technologies, 24(8), 3425-3435. https://doi.org/10.1007/s00542- 018-3735-3
  • Yayli, M. Ö. (2019). Stability analysis of a rotationally restrained microbar embedded in an elastic matrix using strain gradient elasticity. Curved and Layered Structures, 6(1), 1-10. https://doi.org/10.1515/cls-2019-0001
  • Zahedinejad, P., Zhang, C., Zhang, H., ve Ju, S. (2020). A Comprehensive Review on Vibration Analysis of Functionally Graded Beams. International Journal of Structural Stability and Dynamics, 20(04), 2030002. https://doi.org/10.1142/S0219455420300025
  • Zghal, S., Ataoui, D. ve Dammak, F. (2022). Static bending analysis of beams made of functionally graded porous materials. Mechanics Based Design of Structures and Machines, 50(3), 1012-1029. https://doi.org/10.1080/15397734.2020.1748053

Static Analysis of Porous Functionally Graded Cantilever Nano-Beams Via Modified Couple Stress Theory

Yıl 2024, Cilt: 29 Sayı: 2, 393 - 412, 30.08.2024

Uğur Kafkas

https://doi.org/10.17482/uumfd.1459934

Öz

Porosity formation is a common phenomenon in functionally graded beams due to various problems during the manufacturing process. This study uses the finite element method within the modified couple stress theory framework to investigate vertical displacements of porous functionally graded cantilever nano-beams under static loads. Power law theory is used for the material distribution of the functionally graded beams, and two models are used for the porosity distribution, namely even and uneven distribution. Within the scope of the study, the effect of porosity distribution models, porosity parameter, material length scale parameter from modified couple stress theory and power law parameter on the vertical displacements of non-porous and porous functionally graded cantilever nano-beams are presented in tables and figures. It is concluded that the material length scale parameter has an increasing effect on the stiffness of the nano-beam and that nano-beams with uneven porosity distribution behave more rigidly than those with even porosity distribution.

Anahtar Kelimeler

Functionally graded material Porosity Nano-beam Modified couple stress theory Finite element method

