R. Garcia Lage

Abstract: In this paper a partial mixed layerwise finite element model for adaptive plate structures is presented. Static analysis of magneto-electro-elastic laminated plate structures is considered. The mixed finite element formulation is obtained by considering a Reissner mixed variational principle. The mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables. The other fields are calculated by post-computation through constitutive equations. The numerical results obtained by the present model are in good agreement with available three-dimensional analytical solutions.

Abstract: This paper deals with the development of a layerwise finite element model for piezolaminated plate structures. A Reissner mixed variational principle is used to formulate the finite element model. The mixed functional is formulated using transverse stresses, transverse electrical displacement (if continuity, across the thickness, is required), displacement components and electrical potential as primary variables. The present model in contrast with the standard layerwise displacement finite element model, fulfils the continuity of all primary variables across the interface between adjacent layers. Only the in-plane stress components and electric displacements are evaluated in the post-computation through the piezolaminate constitutive equations. The applicability and performance of the proposed finite element model is illustrated with two examples. The predictions of the primary variables and the efficiency of the model, mainly with reference to the interlaminar stresses are discussed and compared with alternative three-dimensional solutions. The present solutions are found to be in good agreement.

Abstract: This paper deals with the development of a layerwise finite element model for piezo-laminated plate structures. A Reissner mixed variational equation is used to derive the governing equations, using transverse stresses, transverse electrical displacement, displacement components and electrical potential as primary variables. The present model in contrast with the standard layerwise displacement finite elements fulfils the continuity of all primary variables at the interface between adjacent layers. Only the layers in-plane stress components and corresponding electric displacements are evaluated by post-processing through the piezolaminated constitutive equations. The applicability and performance of the proposed model is illustrated with an example. The predictions of the primary variables and the efficiency of the model mainly related with the interlaminar stresses are discussed and compared with alternative three-dimensional solutions.

Abstract: In this paper, a mixed layerwise finite element model for adaptive plate structures is presented. Static and free-vibration analysis of piezoelectric laminated plate structures is considered. A modified Reissner mixed variational principle is used to formulate the finite element model. The mixed functional is formulated using transverse stresses, displacement components and electrical potential as primary variables. The present model, in contrast with the standard layerwise displacement finite element model, fulfils the continuity of all primary variables across the interface between adjacent layers. The in-plane stress components and the electric displacements are evaluated in the post-computation through the piezolaminate constitutive equations. Two illustrative examples are presented for comparison. The predictions of the primary variables and the efficiency of the model, mainly with reference to the interlaminar stresses are discussed and compared with alternative three-dimensional solutions. The present solutions are found to be in good agreement with the benchmark solutions for the static and modal analysis problems.

Abstract: Walsh series are used to develop a finite-element model based on first-order shear deformation theory that enables accurate prediction of static and dynamic response of laminated composite plates. The model is based on a single-layer quadrilateral plate element with mixed formulation, which can be applied to any arbitrary layup. The model has as degrees of freedom stress resultants and generalized displacements. The accuracy and efficiency of the model developed is discussed with four illustrative cases, for static and natural frequencies results, which are compared with alternative solutions.

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Abstract: Lagrangian dynamics of mechanical systems 1.1 Introduction 1.2 Kinetic state functions 1.3 Generalized coordinates, kinematic constraints 1.4 The principle of virtual work 1.5 D'Alembert's principle 1.6 Hamilton's principle 1.7 Lagrange's equations 1.8 Lagrange's equations with constraints 1.9 Conservation laws 1.10 More on continuous systems 1.11 References 2 Dynamics of electrical networks 2.1 Introduction 2.2 Constitutive equations for circuit elements 2.3 Kirchhoff's laws 2.4 Hamilton's principle for electrical networks 2.5 Lagrange's equations 2.6 References 3 Electromechanical Systems 3.1 Introduction 3.2 Constitutive relations for transducers 3.3 Hamilton's Principle 3.4 Lagrange's equations 3.5 Examples 3.6 General electromechanical transducer 3.7 References 4 Piezoelectric Systems 4.1 Introduction 4.2 Piezoelectric transducer 4.3 Constitutive relations of a discrete transducer 4.4 Structure with a discrete piezoelectric transducer 4.5 Multiple transducer systems 4.6 General piezoelectric structure 4.7 Piezoelectric material 4.8 Hamilton's principle 4.9 Rosen's piezoelectric transformer 4. 10 References 5 Piezoelectric laminates 5.1 Piezoelectric beam actuator 5.2 Laminar sensor 5.3 Spatial modal filters 5.4 Active beam with collocated actuator-sensor 5.5 Piezoelectric laminates 5.6 References 6 Active and Passive Damping with Piezoelectric Transducers 6.1 Introduction 6.2 Active strut, open-loop FRF 6.3 Active damping via 1FF 6.4 Admittance of the piezoelectric transducer 6.5 Damping via resistive shunting 6.6 Inductive shunting 6.7 Decentralized control 6.8 General piezoelectric structure 6.9 Self-sensing 6.10 Other active damping strategies 6.11 Remark 6.12 References Bibliography Index

Abstract: An approximate solution for the free vibration problem of two-dimensional magneto-electro-elastic laminates is presented to determine their fundamental behavior. The laminates are composed of linear homogeneous elastic, piezoelectric, or magnetostrictive layers with perfect bonding between each interface. The solution for the elastic displacements, electric potential, and magnetic potential is obtained by combining a discrete layer approach with the Ritz method. The model developed here is not dependent on specific boundary conditions, and it is presented as an alternative to the exact or analytical approaches which are limited to a very specific set of edge conditions. The natural frequencies and through-thickness modal behavior are computed for simply supported and cantilever laminates. Solutions for the simply supported case are compared with the known exact solution for piezoelectric laminates, and excellent agreement is obtained. The present approach is also validated by comparing the natural frequencies of a two-layer cantilever plate with known analytical solution and with results obtained using commercial finite element software.

Abstract: This paper discusses the different electromagnetic boundary conditions on the crack-faces in magnetoelectroelastic materials, which possess coupled piezoelectric, piezomagnetic and magnetoelectric effects. A notch of finite thickness in these materials containing air (or vacuum) is also addressed. Four ideal crack-face electromagnetic boundary condition assumptions, that is, (a) electrically and magnetically impermeable crack, (b) electrically impermeable and magnetically permeable crack, (c) electrically permeable and magnetically impermeable crack and (d) electrically and magnetically permeable crack, are investigated separately. The influence of notch thickness on the field intensity factors at notch tips and the electromagnetic field inside the notch are obtained in closed-form. The results are compared with the ideal crack solutions. Applicability of crack-face electromagnetic boundary condition assumptions is discussed.

Abstract: In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. Green’s function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].