\شماره٪٪۱
Van Do, T., Nguyen, D.K., Duc, N.D. and et al.
``Analysis of bi-directional functionally graded plates by FEM
and a new third-order shear deformation plate theory'', {\it Thin-Walled
Struct}, {\bf 119}, pp. 687-699 (2017).
\شماره٪٪۲
Mahamood, R.-M., Akinlabi, E.-T., Shukla, M. and et al.
``Functionally graded material: an overview'', International Association
of Engineers (IAENG) (2012).
\شماره٪٪۳
Tu, T.M., Quoc, T.H. and Van Long, N. ``Vibration analysis
of functionally graded plates using the eight-unknown higher
order shear deformation theory in thermal envi-ronments'', {\it Aerosp.
Sci. Technol}, {\bf 84}, pp. 698-711 (2019).
\شماره٪٪۴
Duc, N.D. and Quan, T.Q. ``Nonlinear stability analysis of
double-curved shallow fgm panels on elastic foundations in thermal
environments'', {\it Mech. Compos. Mater}, {\bf 48}(4), pp. 435-448 (2012).
\شماره٪٪۵
Nguyen, T.-T., Thang, P.T. and Lee, J. ``Flexural-torsional
stability of thin-walled func-tionally graded open-section beams,''
{\it Thin-Walled Struct}, {\bf 110}, pp. 88-96 (2017).
\شماره٪٪۶
Kieback, B., Neubrand, A. and Riedel, H. ``Processing techniques
for functionally grad-ed materials'', {\it Mater. Sci. Eng. A Struct.
Mater}, {\bf 362}(1-2), pp. 81-106 (2003).
\شماره٪٪۷
Wang, Y.Q. and Zu, J.W. ``Vibration characteristics of moving
sigmoid functionally graded plates containing porosities'', {\it Int.
J. Mech. Mater. Des}, {\bf 14}(4), pp. 473-489 (2018).
\شماره٪٪۸
Liu, W. and DuPont, J.N. ``Fabrication of functionally graded
TiC/Ti composites by La-ser Engineered Net Shaping'', {\it Scr. Mater},
{\bf 48}(9), pp. 1337-1342 (2003).
\شماره٪٪۹
Watanabe, Y., Inaguma, Y., Sato, H. and et al.
``A novel fabrication method for functionally graded materials
under centrifugal force: The centrifugal mixed-powder method'',
{\it Materials (Basel)}, {\bf 2}(4), pp. 2510-2525 (2009).
\شماره٪٪۱۰
Jin, G.Q. and Li, W.D. ``Adaptive rapid prototyping/manufacturing
for functionally graded material-based biomedical models'', {\it Int.
J. Adv. Manuf. Technol}, {\bf 65}(1-4), pp. 97-113 (2013).
\شماره٪٪۱۱
Li, X.-F. ``A unified approach for analyzing static and dynamic
behaviors of functional-ly graded Timoshenko and Euler-Bernoulli
beams'', {\it J. Sound Vib}, {\bf 318}(4-5) pp. 1210-1229 (2008).
\شماره٪٪۱۲
Kadoli, R., Akhtar, K. and Ganesan, N. ``Static analysis of
functionally graded beams using higher order shear deformation
theory'', {\it Appl. Math. Model}, {\bf 32}(12), pp. 2509-2525 (2008).
\شماره٪٪۱۳
Lu, C.F., Chen, W.Q., Xu, R.Q. and et al. ``Semi-analytical
elasticity solutions for bi-directional functionally graded beams'',
{\it Int. J. Solids Struct}, {\bf 45}(1), pp. 258-275 (2008).
\شماره٪٪۱۴
Zhao, L., Zhu, J. and Wen, X.D. ``Exact analysis of bi-directional
functionally graded beams with arbitrary boundary conditions
via the symplectic approach'', {\it Struct. Eng. Mech}, {\bf 59}(1), pp.
101-122 (2016).
\شماره٪٪۱۵
Wang, Z.-H., Wang, X.-H., Xu, G.-D. and et al.
