Yıl 2018, Cilt 6, Sayı 2, Sayfalar 164 - 178 2018-08-03
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## trenAnalytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam TheoryAnalytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory

#### Armağan Karamanlı [1]

##### 50 82

This paper is dedicated to present a Ritz-type analytical solution for buckling behavior of two directional functionally graded beams (2D-FGBs) subjected to various sets of boundary conditions by employing a third order shear deformation theory. The material properties of the beam vary in both axial and thickness directions according to the power-law distribution. The axial, transverse deflections and rotation of the cross sections are expressed in polynomial forms to obtain the buckling load. The auixiliary functions are added to displacement functions to satisfy the boundary conditions. Simply supported – Simply supported (SS), Clamped-Simply supported (CS), Clamped – clamped (CC) and Clamped-free (CF) boundary conditions are considered. Computed results are compared with earlier works for the verification and convergence studies. The effects of the different gradient indexes, various aspect ratios and boundary conditions on the buckling responses of the two directional functionally graded beams are investigated.

This paper is dedicated to present a Ritz-type analytical solution for buckling behavior of two directional functionally graded beams (2D-FGBs) subjected to various sets of boundary conditions by employing a third order shear deformation theory. The material properties of the beam vary in both axial and thickness directions according to the power-law distribution. The axial, transverse deflections and rotation of the cross sections are expressed in polynomial forms to obtain the buckling load. The auixiliary functions are added to displacement functions to satisfy the boundary conditions. Simply supported – Simply supported (SS), Clamped-Simply supported (CS), Clamped – clamped (CC) and Clamped-free (CF) boundary conditions are considered. Computed results are compared with earlier works for the verification and convergence studies. The effects of the different gradient indexes, various aspect ratios and boundary conditions on the buckling responses of the two directional functionally graded beams are investigated.

