A finite element semi-analytical model for laminated axisymmetric shells: statics, dynamics and buckling

Fundamental frequency of a cantilever composite cylindrical shell

“…(19) can be reduced if the displacements u, v, and w are presented by the following trigonometry series:…”

“…(20) into Eq. (19) and integrating with regard to coordinate b yields the following one-dimensional variational equation:…”

“…Dai et al developed a method to study the free vibrations of an isotropic circular shell with various boundary conditions in which the displacements were represented as Fourier series, such that both the governing differential equations based on Flugge's theory and the boundary conditions were satisfied [18]. Semi-analytical approaches to the free vibration analyses of axisymmetric laminated shells with various combinations of boundary conditions were developed by Pinto Correia et al [19,20] and Santos et al [21]. Liu et al derived exact characteristic equations for free vibrations of thin-walled orthotropic cylindrical shells [22].…”

Fundamental frequency of the laminated composite cylindrical shell with clamped edges

“…Semi-analytical approaches to the free vibration analyses of axisymmetric laminated shells with various combinations of boundary conditions were developed by Pinto Correia et al [10,11] and Santos et al [12]. Liu et al derived exact characteristic equations for free vibrations of thin-walled orthotropic cylindrical shells [13].…”

Thermal buckling of laminated composite conical shell panel with and without piezoelectric layer with random material properties

“…Email: bnsingh@aero.iitkgp.ernet.in istic. Notably among them are due to Correia et al [8,9], Bhimaraddi et al [2], Thangaratnam [14], Abdullah [1], Correia et al [7] and Reddy [10]. Extensive literature is available on the response analysis of the structures with deterministic material properties to random excitations [6].…”