Paolo Gaudenzi

An Iterative Finite Element Procedure for the Analysis of Piezoelectric Continua

In this paper an iterative finite element procedure is presented for the analysis of twoand three-dimensional piezoelectric continua. The procedure is applied to the steady-state analysis of two-dimensional media subjected to mechanical and electrical loading.

A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates

Abstract A layerwise polynomial expansion along the thickness direction for displacements is assumed to analyse the behaviour of an arbitrary laminated composite plate. In contrast with other proposed approaches and in order to take into account the transverse normal stress distribution, out-of-plane displacements are not assumed to be constant along the thickness. Based on the proposed kinematic assumptions the continuity of the interlaminar stress components at the interface can be also achieved. A finite element procedure is established and plate models are derived in which the stress field is obtained directly from the constitutive relations and not by the integration of the three-dimensional equilibrium equations. Comparisons among the numerical results obtained with the proposed layerwise models, single-layer models, the classical laminate theory and exact three-dimensional elasticity solutions are presented and briefly discussed.

Optimal placement of PZT actuators for the control of beam dynamics

The dynamics of a flexural beam actuated by induced strain surface bonded (piezoelectric) actuators is considered. The bending moment produced by the single actuator is evaluated by means of the pin-force model. A modal approach is then used to build special dynamic influence functions which explicitly account for the size and the position of the actuator. Simple optimal geometrical conditions are then obtained and illustrated for several cases with different boundary conditions.

Control of beam vibrations by means of piezoelectric devices: theory and experiments

Abstract The problem of the attenuation of the vibration effects in active cantilever beams has been approached by two strategies, position and velocity control, which have been simulated numerically and analysed experimentally. The numerical simulation has been developed by means of a finite element approach based on an Euler–Bernoulli model and subsequent modal factorisation. Each device as well as each electronic circuit, present in the single-input single-output control system has been modelled and the results of the numerical simulations have been compared with the ones obtained in the experimental tests. A good correspondence has been obtained in all the examined cases.

Post-buckling behavior of composite panels in the presence of unstable delaminations

The analysis of the non-linear behavior of delaminated composites panels under compression is considered. A modification to the incremental continuation method (by Riks) for the analysis of the non-linear behavior of damaged composites is proposed to improve the numerical treatment of the analysis of unstable delamination growth. The theoretical formulation of this modification is first presented in conjunction with a general formulation of the continuation method and the modified virtual crack closure technique (MVCCT) for the evaluation of delamination growth. Finally, numerical results for delaminated composite plates through the width and circular delaminations are presented and compared with existing experimental and numerical data.

MULTI-LAYER HIGHER-ORDER FINITE ELEMENTS FOR THE ANALYSIS OF FREE-EDGE STRESSES IN COMPOSITE LAMINATES

The analysis of the free-edge stress distributions in composite laminates under uniaxial tension is approached by a finite element technique based on a multi-layer higher-order laminate theory. Several finite elements corresponding to different through-thickness assumed distributions of the displacement unknowns are developed. Numerous stacking sequences are examined in the applications. The results are compared with the ones obtained by various investigators with other modelling approaches. The use of the proposed technique is demonstrated to be simple and effective both for the analysis of in-plane and out-of-plane distributions of intralaminar and, noticeably, interlaminar stress components.

ON THE ELECTROMECHANICAL RESPONSE OF ACTIVE COMPOSITE MATERIALS WITH PIEZOELECTRIC INCLUSIONS

Abstract The electromechanical response of a two-phases dielectric material with an active piezoelectric part is considered. The variational formulation of the problem is presented and a finite element procedure which allows to compute the coupled electro-mechanical response is proposed. A simple geometry of a possible active composite material is studied under different loading conditions. The relevant linear response is then shown in terms of the electrical and mechanical variables.

Multi-layer higher-order finite elements for the analysis of free-edge stresses in piezoelectric actuated laminates

The static interaction between a laminate and distributed piezoelectric actuators is considered. In particular the problem of the stress concentration at the free edge of the active elements of a piezoelectric composite is investigated. A finite element model for the laminated composite plate is developed using a multi-layer higher-order finite element approach. A typical configuration is considered, in which two active layers are bonded on the top and bottom of a passive substructure. A pure bending case is investigated. The obtained results provide useful information of the typical static response. A parametric study is also performed on the effects of the main geometrical characteristics on the intensity and the extension of edge effect.

Structural Health Monitoring for Future Space Vehicles

Structural health monitoring (SHM) is certainly one of the key technologies required to achieve the goal for new space vehicles of having reduced maintenance costs with increased levels of safety. For the time being, sensor technology has reached a good technology readiness level, but the integration of these technologies into the design process of a space vehicle has not received much consideration. The present article aims at giving a reference about the existing technologies on the matter and an introduction to some of the key issues for the integration of a SHM system into the design process of future space vehicles. In addition, the accident that occurred to the space shuttle Columbia is analyzed in order to show how SHM could be effective for the improvement of safety in future space vehicles. Furthermore, since important changes to aeronautical design procedures have been introduced as a consequence of catastrophic events, the evolution of aeronautical design practices in parallel with accidents has been examined.

A general formulation of higher-order theories for the analysis of laminated plates

The structural analysis of laminated plates is approached by means of a displacement-based method. The displacement unknowns are expanded in power series through the thickness of the laminate. A general higher-order theory is developed both for single-layer and for multiple-layer models. As particular cases, zig-zag models or simple higher-order models already developed in the literature are obtained. The possibility of getting simplified forms of displacements based on a priori assumptions about stresses is discussed. In the case of the single-layer approach the equilibrium equations of the laminated plate valid for whichever order are then derived using a variational method. Closed-form solutions are then obtained for simple laminates.