| 1. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A hierarchy of dynamic equations for micropolar plates
- 2015
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Ingår i: Journal of Sound and Vibration. - : Elsevier BV. - 1095-8568 .- 0022-460X. ; 357, s. 427-436
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Tidskriftsartikel (refereegranskat)abstract
- This work considers homogeneous isotropic micropolar plates adopting a power series expansion method in the thickness coordinate. Variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order for extensional and flexural displacement cases. The plate equations are asymptotically correct to all studied orders. Numerical results are presented for various orders of the present method, other approximate theories as well as the exact three dimensional theory. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering plate equations using low order truncation.
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| 2. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A hierarchy of dynamic equations for solid isotropic circular cylinders
- 2014
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Ingår i: Wave Motion. - : Elsevier BV. - 0165-2125. ; 51:2, s. 206-221
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Tidskriftsartikel (refereegranskat)abstract
- This work considers homogeneous isotropic circular cylinders adopting a power series expansion method in the radial coordinate. Equations of motion together with consistent sets of end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton’s principle. Time domain partial differential equations are obtained for longitudinal, torsional, and flexural modes, where these equations are asymptotically correct to all studied orders. Numerical examples are presented for different sorts of problems, using exact theory, the present series expansion theories of different order, and various classical theories. These results cover dispersion curves, eigenfrequencies and the corresponding displacement and stress distributions, as well as fix frequency motion due to prescribed end displacement or lateral distributed forces. The results illustrate that the present approach may render benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.
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| 3. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A hierarchy of dynamic equations for solid isotropic micropolar circular cylinders
- 2019
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Ingår i: Journal of Sound and Vibration. - : Elsevier BV. - 1095-8568 .- 0022-460X. ; 440, s. 70-82
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Tidskriftsartikel (refereegranskat)abstract
- This work considers the derivation procedure and evaluation of dynamic equations for isotropic micropolar circular cylinders by adopting a power series expansion method in the radial coordinate. Variationally consistent equations of motion together with pertinent sets of boundary conditions are expressed in a systematic fashion up to arbitrary order. The numerical results cover eigenfrequencies, mode shapes and field distributions over cross sections for axisymmetric and flexural motion adopting different sets of end boundary conditions for equations of different truncation orders of the present method. The results illustrate that the present approach may render benchmark solutions provided that higher order equations are used, and act as accurate approximate engineering solution for lower order equations.
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| 4. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A hierarchy of micropolar plate equations
- 2016
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Ingår i: 29th Nordic Seminar on Computational Mechanics.
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Konferensbidrag (refereegranskat)abstract
- This work considers homogeneous isotropic micropolar plates adopting a powerseries expansion method in the thickness coordinate. Equations of motion, forextensional and flexural case, together with consistent sets of end boundary conditionsare derived in a systematic fashion up to arbitrary order. The plateequations are asymptotically correct to all studied orders. Numerical results arepresented for various orders of the present method, other approximate theories aswell as the exact three dimensional theory. The results illustrate that the presentapproach may render benchmark solutions provided higher order truncatio
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| 5. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A rational derivation of dynamic higher order equations for functionally graded micropolar plates
- 2016
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Ingår i: Composite Structures. - : Elsevier BV. - 0263-8223. ; 153, s. 234-241
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Tidskriftsartikel (refereegranskat)abstract
- The dynamics of functionally graded micropolar plates is considered. The derivation process is based on power series expansions in the thickness coordinate. Using the three-dimensional equations of motion for micropolar continuum, variationally consistent equations of motion and end boundary conditions are derived in a systematic fashion up to arbitrary order. Numerical results are presented for simply supported plates using different material distributions for both low and high order truncation orders. These results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering plate equations using low order truncation.
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| 6. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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A systematic approach to derive dynamic equations for homogeneous and functionally graded micropolar plates
- 2017
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Ingår i: Procedia Engineering. - : Elsevier BV. - 1877-7058 .- 1877-7058. ; 199, s. 1429-1434
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Konferensbidrag (refereegranskat)abstract
- This work considers a systematic derivation process to obtain hierarchies of dynamical equations for micropolar plates being either homogeneous or with a functionally graded (FG) material variation over the thickness. Based on the three dimensional micropolar continuum theory, a power series expansion technique of the displacement and micro-rotation fields in the thickness coordinate of the plate is adopted. The construction of the sets of plate equations is systematized by the introduction of recursion relations which relates higher order powers of displacement and micro-rotation terms with the lower order terms. This results in variationally consistent partial differential plate equations of motion and pertinent boundary conditions. Such plate equations can be constructed in a systematic fashion to any desired truncation order, where each equation order is hyperbolic and asymptotically correct. The resulting lowest order flexural plate equation is seen to be of a generalized Mindlin type. The numerical results illustrate that the present approach may render accurate solutions of benchmark type for both homogeneous and functionally graded micropolar plates provided higher order truncations are used. Moreover, low order truncations render new sets of plate equations that can act as engineering plate equations, e.g. of a generalized Mindlin type.
