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 >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³, L. Starek³

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 247-262, 2007, DOI:10.3970/cmes.2007.019.247

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals on the surfaces of subdomains.… 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 >

J.A. Sanz, M. Solis, J. Dominguez¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 215-230, 2007, DOI:10.3970/cmes.2007.017.215

Abstract A general mixed boundary element formulation for three-dimensional piezoelectric fracture mechanics problems is presented in this paper. The numerical procedure is based on the extended displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels appearing in the formulation are analytically transformed into weakly singular and regular integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a direct way in a computer code. Electric and stress intensity factors are directly computed from nodal values at quarter-point elements. Crack problems in 3D piezoelectric bounded and unbounded solids are solved. The obtained… More >

G. Dziatkiewicz¹ and P. Fedelinski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 35-46, 2007, DOI:10.3970/cmes.2007.017.035

Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity method (DRM). The boundary quantities… More >

Daiki Shiozawa¹, Shiro Kubo², Takahide Sakagami², Masaaki Takagi²

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.1, pp. 27-36, 2006, DOI:10.3970/cmes.2006.011.027

Abstract The passive electric potential CT (computed tomography) method using piezoelectric film was applied to the identification of plural through cracks. The use of piezoelectric material made it possible to obtain electric potential field without applying electric current. For identification of cracks an inverse analysis scheme based on the least residual method was applied, in which square sum of residuals is evaluated between the measured electric potential distributions and those computed by using the finite element method. Akaike information criterion (AIC) was used to estimate the number of cracks. Numerical simulations were carried out on the identification of plural cracks and… 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 >

Chih-Ping Wu^1,2, Kuan-Hao Chiu², Yung-Ming Wang²

CMC-Computers, Materials & Continua, Vol.8, No.2, pp. 93-132, 2008, DOI:10.3970/cmc.2008.008.093

Abstract The article is to present an overview of various three-dimensional (3D) analytical approaches for the analysis of multilayered and functionally graded (FG) piezoelectric plates and shells. The reported 3D approaches in the literature are classified as four different approaches, namely, Pagano's classical approach, the state space approach, the series expansion approach and the asymptotic approach. Both the mixed formulation and displacement-based formulation for the 3D analysis of multilayered piezoelectric plates are derived. The analytical process, based on the 3D formulations, for the aforementioned approaches is briefly interpreted. The present formulations of multilayered piezoelectric plates can also be used for the… More >

Chih-Ping Wu^1,2, Kuo-Yen Liu²

CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 177-200, 2007, DOI:10.3970/cmc.2007.006.177

Abstract Based on the three-dimensional (3D) piezoelectricity, we present the exact solutions of simply-supported, doubly curved functionally graded (FG) elastic and piezoelectric shells using a state space approach. A set of the dimensionless coordinates and field variables is introduced in the present formulation to prevent from the ill-conditioned problem in the relevant computation. By means of direct elimination, we reduce the twenty-two basic differential equations to a set of eight state variable equations (or state equations) with variable coefficients of the thickness coordinate. By means of the successive approximation method, we artificially divide the shell into a NL-layered shell and the… 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 >