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Isogeometric technique for dynamic instability analysis of nanocomposite folded plates based on higher-order shear deformation theory
https://orcid.org/0000-0002-1771-8129
Abstract This paper proposes a dynamic instability isogeometric analysis (IGA) of functionally graded (FG) folded plates strengthened by carbon nanotubes (CNTs) under a uniform in-plane loading. The folded plates are modeled by two patches to overcome the existing discontinuity in the geometry. A recently developed logarithmic higher-order shear deformation theory (HSDT) is used to describe the kinematic relations of each patch. Then, IGA in conjunction with Hamilton’s principle is used to discretize the governing equations of the patch. Afterwards, an appropriate coordinate transformation is applied to transfer the patch stiffness, mass and geometric stiffness matrices to the global coordinates. Moreover, the continuity conditions along the joined line are enforced by means of the bending strip method (BSM). The final form of the governing equations, describing the dynamic instability behavior of folded plates, is solved by Bolotin’s method in order to estimate the boundaries of the principal instability regions with the first and second-order approximations. Various types of numerical examples are investigated to verify the precision and reliability of the present solution method. These comparative studies confirm that the proposed logarithmic HSDT-based isogeometric formulation can precisely predict natural frequencies, critical buckling loads and principal instability regions of FG carbon nanotube-reinforced composite (CNTRC) folded plates. The effects of first and second-order approximations, various configurations of CNTRCs, in-plane loading behavior and geometrical parameters on the aforementioned mechanical analyses of the plate are investigated.
Highlights The effective and powerful isogeometric method is employed for precise modeling of folded plates. The folded plate is reinforced with CNTs where the distribution of CNTs may be uniform or functionally graded along the thickness of the structure. The folded plate is modeled by two patches where the bending strip method is applied to enforce the continuity condition. The free vibration, buckling and dynamic instability behaviors of FG-CNTRC folded plates are predicted with a low computational cost.
Isogeometric technique for dynamic instability analysis of nanocomposite folded plates based on higher-order shear deformation theory
https://orcid.org/0000-0002-1771-8129
Abstract This paper proposes a dynamic instability isogeometric analysis (IGA) of functionally graded (FG) folded plates strengthened by carbon nanotubes (CNTs) under a uniform in-plane loading. The folded plates are modeled by two patches to overcome the existing discontinuity in the geometry. A recently developed logarithmic higher-order shear deformation theory (HSDT) is used to describe the kinematic relations of each patch. Then, IGA in conjunction with Hamilton’s principle is used to discretize the governing equations of the patch. Afterwards, an appropriate coordinate transformation is applied to transfer the patch stiffness, mass and geometric stiffness matrices to the global coordinates. Moreover, the continuity conditions along the joined line are enforced by means of the bending strip method (BSM). The final form of the governing equations, describing the dynamic instability behavior of folded plates, is solved by Bolotin’s method in order to estimate the boundaries of the principal instability regions with the first and second-order approximations. Various types of numerical examples are investigated to verify the precision and reliability of the present solution method. These comparative studies confirm that the proposed logarithmic HSDT-based isogeometric formulation can precisely predict natural frequencies, critical buckling loads and principal instability regions of FG carbon nanotube-reinforced composite (CNTRC) folded plates. The effects of first and second-order approximations, various configurations of CNTRCs, in-plane loading behavior and geometrical parameters on the aforementioned mechanical analyses of the plate are investigated.
Highlights The effective and powerful isogeometric method is employed for precise modeling of folded plates. The folded plate is reinforced with CNTs where the distribution of CNTs may be uniform or functionally graded along the thickness of the structure. The folded plate is modeled by two patches where the bending strip method is applied to enforce the continuity condition. The free vibration, buckling and dynamic instability behaviors of FG-CNTRC folded plates are predicted with a low computational cost.
Isogeometric technique for dynamic instability analysis of nanocomposite folded plates based on higher-order shear deformation theory
https://orcid.org/0000-0002-1771-8129
Abstract This paper proposes a dynamic instability isogeometric analysis (IGA) of functionally graded (FG) folded plates strengthened by carbon nanotubes (CNTs) under a uniform in-plane loading. The folded plates are modeled by two patches to overcome the existing discontinuity in the geometry. A recently developed logarithmic higher-order shear deformation theory (HSDT) is used to describe the kinematic relations of each patch. Then, IGA in conjunction with Hamilton’s principle is used to discretize the governing equations of the patch. Afterwards, an appropriate coordinate transformation is applied to transfer the patch stiffness, mass and geometric stiffness matrices to the global coordinates. Moreover, the continuity conditions along the joined line are enforced by means of the bending strip method (BSM). The final form of the governing equations, describing the dynamic instability behavior of folded plates, is solved by Bolotin’s method in order to estimate the boundaries of the principal instability regions with the first and second-order approximations. Various types of numerical examples are investigated to verify the precision and reliability of the present solution method. These comparative studies confirm that the proposed logarithmic HSDT-based isogeometric formulation can precisely predict natural frequencies, critical buckling loads and principal instability regions of FG carbon nanotube-reinforced composite (CNTRC) folded plates. The effects of first and second-order approximations, various configurations of CNTRCs, in-plane loading behavior and geometrical parameters on the aforementioned mechanical analyses of the plate are investigated.
Highlights The effective and powerful isogeometric method is employed for precise modeling of folded plates. The folded plate is reinforced with CNTs where the distribution of CNTs may be uniform or functionally graded along the thickness of the structure. The folded plate is modeled by two patches where the bending strip method is applied to enforce the continuity condition. The free vibration, buckling and dynamic instability behaviors of FG-CNTRC folded plates are predicted with a low computational cost.
Isogeometric technique for dynamic instability analysis of nanocomposite folded plates based on higher-order shear deformation theory
Mohammadi, H. (author) / Weeger, O. (author) / Shojaee, M. (author)
Thin-Walled Structures ; 177
2022-05-19
Article (Journal)
Electronic Resource
English
Isogeometric analysis of functionally graded plates using higher-order shear deformation theory
| British Library Online Contents | 2013
| British Library Online Contents | 2013
| British Library Online Contents | 2016