J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 217-234, 2007, DOI:10.3970/cmes.2007.022.217

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered here. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated than in a homogeneous counterpart. Two-dimensional analyzed domain is subdivided into small circular subdomains surrounding nodes randomly spread over the whole domain. A unit step function is used as the test functions in the… More >

A. Arockiarajan¹, A. Menzel²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 55-72, 2007, DOI:10.3970/cmes.2007.020.055

Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic approach -- a purely phenomenologically… More >

A. Arockiarajan¹, A. Menzel²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 163-178, 2007, DOI:10.3970/cmes.2007.019.163

Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic approach -- a purely phenomenologically… More >

K.H. Chen^1,2, J.H. Kao³, J.T. Chen⁴

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 253-280, 2009, DOI:10.3970/cmc.2009.009.253

Abstract In this paper, solving antiplane piezoelectricity problems with multiple inclusions are attended by using the regularized meshless method (RMM). This is made possible that the troublesome singularity in the MFS disappears by employing the subtracting and adding-back techniques. The governing equations for linearly electro-elastic medium are reduced to two uncoupled Laplace's equations. The representations of two solutions of the two uncoupled system are obtained by using the RMM. By matching interface conditions, the linear algebraic system is obtained. Finally, typical numerical examples are presented and discussed to demonstrate the accuracy of the solutions. More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², F. Garcia-Sanche³, M. Wünsche²

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 109-118, 2006, DOI:10.3970/cmc.2006.004.109

Abstract Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of motion with an inertial term.… More >

Chih-Ping Wu¹, Yun-Siang Syu

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 87-108, 2006, DOI:10.3970/cmc.2006.004.087

Abstract Based on the three-dimensional (3D) piezoelectricity, we presented asymptotic solutions for multilayered piezoelectric hollow cylinders using the method of perturbation. The material properties in the general formulation are firstly regarded to be heterogeneous through the thickness, and then specified as the layerwise step functions in the cases of multilayered cylinders. The transverse normal load and normal electric displacement are respectively applied on the lateral surfaces of the cylinders. The boundary conditions of cylinders are considered to be simply supported at the two edges. In the formulation the twenty-two basic equations of piezoelectricity are reduced to eight differential equations in terms… More >

M. C. Ray¹, L. Dong², S. N. Atluri³

CMC-Computers, Materials & Continua, Vol.47, No.3, pp. 143-177, 2015, DOI:10.3970/cmc.2015.047.143

Abstract This paper is concerned with the development of new simple 4-noded locking-alleviated smart finite elements for modeling the smart composite beams. The exact solutions for the static responses of the overall smart composite beams are also derived for authenticating the new smart finite elements. The overall smart composite beam is composed of a laminated substrate conventional composite beam, and a piezoelectric layer attached at the top surface of the substrate beam. The piezoelectric layer acts as the actuator layer of the smart beam. Alternate finite element models of the beams, based on an “equivalent single layer high order shear deformation… More >