Kaynakça

  • Akbaş, Ş. D. (2017). Static, Vibration, and Buckling Analysis of Nanobeams. Nanomechanics. InTech. https://doi.org/10.5772/67973
  • Akbaş, Ş. D. (2018). Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  • Akgöz, B. ve Civalek, Ö. (2011). Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Science, 49(11), 1268-1280. https://doi.org/10.1016/j.ijengsci.2010.12.009
  • Akgöz, B., ve Civalek, Ö. (2012). Investigation of Size Effects on Static Response of SingleWalled Carbon Nanotubes Based on Strain Gradient Elasticity. International Journal of Computational Methods, 09(02), 1240032. https://doi.org/10.1142/S0219876212400324
  • Akgöz, B. ve Civalek, Ö. (2015). Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Composite Structures, 134, 294-301. https://doi.org/10.1016/j.compstruct.2015.08.095
  • Alnujaie, A., Akbas, S. D., Eltaher, M. A. ve Assie, A. E. (2021). Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems, 27(4), 679-689. https://doi.org/https://doi.org/10.12989/sss.2021.27.4.669
  • Arefi, M., ve Amabili, M. (2021). A comprehensive electro-magneto-elastic buckling and bending analyses of three-layered doubly curved nanoshell, based on nonlocal threedimensional theory. Composite Structures, 257, 113100. https://doi.org/10.1016/j.compstruct.2020.113100
  • Arefi, M., Mohammad-Rezaei Bidgoli, E., Dimitri, R., Bacciocchi, M. ve Tornabene, F. (2019). Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets. Composites Part B: Engineering, 166, 1-12. https://doi.org/10.1016/j.compositesb.2018.11.092
  • Arshad, S. H., Naeem, M. N., ve Sultana, N. (2007). Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 221(12), 1483-1495. https://doi.org/10.1243/09544062JMES738
  • Askari, A. R. ve Tahani, M. (2015). Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory. Journal of Mechanical Science and Technology, 29(5), 2135-2145. https://doi.org/10.1007/s12206-015-0435-0
  • Avcar, M. (2019). Free vibration of imperfect sigmoid and power law functionally graded beams. Steel and Composite Structures, 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  • Chen, D., Gao, K., Yang, J. ve Zhang, L. (2023). Functionally graded porous structures: Analyses, performances, and applications – A Review. Thin-Walled Structures, 191, 111046. https://doi.org/10.1016/j.tws.2023.111046
  • Civalek, Ö., Ersoy, H., Uzun, B. ve Yaylı, M. Ö. (2023). Dynamics of a FG porous microbeam with metal foam under deformable boundaries. Acta Mechanica, 234(11), 5385-5404. https://doi.org/10.1007/s00707-023-03663-7
  • Civalek, Ö., Uzun, B., ve Yaylı, M. Ö. (2020). Frequency, bending and buckling loads of nanobeams with different cross sections. Advances in Nano Research, 9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091
  • Daghigh, H., Daghigh, V., Milani, A., Tannant, D., Lacy, T. E. ve Reddy, J. N. (2020). Nonlocal bending and buckling of agglomerated CNT-Reinforced composite nanoplates. Composites Part B: Engineering, 183, 107716. https://doi.org/10.1016/j.compositesb.2019.107716
  • Dastjerdi, S., ve Akgöz, B. (2019). On the statics of fullerene structures. International Journal of Engineering Science, 142, 125-144. https://doi.org/10.1016/j.ijengsci.2019.06.002
  • Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T. ve Eremeyev, V. A. (2022). On the deformation and frequency analyses of SARS-CoV-2 at nanoscale. International Journal of Engineering Science, 170, 103604. https://doi.org/10.1016/j.ijengsci.2021.103604
  • Demir, Ç. ve Civalek, Ö. (2017). On the analysis of microbeams. International Journal of Engineering Science, 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016
  • Eltaher, M. A., Emam, S. A. ve Mahmoud, F. F. (2012). Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation, 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  • Eltaher, M. A., Khairy, A., Sadoun, A. M. ve Omar, F.-A. (2014). Static and buckling analysis of functionally graded Timoshenko nanobeams. Applied Mathematics and Computation, 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
  • Esen, I. ve Özmen, R. (2022). Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity. Composite Structures, 296, 115878. https://doi.org/10.1016/j.compstruct.2022.115878
  • Fouda, N., El-Midany, T. ve Sadoun, A. M. (2017). Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of applied and computational mechanics, 3(4), 274-282. https://doi.org/10.22055/JACM.2017.21924.1121
  • Güçlü, G., ve Artan, R. (2020). Large elastic deflections of bars based on nonlocal elasticity. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 100(4), e201900108. https://doi.org/10.1002/zamm.201900108
  • Hamed, M. A., Sadoun, A. M. ve Eltaher, M. A. (2019). Effects of porosity models on static behavior of size dependent functionally graded beam. Structural Engineering and Mechanics, An Int’l Journal, 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089
