Cristóvão M. Mota Soares

Modelling and design of adaptive composite structures

Recent developments in adaptive composite structures with distributed piezoelectric actuators and sensors have attracted significant attention in the research community due to their potential commercial benefits in a wide range of applications such as vibration suppression, shape control, noise attenuation and precision positioning. The complexity in the design and fabrication of the adaptive laminated composites has resulted in a need to develop reliable and refined models to study their material properties and mechanical behaviour. Here, higher order finite element formulations and an analytical closed form solution have been developed to study the mechanics of adaptive composite structures with embedded and/or bonded piezoelectric actuators and sensors. Optimization of adaptive composite structures is also an important design aspect in order to maximize actuator performance. Two optimization schemes are considered in this study where the design variables are the layer thickness, actuator size and location. To demonstrate the validity, usefulness and eAciency of the proposed models several illustrative examples are presented and discussed. ” 2000 Elsevier Science S.A. All rights reserved.

Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

Abstract 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 motivation for the present developments is the lack of studies in the behavior of adaptive structures using geometrically non-linear models, where only very few published works were found in the open literature. 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 non-conforming 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.

Active control of axisymmetric shells with piezoelectric layers: a mixed laminated theory with a high order displacement field

This paper presents the development of a semi-analytical axisymmetric shell finite element model with embedded and/or surface bonded piezoelectric ring actuators and/or sensors for active damping vibration control of the structure. A mixed finite element approach is used, which combines the equivalent single-layer higher order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electric potential of each piezoelectric layer of the frusta conical finite element. To achieve a mechanism of active control of the dynamic response of the structure a feedback control algorithm is used coupling the sensor and active piezoelectric layers. Two illustrative examples are presented and discussed.

Buckling and dynamic behaviour of laminated composite structures using a discrete higher-order displacement model

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 and free vibrations of multilaminated plates and shells. The effects of different number of layers, lamination angles, material anisotropy, and length or radius to thickness ratios are studied.

Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects

In this paper, a variation of Murakamis Zig-Zag theory is proposed for the analysis of functionally graded plates. The new theory includes a hyperbolic sine term for the in-plane displacements expansion and accounts for through-the-thickness deformation, by considering a quadratic evolution of the transverse displacement with the thickness coordinate. The governing equations and the boundary conditions are obtained by a generalization of Carreras Unified Formulation, and further interpolated by collocation with radial basis functions. Numerical examples on the static analysis of functionally graded sandwich plates demonstrate the accuracy of the present approach. The thickness stretching effect on such problems is studied.

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

Abstract In this paper a numerical method for the structural analysis of laminated axisymmetric shells based on the high-order theory is presented. A higher order displacement field is used with the longitudinal and circumferential components of the displacement given by power series of the transversal coordinate and the condition of zero stress in the top and bottom surfaces of the shell is imposed. In the element formulation the circumferential dependence is carried out by expanding the dependent variables and loading in truncated Fourier series which leads to a semi-analytical element. A special emphasis is given to the coupling effect between the symmetric and anti-symmetric terms for laminated materials with anisotropic properties.

Optimal design of piezolaminated structures

This paper presents refined finite element models based on higher-order displacement fields to study the mechanical and electrical behavior of laminated composite plate structures with embedded and/or surface bonded piezoelectric actuators and sensors. Sensitivity analysis and optimization techniques are also applied in order to maximize the piezoelectric actuator efficiency, improve the structural performance and/or minimize the weight of the structure. The application of structural optimization to the static shape control of adaptive structures is also addressed. To show the performance of the proposed models, several illustrative and simple examples are presented.

Refined models for the optimal design of adaptive structures using simulated annealing

This paper deals with refined finite element models based on higher-order displacement fields applied to the mechanical and electrical behavior of laminated composite plate structures with embedded and/or surface bonded piezoelectric actuators and sensors. Simulated annealing, a stochastic global optimization technique is implemented to find the optimal location of piezoelectric actuators in order to maximize its efficiency. The same technique is also used to solve optimization problems of piezolaminated plate structures where the discrete design variables are the ply orientation angles of orthotropic layers. The implemented scheme helps to recover from the premature convergence to a local optimum, without the need of reinitiating the optimal design process, as it is the case of the gradient-based methods with continuous design variables. To show the performance of the proposed optimization methods, two illustrative and simple examples are presented and discussed.

Buckling behaviour of laminated composite structures using a discrete higher-order displacement model

A higher-order theory is used to develop a discrete finite element model for the linear buckling analysis of multilaminated composite plate-shell structures. This model is based on an eight node isoparametric element with 10 degrees of freedom per node. The geometric stiffness matrix is developed by taking into consideration the effects of the higher order terms on the initial in-plane and transverse shear stresses. The model is applied to study several cases that take into consideration different number of layers, lamination angles, length-to-thickness ratio, as well as symmetry and non-symmetry on the laminates. The accuracy of the present formulation is evaluated by comparing the present results with alternative solutions.

Dynamic Analysis of Functionally Graded Plates and Shells by Radial Basis Functions

A meshless numerical method with a first-order shear deformation theory is used to study the linear transient response of functionally graded plates and shells. The present meshless method is based on the combination of pseudospectral methods and a collocation method with radial basis functions. A Newmark algoritm is used to advance the analysis in time. Results obtained are compared with analytical solutions.