• [1] R. Kadoli, K. Akhtar, N. Ganesan, “Static analysis of functionally graded beams using higher order shear deformation theory”, Appl. Math. Model., vol. 32, pp. 2509-2525, 2008.
• [2] X.F. Li, “A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, Journal of Sound and Vibration”, vol. 318, pp. 1210-1229, 2008.
• [3] S.R. Li, D.F. Cao, Z.Q. Wan, “Bending solutions of FGM Timoshenko beams from those of the homogenous Euler–Bernoulli beams”, Appl. Math. Model., vol. 37, pp. 7077-7085, 2013.
• [4] M. Aydogdu, V. Taskin, “Free vibration analysis of functionally graded beams with simply supported edges”, Materials&Design., vol. 28, pp. 1651–1656, 2007.
• [5] M. Simsek, “Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories”, Nuc. Eng. and Des., vol. 240, pp. 697–705, 2010.
• [6] M. Simsek, “Vibration analysis of a functionally graded beam under a moving mass by using different beam theories”, Compos. Struct., vol. 92, pp. 904–917, 2010.
• [7] K.K. Pradhan, S. Chakraverty, “Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method”, Compos. Part B., vol. 51, pp. 175–184, 2013.
• [8] H. Su, J.R. Banerjee, C.W. Cheung, “Dynamic stiffness formulation and free vibration analysis of functionally graded beams”, Compos. Struct., vol. 106, pp. 854–862, 2013.
• [9] S.R. Li, Z.G. Wan, J.H. Zhang, “Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories”, Applied Mathematics and Mechanics, vol. 35, pp. 591–606, 2014.
• [10] M. Aydogdu, “Semi-inverse method for vibration and buckling of axially functionally graded beams”, Journal of Reinforced Plastics&Composites, vol. 27, pp. 683–691, 2008.
• [11] Y. Huang, X.F. Li, “Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity”, Journal of Engineering Mechanics, vol. 137, no.1, pp. 73–81, 2011.
• [12] X.F. Li, B.L. Wang, J.C. Han, “A higher-order theory for static and dynamic analyses of functionally graded beams”, Archive of Applied Mechanics, vol. 80, pp. 1197-1212, 2010.
• [13] T.P. Vo, H.T. Thai, T.K. Nguyen, F. Inam, J. Lee, “Static behaviour of functionally graded sandwich beams using a quasi-3D theory”, Compos. Part B, vol. 68, pp. 59-74, 2015.
• [14] M. Filippi, E. Carrera, A.M. Zenkour, “Static analyses of FGM beams by various theories and finite elements”, Compos. Part B, vol. 72, pp. 1-9, 2015.
• [15] D.S. Mashat, E. Carrera, A.M. Zenkour, S.A.A. Khateeb, M. Filippi, “Free vibration of FGM layered beams by various theories and finite elements”, Compos. Part B, vol. 59, pp. 269–278, 2014.
• [16] T.P. Vo, H.T. Thai, T.K. Nguyen, F. Inam, J. Lee, “A quasi-3D theory for vibration and buckling of functionally graded sandwich beams”, Compos. Struct., vol. 119, pp. 1–12,2015.
• [17] J.L. Mantari, J. Yarasca, “A simple and accurate generalized shear deformation theory for beams”, Compos. Struct., vol. 134, pp. 593–601, 2015.
• [18] J.L. Mantari, “A refined theory with stretching effect for the dynamics analysis of advanced composites on elastic foundation”, Mech. Mater., vol. 86, pp. 31–43, 2015.
• [19] J.L. Mantari, “Refined and generalized hybrid type quasi-3D shear deformation theory for the bending analysis of functionally graded shells”, Compos. Part B, vol. 83, pp. 142–152, 2015.
• [20] T.K. Nguyen, T.P. Vo, B.D. Nguyen, J. Lee, “An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory”, Compos. Struct., vol. 156, pp. 238-252, 2016.
• [21] T.P. Vo, H.T. Thai, T.K. Nguyen, A. Maheri, J. Lee, “Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory”, Eng. Struct., vol. 64, pp. 12–22, 2014.
• [22] T.K. Nguyen, T.T.P. Nguyen, T.P. Vo, H.T. Thai, “Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory”, Compos. Part B, vol. 76, pp. 273–285, 2015.
• [23] M. Nemat-Alla, “Reduction of thermal stresses by developing two-dimensional functionally graded materials”, Int. Journal of Solids and Structures, vol. 40, pp. 7339–7356, 2003.
• [24] A.J. Goupee, S.S. Vel, “Optimization of natural frequencies of bidirectional functionally graded beams”, Struct. Multidisc. Optim., vol. 32, pp. 473–484, 2006.
• [25] C.F. Lü, W.Q. Chen, R.Q. Xu, C.W. Lim, “Semi-analytical elasticity solutions for bidirectional functionally graded beams”, Int. Journal of Solids and Structures, vol. 45, pp. 258–275, 2008.
• [26] L. Zhao, W.Q. Chen, C.F. Lü, “Symplectic elasticity for two-directional functionally graded materials”, Mech. Mater., vol. 54, pp. 32–42, 2012.
• [27] M. Nazargah, “Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach”, Aerospace Science and Technology, vol. 45, pp. 154-164, 2015.
• [28] M. Simsek, “Bi-Directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions”, Compos. Struct., vol. 141, pp. 968–978, 2015.
• [29] M. Simsek, “Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions”, Compos. Struct., vol. 149 pp. 304–314, 2016.
• [30] A. Karamanli, “Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method”, Compos. Struct., vol. 160, pp. 653-669, 2017.
• [31] A. Pydah, R.C. Batra, “Shear deformation theory using logarithmic function for thick circular beams and analytical solution for bi-directional functionally graded circular beams”, Compos. Struct., vol. 172, pp. 45-60, 2017.
• [32] A. Karamanli, “Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory”, Compos. Struct., vol. 174, pp. 70-86, 2017.
• [33] T.V. Do, D.K. Nguyen, D.D. Nguyen, D.H. Doan, T.Q. Bui, “Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory”, Thin-Walled Struct., vol. 119, pp. 687-699, 2017.
• [34] A. Karamanli, “Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory”, (submitted for publication).
Birincil Dil en Mühendislik Mayıs Makaleler Orcid: 0000-0003-3990-6515Yazar: Armağan Karamanlı (Sorumlu Yazar)Ülke: Turkey
 Bibtex @araştırma makalesi { apjes357539, journal = {Akademik Platform Mühendislik ve Fen Bilimleri Dergisi}, issn = {}, eissn = {2147-4575}, address = {Akademik Platform}, year = {2018}, volume = {6}, pages = {164 - 178}, doi = {10.21541/apjes.357539}, title = {Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory}, key = {cite}, author = {Karamanlı, Armağan} } APA Karamanlı, A . (2018). Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory. Akademik Platform Mühendislik ve Fen Bilimleri Dergisi, 6 (2), 164-178. DOI: 10.21541/apjes.357539 MLA Karamanlı, A . "Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 (2018): 164-178 Chicago Karamanlı, A . "Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 (2018): 164-178 RIS TY - JOUR T1 - Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory AU - Armağan Karamanlı Y1 - 2018 PY - 2018 N1 - doi: 10.21541/apjes.357539 DO - 10.21541/apjes.357539 T2 - Akademik Platform Mühendislik ve Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 164 EP - 178 VL - 6 IS - 2 SN - -2147-4575 M3 - doi: 10.21541/apjes.357539 UR - http://dx.doi.org/10.21541/apjes.357539 Y2 - 2018 ER - EndNote %0 Akademik Platform Mühendislik ve Fen Bilimleri Dergisi Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory %A Armağan Karamanlı %T Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory %D 2018 %J Akademik Platform Mühendislik ve Fen Bilimleri Dergisi %P -2147-4575 %V 6 %N 2 %R doi: 10.21541/apjes.357539 %U 10.21541/apjes.357539 ISNAD Karamanlı, Armağan . "Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory". Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 6 / 2 (Ağustos 2018): 164-178. http://dx.doi.org/10.21541/apjes.357539