  • Ike, C. C. (2019). Point Collocation Method for the Analysis of Euler-Bernoulli Beam on Winkler Foundation. International Journal of Darshan Institute on Engineering Research and Emerging Technologies, 7(2), 1. https://doi.org/10.32692/IJDI-ERET/7.2.2018.1801
  • Jalaei, M. H. ve Civalek, Ӧ. (2019). On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. International Journal of Engineering Science, 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013
  • Jia, X. L., Ke, L. L., Zhong, X. L., Sun, Y., Yang, J. ve Kitipornchai, S. (2018). Thermalmechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory. Composite Structures, 202, 625-634. https://doi.org/10.1016/j.compstruct.2018.03.025
  • Kafkas, U., Uzun, B., Yaylı, M. Ö., ve Güçlü, G. (2023). Thermal vibration of perforated nanobeams with deformable boundary conditions via nonlocal strain gradient theory. Zeitschrift für Naturforschung A, 78(8). https://doi.org/10.1515/zna-2023-0088
  • Kafkas, U., Ünal, Y., Yaylı, M. Ö., ve Uzun, B. (2023). Buckling analysis of perforated nano/microbeams with deformable boundary conditions via nonlocal strain gradient elasticity. Advances in Nano Research, 15(4), 339-353. https://doi.org/10.12989/anr.2023.15.4.339
  • Kahya, V. ve Turan, M. (2018). Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element. Composites Part B: Engineering, 146, 198- 212. https://doi.org/10.1016/j.compositesb.2018.04.011
  • Karamanli, A., ve Vo, T. P. (2022). Finite element model for free vibration analysis of curved zigzag nanobeams. Composite Structures, 282, 115097. https://doi.org/10.1016/J.COMPSTRUCT.2021.115097
  • Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. ve Tong, P. (2003). Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  • Li, Y. S. ve Pan, E. (2015). Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory. International Journal of Engineering Science, 97, 40-59. https://doi.org/10.1016/j.ijengsci.2015.08.009
  • Logan, D. L. (2011). A first course in the finite element method (4. bs). Thomson.
  • Ma, H., Gao, X. ve Reddy, J. (2008). A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. Journal of the Mechanics and Physics of Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  • Ma, H. M., Gao, X.-L. ve Reddy, J. N. (2011). A non-classical Mindlin plate model based on a modified couple stress theory. Acta Mechanica, 220(1-4), 217-235. https://doi.org/10.1007/s00707-011-0480-4
  • Mercan, K., Numanoglu, H. M., Akgöz, B., Demir, C. ve Civalek, Ö. (2017). Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix. Archive of Applied Mechanics, 87(11), 1797-1814. https://doi.org/10.1007/s00419- 017-1288-z
  • Mollamahmutoğlu, Ç., ve Mercan, A. (2019). A novel functional and mixed finite element analysis of functionally graded micro-beams based on modified couple stress theory. Composite Structures, 223, 110950. https://doi.org/10.1016/j.compstruct.2019.110950
  • Murmu, T., ve Pradhan, S. C. (2009). Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E: Low-dimensional Systems and Nanostructures, 41(7), 1232- 1239. https://doi.org/10.1016/J.PHYSE.2009.02.004
  • Najafzadeh, M., Adeli, M. M., Zarezadeh, E. ve Hadi, A. (2020). Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field. Mechanics Based Design of Structures and Machines. https://doi.org/10.1080/15397734.2020.1733602
  • Numanoğlu, H. M. (2021). Examination of How Size-Effect Modifies the Stiffness and Mass Matrices of Nanotrusses/Nanoframes. International Journal of Engineering and Applied Sciences, 13(4), 155-165. https://doi.org/10.24107/ijeas.1036574
  • Numanoğlu, H. M., Akgöz, B. ve Civalek, Ö. (2018). On dynamic analysis of nanorods. International Journal of Engineering Science, 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001
  • Park, S. K. ve Gao, X.-L. (2006). Bernoulli–Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16(11), 2355-2359. https://doi.org/10.1088/0960-1317/16/11/015
  • Polat, S. C. ve Bağdatlı, S. M. (2023). Investigation of stepped microbeam vibration motions according to modified couple stress theory. Zeitschrift für Naturforschung A, 78(5), 379-393. https://doi.org/10.1515/zna-2022-0286
  • Reddy, J. N. (2007). Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2-8), 288-307. https://doi.org/10.1016/J.IJENGSCI.2007.04.004
  • Reddy, J. N. (2022). Theories and Analyses of Beams and Axisymmetric Circular Plates. Boca Raton: CRC Press. https://doi.org/10.1201/9781003240846
  • Saraçoğlu, M. H., Güçlü, G. ve Uslu, F. (2022). Deflection analysis of functionally graded equal strength beams. European Mechanical Science, 6(2), 119-128. https://doi.org/10.26701/ems.1015629
  • Soltani, M., Atoufi, F., Mohri, F., Dimitri, R. ve Tornabene, F. (2021). Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials. Thin-Walled Structures, 159, 107268. https://doi.org/10.1016/j.tws.2020.107268
