Isogeometric technique for dynamic instability analysis of nanocomposite folded based on-order shear deformation

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.