Retired professor of Solid MechanicsResearch in Structural mechanics, finite element method, several topics as nonlinear analysis, vibrations and buckling, considering different types of materials.
This work involves the design optimization of metal–ceramic through the thickness of functionally... more This work involves the design optimization of metal–ceramic through the thickness of functionally graded material (FGM) plates subjected to thermomechanical loadings. Constrained optimization was performed for minimum mass and minimum material cost of the FGM plates. The design process of FGM plate structures requires a good choice of metal and ceramic materials and the adequate definition of the components volume fractions through the thickness direction in order to accomplish a certain structural behavior, while optimizing the material costs and/or the plate mass. Here, the optimization problems are solved with the simulated annealing (SA) algorithm, not requiring the calculation of the derivatives of the objective or constraint functions. Constrained single objective optimization cases are studied, and validated with alternative solutions, considering the p-index and the FGM plate thickness as design variables. New optimization cases, involving additionally the metal and ceramic ...
Resumo. Neste trabalho apresenta-se um modelo de elementos finitos, baseado na teoria clássica de... more Resumo. Neste trabalho apresenta-se um modelo de elementos finitos, baseado na teoria clássica de placas, para a análise linear e não-linear de estruturas do tipo placa/casca integrando sensores e actuadores piezoeléctricos. É usado um simples e eficiente elemento placa/casca triangular plano de 3 nós, e em cuja formulação se introduz um grau de liberdade referente ao potencial eléctrico, por cada camada piezoeléctrica do elemento finito. É utilizada a formulação Lagrangeana actualizada associada à tecnica de Newton-Raphson para a solução iterativa das equações de equilibrio .O modelo pode ser aplicado a cascas piezolaminadas com geometria e carregamento arbitrários. Apresentam-se vários exemplos ilustrativos cujos resultados mostram a eficiencia do modelo proposto.
A sinus shear deformable theory is used to develop discrete model for the sensitivity analysis an... more A sinus shear deformable theory is used to develop discrete model for the sensitivity analysis and optimisation of moderate thickness and thin multi-layered angle ply composite plate structure. The structural analysis and sensitivity analysis formulation is developed for a family of C 1 six-node triangular finite element. The finite element has been shown to have good properties (e.g. no spurious energy mode, very fast convergence, no shear locking). The design sensitivity of static structural response for objective and/or constraint functions with respect to ply angle and ply thickness for linear and non-linear geometric analysis are developed. The design sensitivities are evaluated analytically despite their complexity. Construction of the sensitivity matrix is thus computed at the same time as the assembly of the structural stiffness matrix. The validity of analytical sensitivity is demonstrated by comparison with finite different approximations.
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structu... more This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuators or sensors layers and/or patches. The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. The finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equations.The model is applied in the solution of four illustrative cases, and the results are compared and discussed with alternative solutions when available.
Resumo. Neste trabalho apresenta-se um modelo de elementos finitos baseado na teoria de deformaca... more Resumo. Neste trabalho apresenta-se um modelo de elementos finitos baseado na teoria de deformacao de corte de 3a ordem, o qual e aplicado ao controlo activo de vibracoes, incluindo o fenomeno de ressonância, em estruturas laminadas. Sensores e actuadores piezoelectricos na forma de lâminas estao colados nas superficies superior e inferior do laminado, permitindo assim um sistema de controlo, ligando os efeitos piezoelectricos directo e converso, atraves dum algoritmo baseado na realimentacao com velocidade negativa. As estruturas sao forcadas a vibrar num determinado modo, e a sua amplitude no tempo e calculada usando o metodo de Newmark. Apresenta-se uma aplicacao ilustrativa.
Abstract. Composite structures incorporating piezoelectric sensors and actuators are increasingly... more Abstract. Composite 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 suppression, shape control and precision positioning. This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch, which 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 distribution is search to reach the specified structure transverse displacement distribution (shape ...
Abstract. This paper presents a finite element formulation based on the classical laminated plate... more Abstract. This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch. An optimization of the electric potential distribution is performed, in order to reach the specified structure transverse displacement distribution, minimizing an error function (shape control). A gradient based algorithm is used for this purpose. Results are presented and discussed.
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
This paper presents a finite element formulation based on the classical laminated plate theory fo... more This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch. An optimization of the electric potential distribution is performed, in order to reach the specified structure transverse displacement distribution, minimizing an error function (shape control). A gradient based algorithm is used for this purpose. Results are presented and discussed.