  • Tadi Beni, Y., Mehralian, F. ve Zeighampour, H. (2016). The modified couple stress functionally graded cylindrical thin shell formulation. Mechanics of Advanced Materials and Structures, 23(7), 791-801. https://doi.org/10.1080/15376494.2015.1029167
  • Talha, M. ve Singh, B. N. (2010). Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling, 34(12), 3991- 4011. https://doi.org/10.1016/j.apm.2010.03.034
  • Togun, N. ve Bağdatli, S. M. (2016). Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255-262. https://doi.org/10.1016/j.compositesb.2016.04.074
  • Tran, T. T. ve Le, P. B. (2023). Nonlocal dynamic response analysis of functionally graded porous L-shape nanoplates resting on elastic foundation using finite element formulation. Engineering with Computers, 39(1), 809-825. https://doi.org/10.1007/s00366-022-01679-6
  • Tsiatas, G. C. (2009). A new Kirchhoff plate model based on a modified couple stress theory. International Journal of Solids and Structures, 46(13), 2757-2764. https://doi.org/10.1016/j.ijsolstr.2009.03.004
  • Turan, M. (2022). Fonksiyonel Derecelendirilmiş Gözenekli Kirişlerin Sonlu Elemanlar Yöntemiyle Statik Analizi. Mühendislik Bilimleri ve Tasarım Dergisi, 10(4), 1362-1374. https://doi.org/10.21923/jesd.1134356
  • Turan, M., ve Kahya, V. (2018). Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi. Karadeniz Fen Bilimleri Dergisi, 8(2), 119-130. https://doi.org/10.31466/kfbd.453833
  • Turan, M., ve Kahya, V. (2021). Fonksiyonel derecelendirilmiş sandviç kirişlerin Navier yöntemiyle serbest titreşim ve burkulma analizi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 36(2), 743-758. https://doi.org/10.17341/gazimmfd.599928
  • Uzun, B., Kafkas, U., Deliktaş, B. ve Yaylı, M. Ö. (2022). Size-Dependent Vibration of Porous Bishop Nanorod with Arbitrary Boundary Conditions and Nonlocal Elasticity Effects. Journal of Vibration Engineering & Technologies. https://doi.org/10.1007/s42417-022- 00610-z
  • Uzun, B., Kafkas, U. ve Yaylı, M. Ö. (2020). Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 100(12), e202000039. https://doi.org/10.1002/ZAMM.202000039
  • Uzun, B., Kafkas, U. ve Yaylı, M. Ö. (2021). Free vibration analysis of nanotube based sensors including rotary inertia based on the Rayleigh beam and modified couple stress theories. Microsystem Technologies, 27(5), 1913-1923. https://doi.org/10.1007/s00542-020- 04961-z
  • Uzun, B. ve Yaylı, M. Ö. (2022a). Porosity dependent torsional vibrations of restrained FG nanotubes using modified couple stress theory. Materials Today Communications, 32, 103969. https://doi.org/10.1016/J.MTCOMM.2022.103969
  • Uzun, B. ve Yaylı, M. Ö. (2022b). A Finite Element Solution for Bending Analysis of a Nanoframe using Modified Couple Stress Theory. International Journal of Engineering and Applied Sciences, 14(1), 1-14. https://doi.org/10.24107/ijeas.1064690
  • Uzun, B. ve Yayli, M. Ö. (2024). Rotary inertia effect on dynamic analysis of embedded FG porous nanobeams under deformable boundary conditions with the effect of neutral axis. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46(2), 111. https://doi.org/10.1007/s40430-023-04605-z
  • Wang, L. (2010). Size-dependent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 26(4), 675-684. https://doi.org/10.1016/j.jfluidstructs.2010.02.005
  • Wang, Y. Q. ve Zu, J. W. (2017). Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerospace Science and Technology, 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023
  • Wattanasakulpong, N. ve Ungbhakorn, V. (2014). Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  • Xia, W., Wang, L. ve Yin, L. (2010). Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. International Journal of Engineering Science, 48(12), 2044-2053. https://doi.org/10.1016/j.ijengsci.2010.04.010
  • Yang, F., Chong, A. C. M., Lam, D. C. C. ve Tong, P. (2002). Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10), 2731- 2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  • Yayli, M. Ö. (2018). Torsional vibrations of restrained nanotubes using modified couple stress theory. Microsystem Technologies, 24(8), 3425-3435. https://doi.org/10.1007/s00542- 018-3735-3
  • Yayli, M. Ö. (2019). Stability analysis of a rotationally restrained microbar embedded in an elastic matrix using strain gradient elasticity. Curved and Layered Structures, 6(1), 1-10. https://doi.org/10.1515/cls-2019-0001
  • Zahedinejad, P., Zhang, C., Zhang, H., ve Ju, S. (2020). A Comprehensive Review on Vibration Analysis of Functionally Graded Beams. International Journal of Structural Stability and Dynamics, 20(04), 2030002. https://doi.org/10.1142/S0219455420300025
  • Zghal, S., Ataoui, D. ve Dammak, F. (2022). Static bending analysis of beams made of functionally graded porous materials. Mechanics Based Design of Structures and Machines, 50(3), 1012-1029. https://doi.org/10.1080/15397734.2020.1748053
Toplam 71 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İnşaat Mühendisliği (Diğer)
Bölüm Araştırma Makaleleri
Yazarlar

