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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.
- Design of laminated structures using piezoelectric materialsPublication . Simões Moita, José Mateus; Herskovits, José; Soares, Cristovão M. Mota; Soares, Carlos A. MotaComposite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the offer of potential benefits in a wide range of engineering applications such as vibration and noise supression, shape control and precisition positioning. This paper presents a finit element formulation based on classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezsoelectric elementlayer or patch, witch are surface bonded on the laminate. An optimization of the patches position is performed to maximize the piezoelectric actuators efficiency as well as, the electric potential distribuition is search to reach the specified structure transverse displacement distribuition (shape control). A gradient based algorithm is used for this purpose. The model is applied in the optimization of illustrative laminated plate cases, and the results are presented and discussed.
- Elastoplastic and nonlinear analysis of functionally graded axisymmetric shell structures under thermal environment, using a conical frustum finite element modelPublication . Simões Moita, José Mateus; Mota Soares, Cristovao M.; Mota Soares, Carlos A.; Ferreira, Antonio J. M.This work presents the formulation for static bending analysis of functionally graded axisymmetric plate/shell type structures under mechanical loading, and considering different structural behaviours: linear, geometric nonlinear and material nonlinear. The implemented model is based on a simple conical frustum finite element with 2 nodes, and 3 degrees of freedom per node, which includes shear deformation effects, and it shows to be extremely efficient in the analysis of axisymmetric shells subjected to axisymmetric loading. The used of reduced numerical integration procedure is essential for its success when applied to thin shells. The formulation accounts for the calculation of displacements and through-thickness stress distribution. The solutions for some illustrative examples involving variation of volume fractions are obtained, and the results are presented and compared with numerical alternative models when available, and discussed.
- 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.
- Static analysis of composite and hybrid axisymmetric shellsPublication . Soares, Carlos A. Mota; Simões Moita, José Mateus; Araujo, Aurélio L.; Correia, Victor Franco; Soares, Cristóvão M. MotaIn this work, we present formulations for linear and geometrically nonlinear static analyses ofhybrid axisymmetric shell structures. The hybrid structures (F/C/F) are made by layers of compositematerial (C) sandwiched by two functionally graded material layers (F). The analysis is performedusing a finite element model. The numerical solution is obtained by expanding the variables inFourier series in the circumferential direction and using conical frustum finite elements in themeridional direction. The implemented finite element is a simple conical frustum with two nodalcircles. This model uses a small number of discrete layers to model the continuous variation ofthe mechanical properties through the thickness of the functionally graded material (FGM) layers.It requires a reduced number of finite elements to model the geometry of even complex struc-tures, and the integration procedures uses only one Gauss point. From the combination of thosecharacteristics, the resulting model requires extremely low computation time. A computer programhas been developed, and the solutions obtained are discussed and compared with resultsobtained by alternative models available in the literature. The present plate/shell model providesnew insights for future advances to carry out numerical studies involving multi-objective optimiza-tion of axisymmetric structures made of advanced materials.