``Free vibration of two-directional functionally graded beams'',
{\it Compos. Struct}, {\bf 135}, pp. 191-198 (2016).
\شماره٪٪۱۶
Simsek, M. ``Buckling of Timoshenko beams composed of
two-dimensional functional-ly graded material (2D-FGM) having
different boundary conditions'', {\it Compos. Struct}, {\bf 149}, pp. 304-314
(2016).
\شماره٪٪۱۷
Li, L., Li, X. and Hu, Y ``Nonlinear bending of a two-dimensionally
functionally grad-ed beam'', {\it Compos. Struct}, {\bf 184}, pp. 1049-1061
(2018).
\شماره٪٪۱۸
18. Nejad, M.Z. and Hadi, A. ``Eringen's non-local elasticity theory
for bending analysis of bi-directional functionally graded Euler-Bernoulli
nano-beams'', {\it Int. J. Eng. Sci}, {\bf 106}, pp. 1-9 (2016).
\شماره٪٪۱۹
Karamanli, A. and Vo, T.P. ``Size dependent bending analysis
of two directional func-tionally graded microbeams via a quasi-3D
theory and finite element method'', {\it Compos. B. Eng}, {\bf 144}, pp.
171-183 (2018).
\شماره٪٪۲۰
Nejad, M.Z. and Hadi, A. ``Non-local analysis of free vibration
of bi-directional func-tionally graded Euler-Bernoulli nano-beams'',
{\it Int. J. Eng. Sci}, {\bf 105}, pp. 1-11 (2016).
\شماره٪٪۲۱
Shafiei, N., Mirjavadi, S.S., Mohasel Afshari, B. and et al.
``Vibra-tion of two-dimensional imperfect functionally
graded (2D-FG) porous nano-/micro-beams'', {\it Comput. Methods Appl.
Mech. Eng}, {\bf 322}, pp. 615-632 (2017).
\شماره٪٪۲۲
Trinh, L.C., Vo, T.P., Thai, H.-T. and et al. ``Size-dependent
vibration of bi-directional functionally graded microbeams with
arbitrary boundary conditions'', {\it Com-pos. B Eng}, {\bf 134}, pp. 225-245
(2018).
\شماره٪٪۲۳
Nejad, M.Z., Hadi, A. and Rastgoo, A. ``Buckling analysis
of arbitrary two-directional functionally graded Euler-Bernoulli
nano-beams based on nonlocal elasticity theory'', {\it Int. J. Eng.
Sci}, {\bf 103}, pp. 1-10 (2016).
\شماره٪٪۲۴
Li, L. and Xiaohui, R. ``Stiffened plate bending analysis
in terms of refined triangular laminated plate element'', {\it Compos.
Struct}, {\bf 92}(12), pp. 2936-2945 (2010).
\شماره٪٪۲۵
Nemat-Alla, M., Ahmed, K.I.E. and Hassab-Allah, I. ``Elastic--plastic
analysis of two-dimensional functionally graded materials under
thermal loading'', {\it Int. J. Solids Struct}, {\bf
46}(14-15), pp. 2774-2786
(2009).
\شماره٪٪۲۶
Ebrahimi, M.J. and Najafizadeh, M.M. ``Free vibration analysis
of two-dimensional functionally graded cylindrical shells'',
{\it Appl. Math. Model}, {\bf 38}(1), pp. 308-324 (2014).
\شماره٪٪۲۷
Satouri, S., Kargarnovin, M.H., Allahkarami, F. and et al,
``Application of third order shear deformation theory in buckling
analysis of 2D-functionally graded cy-lindrical shell reinforced
by axial stiffeners'', {\it Compos. B Eng}, {\bf 79}, pp. 236-253 (2015).
\شماره٪٪۲۸
Taczala, M., Buczkowski, R. and Kleiber, M. ``Nonlinear buckling
and post-buckling response of stiffened FGM plates in thermal
environments'', {\it Compos. B Eng}, {\bf 109}, pp. 238-247 (2017).