Uğur Kafkas 0000-0003-1730-7810

Erken Görünüm Tarihi 20 Ağustos 2024
Yayımlanma Tarihi 30 Ağustos 2024
Gönderilme Tarihi 27 Mart 2024
Kabul Tarihi 20 Mayıs 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 29 Sayı: 2

Kaynak Göster

APA Kafkas, U. (2024). DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 29(2), 393-412. https://doi.org/10.17482/uumfd.1459934
AMA Kafkas U. DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ. UUJFE. Ağustos 2024;29(2):393-412. doi:10.17482/uumfd.1459934
Chicago Kafkas, Uğur. “DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29, sy. 2 (Ağustos 2024): 393-412. https://doi.org/10.17482/uumfd.1459934.
EndNote Kafkas U (01 Ağustos 2024) DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29 2 393–412.
IEEE U. Kafkas, “DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ”, UUJFE, c. 29, sy. 2, ss. 393–412, 2024, doi: 10.17482/uumfd.1459934.
ISNAD Kafkas, Uğur. “DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 29/2 (Ağustos 2024), 393-412. https://doi.org/10.17482/uumfd.1459934.
JAMA Kafkas U. DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ. UUJFE. 2024;29:393–412.
MLA Kafkas, Uğur. “DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, c. 29, sy. 2, 2024, ss. 393-12, doi:10.17482/uumfd.1459934.
Vancouver Kafkas U. DEĞİŞTİRİLMİŞ GERİLME ÇİFTİ TEORİSİ İLE GÖZENEKLİ FONKSİYONEL DERECELENDİRİLMİŞ KONSOL NANO-KİRİŞLERİN STATİK ANALİZİ. UUJFE. 2024;29(2):393-412.

DUYURU:

30.03.2021- Nisan 2021 (26/1) sayımızdan itibaren TR-Dizin yeni kuralları gereği, dergimizde basılacak makalelerde, ilk gönderim aşamasında Telif Hakkı Formu yanısıra, Çıkar Çatışması Bildirim Formu ve Yazar Katkısı Bildirim Formu da tüm yazarlarca imzalanarak gönderilmelidir. Yayınlanacak makalelerde de makale metni içinde "Çıkar Çatışması" ve "Yazar Katkısı" bölümleri yer alacaktır. İlk gönderim aşamasında doldurulması gereken yeni formlara "Yazım Kuralları" ve "Makale Gönderim Süreci" sayfalarımızdan ulaşılabilir. (Değerlendirme süreci bu tarihten önce tamamlanıp basımı bekleyen makalelerin yanısıra değerlendirme süreci devam eden makaleler için, yazarlar tarafından ilgili formlar doldurularak sisteme yüklenmelidir).  Makale şablonları da, bu değişiklik doğrultusunda güncellenmiştir. Tüm yazarlarımıza önemle duyurulur.

Bursa Uludağ Üniversitesi, Mühendislik Fakültesi Dekanlığı, Görükle Kampüsü, Nilüfer, 16059 Bursa. Tel: (224) 294 1907, Faks: (224) 294 1903, e-posta: mmfd@uludag.edu.tr