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- Free vibrations analysis of composite and hybrid axisymmetric shellsPublication . Simões Moita, José Mateus; Araujo, Aurelio L.; Franco Correia, Victor; Mota Soares, Cristóvão M.The free vibration of laminated composite (C) and hybrid axisymmetric shell structures, consisting of a composite laminated material sandwiched between two functionally graded material laminas (F1/C/F2), is analysed in the present work. The numerical solutions are obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The implemented finite element is a simple conical frustum with two nodal circles, with ten degrees of freedom per nodal circle. This model requires only a reduced number of finite elements to model the geometry of axisymmetric structures, the integration procedures use one Gauss point, and the through the thickness properties variation in FGM laminas is modelled by a small number of virtual layers, resulting a very high computational efficiency. The inhouse developed code presents very good solutions when compared with results obtained by alternative available models.
- Mechanical and thermal buckling of functionally graded axisymmetric shellsPublication . Simões Moita, José Mateus; Araújo, Aurélio L.; Franco Correia, Victor; Mota Soares, Cristóvão M.The buckling analysis of functionally graded materials (FGM) axisymmetric plate-shell type structures under mechanical and termal loading is presented in this work. A numerical solution is obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The finite element model, having two nodal circles and ten degrees of freedom per node, is based in the Kirchhoff-Love theory that includes the transverse shear deformations by introducing a penalty function, which corresponds to the first order shear deformation theory (FSDT), is suitable for both thin and thick axisymmetric plate/shell structures. The reduced number of finite elements, which are required to model even complex structures, combined with the use of a small number of discrete layers to model the continuous variation of the mechanical properties through the thickness of the structure, results in an extremely low computational time required for FGM buckling applications. An in-house program has been developed, and applications in a variety of axisymmetric shells are solved, including circular plates. The solutions obtained in mechanical and thermal buckling are discussed and compared with alternative models.
- Vibrations of functionally graded material axisymmetric shellsPublication . Simões Moita, José Mateus; Araújo, Aurélio L.; Franco Correia, Victor; Soares, Cristóvão M. MotaThe free-vibration analysis of functionally graded materials (FGM) axisymmetric plate-shell type structures are presented in this work. A numerical solution is obtained by expanding the variables in Fourier series in the cir-cumferential direction and using conical frustum finite elements in the meridional direction. The finite element model, having two nodal circles and ten degrees of freedom per node, is based in the Kirchhoff-Love theory that include the transverse shear deformations by introducing a penalty function, and using one Gauss point inte-gration scheme which gave excellent results for both thin and thick axisymmetric plate/shells structures. The reduced number of finite elements, which are required to model even complex structures, combined with the use of a small number of discrete layers to model the continuous variation of the mechanical properties through the thickness of the structure, result in an extremely low computational time required for FGM applications. An in-house program has been developed, and applications in a variety of axysimetric shells are solved, including circular plates. The solutions obtained are discussed and compared with solutions obtained by alternative models.