\شماره٪٪۲۹
Vuong, P.M. and Duc, N.D. ``Nonlinear response and buckling
analysis of eccentrically stiffened FGM toroidal shell segments
in thermal environment'', {\it Aerosp. Sci. Technol}, {\bf 79}, pp. 383-398
(2018).
\شماره٪٪۳۰
Mehrabian, M. and Golmakani, M.E. ``Nonlinear bending analysis
of radial-stiffened annular laminated sector plates with dynamic
relaxation method'', {\it Comput. Math. Appl}, {\bf 69}(10), pp. 1272-1302
(2015).
\شماره٪٪۳۱
Golmakani, M.E. and Emami, M. ``Buckling and large deflection
behaviors of radially functionally graded ring-stiffened circular
plates with various boundary conditions'', {\it Appl. Math. Mech},
{\bf 37}(9), pp. 1131-1152 (2016).
\شماره٪٪۳۲
Hussein, O.S. and Mulani, S.B. ``Optimization of in-plane
functionally graded panels for buckling strength: Unstiffened,
stiffened panels, and panels with cutouts'', {\it Thin-Walled Struct},
{\bf 122}, pp. 173-181 (2018).
\شماره٪٪۳۳
Truong, T.T., Nguyen-Thoi, T. and Lee, J. ``Isogeometric size
optimization of bi-directional functionally graded beams under
static loads'', {\it Compos. Struct}, {\bf 227}, pp. 111259 (2019).
\شماره٪٪۳۴
Nguyen, H.X., Lee, J. and et al. ``Vibration and
lateral buckling optimisa-tion of thin-walled laminated composite
channel-section beams'', {\it Compos. Struct}, {\bf 143}, pp. 84-92 (2016).
\شماره٪٪۳۵
Nguyen, T.-T. and Lee, J. ``Optimal design of thin-walled
functionally graded beams for buckling problems'', {\it Compos. Struct},
{\bf 179}, pp. 459-467 (2017).
\شماره٪٪۳۶
Phi, L.T.M., Nguyen, T.-T., Kang, J. and et al. ``Vibration
and buckling optimization of thin-walled functionally graded
open-section beams'', {\it Thin-Walled Struct}, {\bf 170}, pp. 108586 (2022).
\شماره٪٪۳۷
Nguyen, T.-T. and Lee, J. ``Flexural-torsional vibration and
buckling of thin-walled bi-directional functionally graded beams'',
{\it Compos. B Eng}, {\bf 154}, pp. 351-362 (2018).
\شماره٪٪۳۸
Lei, J., He, Y., Li, Z. and et al. ``Postbuckling
analysis of bi-directional functionally graded imperfect beams
based on a novel third-order shear deformation theory'', {\it Compos.
Struct}, {\bf 209}, pp. 811-829 (2019).
\شماره٪٪۳۹
Reddy, J.N. ``Analysis of functionally graded plates'', {\it Int.
J. Numer Meth Engng}, {\bf 47}, pp. 663-684 (2000).
\شماره٪٪۴۰
Nguyen, T.-T., Kim, N.-I. and Lee, J. ``Free vibration of
thin-walled functionally grad-ed open-section beams'', {\it Compos.
B. Eng}, {\bf 95}, pp. 105-116 (2016).
\شماره٪٪۴۱
Nguyen, T.-T. Thang, P.T. and Lee, J. ``Lateral buckling
analysis of thin-walled func-tionally graded open-section beams'',
{\it Composite Structures}, {\bf 160}, pp. 952-963 (Jan., 2017).
\شماره٪٪۴۲
Vo, T.P. and Lee, J. ``Flexural-torsional behavior of thin-walled
closed-section com-posite box beams'', {\it Engineering Structures},
{\bf 29}(8), pp. 1774-1782 (Aug., 2007).
\شماره٪٪۴۳
Nguyen, T.-T., Kim, N.-I. and Lee, J. ``Analysis of thin-walled
open-section beams with functionally graded materials'', {\it Composite
Structures}, {\bf 138}, pp. 75-83 (Mar., 2016).
