A new simple shear and normal deformations theory for functionally graded beams

Title & Authors
A new simple shear and normal deformations theory for functionally graded beams
Bourada, Mohamed; Kaci, Abdelhakim; Houari, Mohammed Sid Ahmed; Tounsi, Abdelouahed;
Abstract
In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect ($\small{{\varepsilon}_Z{\neq}0}$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton`s principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.
Keywords
functionally graded beam;a simple third-unknown theory;normal strain;neutral surface position;
Language
English
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Flutter suppression of plates subjected to supersonic flow using passive constrained viscoelastic layers and Golla–Hughes–McTavish method, Aerospace Science and Technology, 2016, 52, 70
112.
Interfacial stresses in RC beam bonded with a functionally graded material plate, Structural Engineering and Mechanics, 2016, 60, 4, 693
113.
Correction method of the manned spacecraft low altitude ranging based on γ ray, Aerospace Science and Technology, 2016, 50, 71
114.
Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid, Advances in Materials Science and Engineering, 2016, 2016, 1
115.
Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory, Wind and Structures, 2016, 22, 3, 291
116.
First-principles calculations of typical anisotropic cubic and hexagonal structures and homogenized moduli estimation based on the Y-parameter: Application to CaO, MgO, CH and Calcite CaCO3, Journal of Physics and Chemistry of Solids, 2017, 101, 74
117.
Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory, Structural Engineering and Mechanics, 2016, 57, 4, 617
118.
On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model, Steel and Composite Structures, 2015, 18, 4, 1063
119.
Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures, 2017, 73, 125
120.
Non-linear transient and damping analysis of a long cylindrical sandwich panel with embedded SMA wires, Aerospace Science and Technology, 2015, 47, 98
121.
Thermal stresses in a non-homogeneous orthotropic infinite cylinder, Structural Engineering and Mechanics, 2016, 59, 5, 841
122.
Effect of fiber tension on the deformation of a carbon composite plate for space radio telescopes, Aerospace Science and Technology, 2015, 45, 99
123.
Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams, Mechanics of Advanced Materials and Structures, 2017, 24, 11, 924
124.
Isogeometric buckling analysis of composite variable-stiffness panels, Composite Structures, 2017, 165, 192
125.
Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam, Applied Physics A, 2016, 122, 7
126.
Coupled vibration characteristics of shear flexible thin-walled functionally graded sandwich I-beams, Composites Part B: Engineering, 2017, 110, 229
127.
Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate, Journal of Adhesion Science and Technology, 2016, 30, 12, 1253
128.
Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories, Structural Engineering and Mechanics, 2015, 53, 6, 1143
129.
On thermal stability of plates with functionally graded coefficient of thermal expansion, Structural Engineering and Mechanics, 2016, 60, 2, 313
130.
Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept, Steel and Composite Structures, 2016, 20, 5, 963
131.
Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs, Composite Structures, 2016, 153, 902
132.
Vibration Analysis of Rectangular Magnetostrictive Plate Considering Thickness Variation in Two Directions, International Journal of Applied Mechanics, 2015, 07, 04, 1550059
133.
Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory, Alexandria Engineering Journal, 2017
134.
Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory, Microsystem Technologies, 2017
135.
On the bending and stability of nanowire using various HSDTs, Advances in nano research, 2015, 3, 4, 177
136.
Wave propagation of a functionally graded beam in thermal environments, Steel and Composite Structures, 2015, 19, 6, 1421
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Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems, 2016, 18, 4, 755
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On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2016, 230, 10, 1903
139.
Hygrothermal Effects on the Free Vibration Behavior of Composite Plate Using nth-Order Shear Deformation Theory: a Micromechanical Approach, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017
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Further investigation of the body torques on a square solar sail due to the displacement of the sail attachment points, Aerospace Science and Technology, 2016, 50, 281
141.
A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams, Composite Structures, 2017, 159, 174
142.
Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory, The European Physical Journal Plus, 2018, 133, 2
143.
Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method, Alexandria Engineering Journal, 2017
144.
A simple single variable shear deformation theory for a rectangular beam, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017, 231, 24, 4576
145.
Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness, Engineering Science and Technology, an International Journal, 2016, 19, 3, 1608
146.
A new higher order shear and normal deformation theory for functionally graded beams, Steel and Composite Structures, 2015, 18, 3, 793
147.
Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232, 1, 162
148.
Analytical solution for bending analysis of functionally graded beam, Steel and Composite Structures, 2015, 19, 4, 829
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Rotational effect on Rayleigh, Love and Stoneley waves in non-homogeneous fibre-reinforced anisotropic general viscoelastic media of higher order, Structural Engineering and Mechanics, 2016, 58, 1, 181
150.
Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Composite Structures, 2017, 159, 433
151.
Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium, Brazilian Journal of Physics, 2017, 47, 6, 640
152.
Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory, Steel and Composite Structures, 2016, 20, 4, 889
153.
Designing a stronger interface through graded structures in amorphous/nanocrystalline ZrCu/Cu multilayered films, Nanotechnology, 2016, 27, 22, 225701
154.
A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics, 2015, 54, 4, 693
155.
Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment, Applied Physics A, 2017, 123, 5
156.
Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties, Advances in materials Research, 2016, 5, 4, 205
157.
Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation, Composite Structures, 2017, 160, 152
158.
A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates, Composite Structures, 2018, 184, 688
159.
Elastic buckling of current-carrying double-nanowire systems immersed in a magnetic field, Acta Mechanica, 2016, 227, 12, 3549
160.
Nonlinear bending of a two-dimensionally functionally graded beam, Composite Structures, 2018, 184, 1049
161.
Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions, Composites Part B: Engineering, 2017, 108, 75
162.
Buckling optimization of variable-stiffness composite panels based on flow field function, Composite Structures, 2017, 181, 240
163.
Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials, 2016, 7, 2, 69
164.
A computational shear displacement model for vibrational analysis of functionally graded beams with porosities, Steel and Composite Structures, 2015, 19, 2, 369
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A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates, Steel and Composite Structures, 2016, 22, 3, 473
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Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects, Composite Structures, 2018, 187, 498
167.
A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate, Structural Engineering and Mechanics, 2016, 60, 4, 547
168.
Exact solutions for coupled responses of thin-walled FG sandwich beams with non-symmetric cross-sections, Composites Part B: Engineering, 2017, 122, 121
169.
Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams, Applied Physics A, 2016, 122, 11
170.
Finite element modeling for structural strength of quadcoptor type multi mode vehicle, Aerospace Science and Technology, 2016, 53, 252
171.
Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory, Composite Structures, 2017, 180, 116
172.
Nonlocal vibration analysis of FG nano beams with different boundary conditions, Advances in nano research, 2016, 4, 2, 85
173.
Finite element model updating of a space vehicle first stage motor based on experimental test results, Aerospace Science and Technology, 2015, 45, 422
174.
Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation, Advances in Polymer Technology, 2017
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Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity, Advances in nano research, 2015, 3, 4, 193
176.
A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations, Structural Engineering and Mechanics, 2015, 53, 6, 1215
177.
Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions, Smart Structures and Systems, 2016, 18, 6, 1087
178.
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation, Steel and Composite Structures, 2016, 20, 2, 227
179.
Wave propagation in anisotropic plates using trigonometric shear deformation theory, Mechanics of Advanced Materials and Structures, 2017, 24, 13, 1135
180.
Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation, Steel and Composite Structures, 2016, 22, 1, 91
181.
Effect of shear deformation on adhesive stresses in plated concrete beams: Analytical solutions, Computers and Concrete, 2015, 15, 3, 337
182.
Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, Journal of Thermal Stresses, 2017, 40, 2, 167
183.
Analytical modeling of dynamic behavior of piezo-thermo-electrically affected sigmoid and power-law graded nanoscale beams, Applied Physics A, 2016, 122, 9
184.
A novel four variable refined plate theory for laminated composite plates, Steel and Composite Structures, 2016, 22, 4, 713
185.
Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments, Aerospace Science and Technology, 2015, 47, 434
186.
Low-velocity impact response of functionally graded doubly curved panels with Winkler–Pasternak elastic foundation: An analytical approach, Composite Structures, 2017, 162, 351
187.
An efficient shear deformation theory for wave propagation of functionally graded material plates, Structural Engineering and Mechanics, 2016, 57, 5, 837
188.
Free vibration analysis of pre-stressed FGM Timoshenko beams under large transverse deflection by a variational method, Engineering Science and Technology, an International Journal, 2016, 19, 2, 1003
189.
Dynamic behavior of FGM beam using a new first shear deformation theory, Earthquakes and Structures, 2016, 10, 2, 451
190.
Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam, Applied Physics A, 2017, 123, 1
191.
Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties, Applied Physics A, 2017, 123, 1
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Influence of the porosities on the free vibration of FGM beams, Wind and Structures, 2015, 21, 3, 273
193.
The nonlinear dynamic and vibration of the S-FGM shallow spherical shells resting on an elastic foundations including temperature effects, International Journal of Mechanical Sciences, 2017, 123, 54
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An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations, Wind and Structures, 2016, 22, 3, 329
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Nonlinear Flexural Analysis of Laminated Composite Panel Under Hygro-Thermo-Mechanical Loading — A Micromechanical Approach, International Journal of Computational Methods, 2016, 13, 03, 1650015
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A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates, Steel and Composite Structures, 2016, 22, 2, 257
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A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations, Geomechanics and Engineering, 2016, 11, 2, 289
198.
A refined theory with stretching effect for the flexure analysis of laminated composite plates, Geomechanics and Engineering, 2016, 11, 5, 671
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A parametric study on the stress analysis and transient response of thick-laminated-faced cylindrical sandwich panels with transversely flexible core, Aerospace Science and Technology, 2016, 48, 1
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Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel, Chinese Journal of Aeronautics, 2016, 29, 1, 173
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Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium, Mechanics of Composite Materials, 2018, 53, 6, 827
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Elasticity solution for a cantilever beam with exponentially varying properties, Journal of Applied Mechanics and Technical Physics, 2017, 58, 2, 354
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