Electroelastic Analysis of Piezoelectric Composite Laminates by Boundary Integral Equations

Abstract

A boundary integral representation for the electroelastic state in piezoelectric composite laminates subjected to axial extension, bending, torsion, shear/bending, and electric loadings is proposed. The governing equations are presented in terms of electromechanical generalized variables by the use of a suitable matrix notation. Thus, the three-dimensional electroelasticity solution for piezoelectric composite laminates is generated from a set of two partially coupled differential equations defined on the cross section of each individual ply within the laminate. These ply equations are linked through the interface conditions, which allow restoration of the model of the laminate as a whole. For this model, the corresponding boundary integral representation and the relative boundary integral equations are deduced, and their features are discussed. The formulation presented lays out the analytical foundation for the development of the multidomain boundary element method to determine numerically the electromechanical response of piezoelectric composite laminates. Numerical results showing the characteristics of the method are given, and the fundamental behavior of piezoelectric composite laminates is pointed out for both mechanical and electrical loads. I. Introduction P IEZOELECTRIC materials generate an electric field when subjected to strain fields and undergo deformation when an electric field is applied. This inherent electromechanical coupling, known as direct and converse piezoelectric effects, is widely exploited in the design of many devices working as transducers, sensors, and actuators. In addition, piezoelectric materials are of primary concern in the field of advanced lightweight structures, where the smart structure technology is now emerging. 1−4 When piezoelectric members are bonded or merged within a structure, it is possible to combine the mechanical properties of the host structure with the additional capabilities to sense deformation and to adapt the structural response accordingly. The first attempt at the application of smart structures with sensing and control capabilities was concerned with the application of piezoelectric patches on the surfaces of beams and plates to induce strain actions on the passive structure or detect its deformation. The development of this approach, together with the improvement of composite material technology, led to the concept of distributed sensing and control, which can be accomplished by the introduction of piezoelectric layers within composite laminates. More recently, the idea of distributed structural control properties has been fully developed by the use of active fiber composites. 5 In these fiber-reinforced composites, the fiber and the matrix have additional functions besides their typical roles. The fiber, which generally exhibits a piezoelectric behavior, not only accomplishes the task of structural reinforcement, but it also has the function of both sensor and actuator. In this kind of smart structure, an active control of the mechanical response is performed on the basis of the intrinsic properties of the structure material. Some of the fundamental problems involved in the mechanical testing, analysis, and design, namely, failure modes and strength and stiffness degradation under static and cyclic fatigue loads, are not tractable without a thorough knowledge of the