Mechanics of Advanced Materials and Structures, 2011
In this work a simple and efficient finite element model is developed for vibration analysis of a... more In this work a simple and efficient finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modeled using the classic plate theory and the core is modeled using Reddy's third-order shear deformation theory. The finite element is obtained by assembly of N "elements" through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which can be surface bonded or embedded in the laminate. To achieve a mechanism for the active control of the structural dynamics response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. To calculate the dynamic response of active-passive damped multilayer sandwich plate structures in time domain the Newmark method is considered. Frequency domain response is also calculated and compared with alternative solutions. For both responses, a finite element code is implemented. The model is applied in the solution of some illustrative examples and the results are presented and discussed.
This paper deals with buckling and free vibrations of multilaminated structures of arbitrary geom... more This paper deals with buckling and free vibrations of multilaminated structures of arbitrary geometry and lay-up using a single layer higher order shear deformation theory discrete model. This model is based on an eight-node C0 serendipity finite element with 10 degrees of freedom per node to contemplate general applications. The present model is tested on the evaluation of buckling loads
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
In this work a finite element model is developed for vibration analysis of active-passive damped ... more In this work a finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modelled using the classic plate theory and the core is modelled using the Reissener-Mindlin theory. The finite element is obtained by assembly of N ''elements'' through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The lack of finite element plate-shell models to analyse structures with passive and active damping, is the principal motivation for the present development, where the solution of some illustrative examples and the results are presented and discussed.
... Shape control and dynamic control of structures are some of the current applications of the r... more ... Shape control and dynamic control of structures are some of the current applications of the referred “intelligent structures” described by Crawley and de Luis [2]. Recent surveys can be found in Senthil et al. [3], Benjeddou [4], and Correia et al. [5]. ... Samanta et al. ...
In this paper is presented a higher-order model for static and free vibration analyses of magneto... more In this paper is presented a higher-order model for static and free vibration analyses of magneto-electroelastic plates, which allows the study of thin and thick plates. The finite element model is a single layer triangular plate/shell element with 24 degrees of freedom for the generalized mechanical displacements. Two degrees of freedom are introduced per each element layer, one corresponding to the electrical potential and the other for magnetic potential. Solutions are obtained for different laminations of the magnetoelectro-elastic plate, as well as for the purely elastic plate as a special case. Results are compared with alternative models for static and free vibrations situations.
This work involves the design optimization of metal–ceramic through the thickness of functionally... more This work involves the design optimization of metal–ceramic through the thickness of functionally graded material (FGM) plates subjected to thermomechanical loadings. Constrained optimization was performed for minimum mass and minimum material cost of the FGM plates. The design process of FGM plate structures requires a good choice of metal and ceramic materials and the adequate definition of the components volume fractions through the thickness direction in order to accomplish a certain structural behavior, while optimizing the material costs and/or the plate mass. Here, the optimization problems are solved with the simulated annealing (SA) algorithm, not requiring the calculation of the derivatives of the objective or constraint functions. Constrained single objective optimization cases are studied, and validated with alternative solutions, considering the p-index and the FGM plate thickness as design variables. New optimization cases, involving additionally the metal and ceramic ...
Resumo. Neste trabalho apresenta-se um modelo de elementos finitos, baseado na teoria clássica de... more Resumo. Neste trabalho apresenta-se um modelo de elementos finitos, baseado na teoria clássica de placas, para a análise linear e não-linear de estruturas do tipo placa/casca integrando sensores e actuadores piezoeléctricos. É usado um simples e eficiente elemento placa/casca triangular plano de 3 nós, e em cuja formulação se introduz um grau de liberdade referente ao potencial eléctrico, por cada camada piezoeléctrica do elemento finito. É utilizada a formulação Lagrangeana actualizada associada à tecnica de Newton-Raphson para a solução iterativa das equações de equilibrio .O modelo pode ser aplicado a cascas piezolaminadas com geometria e carregamento arbitrários. Apresentam-se vários exemplos ilustrativos cujos resultados mostram a eficiencia do modelo proposto.
A sinus shear deformable theory is used to develop discrete model for the sensitivity analysis an... more A sinus shear deformable theory is used to develop discrete model for the sensitivity analysis and optimisation of moderate thickness and thin multi-layered angle ply composite plate structure. The structural analysis and sensitivity analysis formulation is developed for a family of C 1 six-node triangular finite element. The finite element has been shown to have good properties (e.g. no spurious energy mode, very fast convergence, no shear locking). The design sensitivity of static structural response for objective and/or constraint functions with respect to ply angle and ply thickness for linear and non-linear geometric analysis are developed. The design sensitivities are evaluated analytically despite their complexity. Construction of the sensitivity matrix is thus computed at the same time as the assembly of the structural stiffness matrix. The validity of analytical sensitivity is demonstrated by comparison with finite different approximations.