\شماره٪٪۴۴
Lanc, D., Vo, T.-P., Turkalj, G. and Lee, J. ``Buckling analysis
of thin-walled func-tionally graded sandwich box beams'', Thin-Walled
Structures, 86, pp. 148-156 (2015).
\شماره٪٪۴۵
Kim, D.-M., Choi, S., Jang, G.-W. and et al. ``Buckling
analysis of thin-walled box beams under arbitrary loads with
general boundary conditions using higher-order beam theory'',
{\it J. Mech. Sci. Technol}, {\bf 33}(5), pp. 2289-2305 (2019).
\شماره٪٪۴۶
Vo, T.-P. and Lee, J. ``Interaction curves for vibration and
buckling of thin-walled composite box beams under axial loads
and end moments'', {\it Appl. Math. Model}, {\bf 34}(10), pp. 3142-3157
(2010).
\شماره٪٪۴۷
Asadi, A., Sheikh, A.H. and Thomsen, O.T. ``Buckling behaviour
of thin-walled lami-nated composite beams having open and closed
sections subjected to axial and end mo-ment loading'', {\it Thin-Walled
Struct}, {\bf 141}, pp. 85-96 (2019).
\شماره٪٪۴۸
48. Kim, N.-I. and Lee, J. ``Theory of thin-walled functionally
graded sandwich beams with single and double-cell sections'',
{\it Compos. Struct}, {\bf 157}, pp. 141-154 (2016).
\شماره٪٪۴۹
Vo, T.-P. and Lee, J. ``Geometrically nonlinear theory of
thin-walled composite box beams using shear-deformable beam theory'',
{\it Int. J. Mech. Sci}, {\bf 52}(1), pp. 65-74 (2010).
\شماره٪٪۵۰
Kim, N.-I. and Lee, J. ``Divergence and flutter behavior of
Beck$\times$s type of laminated box beams'', {\it Int. J. Mech. Sci},
{\bf 84}, pp. 91-101 (2014).
\شماره٪٪۵۱
Kuehn, T., Pasternak, H. and Mittelstedt, C. ``Local buckling
of shear-deformable lam-inated composite beams with arbitrary
cross-sections using discrete plate analysis'', {\it Compos. Struct},
{\bf 113}, pp. 236-248 (2014).
\شماره٪٪۵۲
Sheikh, A.H.; Asadi, A. and Thomsen, O.T. ``Vibration of thin-walled
laminated com-posite beams having open and closed sections'',
{\it Compos. Struct}, {\bf 134}, pp. 209-215 (2015).
\شماره٪٪۵۳
Shin, D., Choi, S., Jang, G.-W. and et al. ``Higher-order
beam theory for static and vibration analysis of composite thin-walled
box beam'', {\it Compos. Struct}, {\bf 206}, pp. 140-154 (2018).
\شماره٪٪۵۴
Kim, N.-I. and Lee, J. ``Exact solutions for coupled analysis
of thin-walled functionally graded beams with non-symmetric single-
and double-cells'', {\it Appl. Math. Model}, {\bf 60}, pp. 661-680 (2018).
\شماره٪٪۵۵
Choi, S. and Kim, Y.-Y. ``Higher-order beam bending theory
for static, free vibration, and buckling analysis of thin-walled
rectangular hollow section beams'', {\it Comput. Struct}, {\bf 248},
pp.1-32 106494
(2021).
\شماره٪٪۵۶
Choi, S. and Kim, Y.-Y. ``Higher-order Vlasov torsion theory
for thin-walled box beams'', {\it Int. J. Mech. Sci}, {\bf 195}, pp.1-35 106231
(2021).
\شماره٪٪۵۷
Gokhan Gunay, M. and Timarci, T. ``Static analysis of thin-walled
laminated composite closed-section beams with variable stiffness'',
{\it Compos. Struct}, {\bf 182}, pp. 67-78 (2017).
)