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| 7. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Dynamic equations for a functionally graded cylinder
- 2016
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Ingår i: 19th International Conference on Composite Structures (ICCS19)....
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Konferensbidrag (refereegranskat)abstract
- This work considers the analysis and derivation of dynamical equations of functionally graded (FG) solid cylinders. The proposed method is based on the 3D equations of motion using a power series expansion of the displacement fields in the radial coordinate of the cylinder. This assumption results in sets of equations of motion together with consistent sets of boundary conditions. These derived equations are hyperbolic and asymptotically correct to all studied order. A hierarchy of partial differential equations is thus constructed in a systematic fashion to any order desired. The construction of the equations are systematized by the introduction of recursion relations which relates higher order displacement terms with the lower order terms. Results for longitudinal, torsional and bending motion are obtained where the material distribution vary with radial and circumferential coordinates. Eigenfrequency results and plots on mode shapes and stress distributions are presented for cylinders using different truncations orders. The approach may render benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.
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| 8. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Dynamic equations for a micropolar cylinder
- 2015
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Ingår i: Proceedings of International Conference on Shells, Plates and Beams (SPB2015), Bologna, ITALY. - 2421-2822. - 9788874888863 ; , s. 37-38
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Konferensbidrag (refereegranskat)abstract
- This work considers the analysis and derivation of dynamical equations of a solid cylindergoverned by micropolar continuum theory. The proposed method is based on a power seriesexpansion of the displacement field and micro-rotation field in the radial coordinate of thecylinder. This assumption results in sets of equations of motion together with sets of boundaryconditions that are variationally consistent. These derived equations are hyperbolic and can beconstructed in a systematic fashion to any order desired where the equations areasymptotically correct to all studied orders. The construction of the equations aresystematized by the introduction of recursion relations that relate higher order displacement and micro-rotation terms to the lower order terms. Results are obtained for cylinders usingdifferent truncations orders of the present theory including higher order benchmark solutions.Numerical examples are presented for dispersion curves, eigenfrequencies with stress anddisplacement distribution plots for simply supported cylinders.
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| 9. |
- Abadikhah, Hossein, 1987, et al.
(författare)
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Dynamic equations for solid isotropic radially functionally graded circular cylinders
- 2018
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Ingår i: Composite Structures. - : Elsevier BV. - 0263-8223. ; 195, s. 147-157
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Tidskriftsartikel (refereegranskat)abstract
- A hierarchy of dynamic equations for solid isotropic functionally graded circular cylinders is derived based on the three dimensional elastodynamic theory. The material parameters are assumed to vary in the radial direction. Using Fourier expansions in the circumferential direction and power series expansions in the radial direction, equations of motion are obtained for longitudinal, torsional, flexural and higher order motion to arbitrary Fourier and power orders. Numerical examples for eigenfrequencies and plots on mode shapes and stress distributions curves are presented for simply supported cylinders for different material distributions. The results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.
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| 10. |
- Abadikhah, Hossein, 1987
(författare)
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Dynamic higher order equations
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The subject of this thesis is to derive and evaluate governing equations and correspondingboundary conditions for solid cylinders and rectangular plates, where the materialconstituting the cylinder or plate are governed by classical elasticity, micropolar elasticityor a functionally graded case of the previously mentioned models. This is achieved by asystematic power series expansion approach, by either adopting a generalized Hamilton'sprinciple or a direct approach.For the solid cylinders a power series expansion in the radial coordinate for the sought fields are adopted. Equations of motion together with consistent sets of end boundaryconditions are derived in a systematic fashion up to arbitrary order using a generalizedHamilton's principle. Governing equations are obtained for longitudinal, torsional, andexural modes. In the case of the rectangular plate, a power series expansion of thesought fields are adopted in the thickness coordinate. Governing equations of motion, forextensional and exural case, together with consistent sets of edge boundary conditionsare derived in a systematic fashion up to arbitrary order with use of the direct approach.Both the governing equations for the solid cylinder and the rectangular plate areasymptotically correct to all studied orders. Numerical examples are presented fordifferent sorts of problems, using exact theory, the present series expansion theories ofdifferent order, various classical theories and other newly developed approximate theories.These results cover dispersion curves, eigenfrequencies, various curves of cross sectionalquantities such as displacements, stresses and micro-rotations, as well as fixed frequencymotion due to prescribed end displacement or lateral distributed forces. The resultsillustrate that the present approach may render benchmark solutions provided higher ordertruncations are used, and act as engineering equations when using low order truncations.
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