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structu... more This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuators or sensors layers and/or patches. The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. The finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equations.The model is applied in the solution of four illustrative cases, and the results are compared and discussed with alternative solutions when available.
Resumo. Neste trabalho apresenta-se um modelo de elementos finitos baseado na teoria de deformaca... more Resumo. Neste trabalho apresenta-se um modelo de elementos finitos baseado na teoria de deformacao de corte de 3a ordem, o qual e aplicado ao controlo activo de vibracoes, incluindo o fenomeno de ressonância, em estruturas laminadas. Sensores e actuadores piezoelectricos na forma de lâminas estao colados nas superficies superior e inferior do laminado, permitindo assim um sistema de controlo, ligando os efeitos piezoelectricos directo e converso, atraves dum algoritmo baseado na realimentacao com velocidade negativa. As estruturas sao forcadas a vibrar num determinado modo, e a sua amplitude no tempo e calculada usando o metodo de Newmark. Apresenta-se uma aplicacao ilustrativa.
Abstract. Composite structures incorporating piezoelectric sensors and actuators are increasingly... more Abstract. Composite 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 suppression, shape control and precision positioning. This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch, which 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 distribution is search to reach the specified structure transverse displacement distribution (shape ...
Abstract. This paper presents a finite element formulation based on the classical laminated plate... more Abstract. This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch. An optimization of the electric potential distribution is performed, in order to reach the specified structure transverse displacement distribution, minimizing an error function (shape control). A gradient based algorithm is used for this purpose. Results are presented and discussed.
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
This paper presents a finite element formulation based on the classical laminated plate theory fo... more This paper presents a finite element formulation based on the 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 piezoelectric element layer or patch. An optimization of the electric potential distribution is performed, in order to reach the specified structure transverse displacement distribution, minimizing an error function (shape control). A gradient based algorithm is used for this purpose. Results are presented and discussed.
Mechanics of Advanced Materials and Structures, 2011
In this work a simple and efficient finite element model is developed for vibration analysis of a... more In this work a simple and efficient finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modeled using the classic plate theory and the core is modeled using Reddy's third-order shear deformation theory. The finite element is obtained by assembly of N "elements" through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which can be surface bonded or embedded in the laminate. To achieve a mechanism for the active control of the structural dynamics response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. To calculate the dynamic response of active-passive damped multilayer sandwich plate structures in time domain the Newmark method is considered. Frequency domain response is also calculated and compared with alternative solutions. For both responses, a finite element code is implemented. The model is applied in the solution of some illustrative examples and the results are presented and discussed.
This paper deals with buckling and free vibrations of multilaminated structures of arbitrary geom... more This paper deals with buckling and free vibrations of multilaminated structures of arbitrary geometry and lay-up using a single layer higher order shear deformation theory discrete model. This model is based on an eight-node C0 serendipity finite element with 10 degrees of freedom per node to contemplate general applications. The present model is tested on the evaluation of buckling loads
A high order shear deformation theory is used to develop a discrete model for the sensitivity ana... more A high order shear deformation theory is used to develop a discrete model for the sensitivity analysis and optimization of laminated plate and shell structures in non-linear response. The geometrically non-linear analysis is based on an updated Lagrangian formulation associated with the Newton–Raphson iterative technique, which incorporates an automatic arc-length procedure. Fiber orientation angles and vectorial distances from middle surface
In this work a finite element model is developed for vibration analysis of active-passive damped ... more In this work a finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modelled using the classic plate theory and the core is modelled using the Reissener-Mindlin theory. The finite element is obtained by assembly of N ''elements'' through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The lack of finite element plate-shell models to analyse structures with passive and active damping, is the principal motivation for the present development, where the solution of some illustrative examples and the results are presented and discussed.
... Shape control and dynamic control of structures are some of the current applications of the r... more ... Shape control and dynamic control of structures are some of the current applications of the referred “intelligent structures” described by Crawley and de Luis [2]. Recent surveys can be found in Senthil et al. [3], Benjeddou [4], and Correia et al. [5]. ... Samanta et al. ...
In this paper is presented a higher-order model for static and free vibration analyses of magneto... more In this paper is presented a higher-order model for static and free vibration analyses of magneto-electroelastic plates, which allows the study of thin and thick plates. The finite element model is a single layer triangular plate/shell element with 24 degrees of freedom for the generalized mechanical displacements. Two degrees of freedom are introduced per each element layer, one corresponding to the electrical potential and the other for magnetic potential. Solutions are obtained for different laminations of the magnetoelectro-elastic plate, as well as for the purely elastic plate as a special case. Results are compared with alternative models for static and free vibrations situations.
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Papers by Jose Moita