Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

Abstract

An efficient meshfree formulation based on the first-order shear deformation theory (FSDT) is presented for the static analysis of laminated composite beams and plates with integrated piezoelectric layers. This meshfree model is constructed based on the element-free Galerkin (EFG) method. The formulation is derived from the variational principle and the piezoelectric stiffness is taken into account in the model. In numerical test problems, bending control of piezoelectric bimorph beams was shown to have the efficiency and accuracy of the present EFG formulation for this class of problems. It is demonstrated that the different boundary conditions and applied actuate voltages affects the shape control of piezolaminated composite beams. The meshfree model is further extended to study the shape control of piezolaminated composite plates. From the investigation, it is found that actuator patches bonded on high strain regions are significant in deflection control of laminated composite plates. IntroductionThe subject of numerical simulation has been dominated by the finite element method (FEM), finite difference method (FDM) and boundary element method (BEM) for the past few decades. Having been thoroughly developed and refined over many years, FEM has become a very popular, effective and versatile tool for the computer solution of complex problems in engineering disciplines. Since finite element solution is highly mesh dependent, its shortcomings such as prolonged time-consuming mesh refinements and elements of distorted shapes and sizes when handling different types of problems, such as crack propagation, high gradient (e.g., shock wave) and shear band strain localization are evident.A new family of methods has been developed to ameliorate the above-mentioned difficulties. In fact, these have drawn considerable attention as the methods employ an approximation of the unknown field based on a scattered set of nodes or particles. This class of methods is the socalled meshless or meshfree methods. In these methods, the domain of interest is discretized by a scattered set of particles instead of elements used in mesh-based methods such as FEM, and thus without having the need for characterization of the interrelationship of the nodes, be able to construct the discrete equations. It is developed by creating new shape functions using the interpolation of field variables at a global level. Owing to the above-mentioned advantages, increasing attention is placed on the development of meshfree methods as alternative to the finite element method.The element-free Galerkin method (EFG) is a truly meshfree one, as it does not need a 'finite element or boundary element mesh', i.e., there is no necessity for explicit meshes in the construction of moving least-square (MLS) shape functions. Although background cells are required for integration, the integration cells need not be compatible to the scattered nodes distributed on the structures, thus they can be generated more easily than the FEM meshes. The consistency of the MLS approxi...

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