José Mateus Simões Moita

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.

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.

Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells

Abstract 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 to the upper surface of each layer are considered as the design variables. Different objectives, such as generalized displacements at specified nodes, volume of structural material, and limit load, and constraints of displacement and stress failure criterion are considered. The design sensitivities are evaluated analytically and are compared with sensitivities evaluated by the global finite difference. Numerical examples are given to show the accuracy of the proposed model in the non-linear response and the corresponding design sensitivity analysis, and to show the applicability in the optimal design.

Analysis of Active-Passive Plate Structures Using a Simple and Efficient Finite Element Model

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 classical 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. 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. The dynamic analysis of active-passive damped multilayer sandwich plate structures is conducted in frequency domain to obtain the natural frequencies and respective loss factors, and in time domain for steady state harmonic motion. For both analyses, a finite element code is implemented. The model is applied in the solution of some illustrative examples and the results are presented and discussed.

Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures

A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton–Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.

Higher Order Model for Analysis of Magneto-Electro-Elastic Plates

In the recent years the study of smart structures has attracted significant researchers. The use of smart materials, such as piezoelectric and/or piezomagnetic materials, in the form of layers or patches embedded and/or surface bonded on laminated composite structures, can provide the so-called adaptive structures. In these cases, the structure behaviour is not defined by the geometry and material properties, but also by the electric and magnetic fields that are applied to the structures, because the piezomagnetic materials have the ability of converting energy from one form to the other (among magnetic, electric, and mechanical energies).