J. Sladek¹, V. Sladek¹, P. Stanak¹, P.H. Wen², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 543-572, 2012, DOI:10.3970/cmes.2012.085.543

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate piezoelectric plates described by the Reissner-Mindlin theory. The piezoelectric layer can be used as a sensor or actuator. A pure mechanical load or electric potential are prescribed on the top of the laminated plate. Both stationary and transient dynamic loads are analyzed here. The bending moment, the shear force and normal force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. Then, the original three-dimensional (3-D) thick plate problem is reduced to a two-dimensional (2-D) problem. Nodal points are randomly distributed… More >

Mohsen Sadeghbeigi Olyaie¹, Mohammad Reza Razfar², Semyung Wang³, Edward J. Kansa⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.1, pp. 55-82, 2011, DOI:10.32604/cmes.2011.082.055

Abstract This paper presents the topology optimization design for a linear micromotor, including multitude cantilever piezoelectric bimorphs. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Certainty variables such as weight of the structure and equilibrium equations are considered as constraints during the topology optimization design process, then a deterministic topology optimization (DTO) is conducted. To avoid the overly stiff behavior in FEM modeling, a relatively new numerical method known as… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², M. Wünsche²

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.068.185

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations,… More >

E. Carrera, S. Brischetto¹, M. Cinefra²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.3, pp. 259-342, 2010, DOI:10.3970/cmes.2010.065.259

Abstract This paper investigates the problem of free vibrations of multilayered plates and shells embedding anisotropic and thickness polarized piezoelectric layers. Carrera's Unified Formulation (CUF) has been employed to implement a large variety of electro-mechanical plate/shell theories. So-called Equivalent Single Layer and Layer Wise variable descriptions are employed for mechanical and electrical variables;linear to fourth order expansions are used in the thickness direction z in terms of power of z or Legendre polynomials. Various forms are considered for the Principle of Virtual Displacements (PVD) and Reissner's Mixed Variational Theorem (RMVT) to derive consistent differential electro-mechanical governing equations. The effect of electro-mechanical… More >

Y.C. Chen¹, Chyanbin Hwu²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 31-50, 2010, DOI:10.3970/cmes.2010.057.031

Abstract The Green's function for anisotropic bimaterials has been investigated around three decades ago. Since the mathematical formulation of piezoelectric elasticity can be organized into the same form as that of anisotropic elasticity by just expanding the dimension of the corresponding matrix to include the piezoelectric effects, the extension of the Green's function to piezoelectric bimaterials can be obtained immediately through the associated anisotropic bimaterials. In this paper, the Green's function for the bimaterials bonded together with one anisotropic material and one piezoelectric material is derived by applying Stroh's complex variable formalism with the aid of analytical continuation method. For this… More >

A. Chakraborty¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 105-132, 2009, DOI:10.3970/cmes.2009.040.105

Abstract A mathematical model is presented in this work that describes the behavior of porous piezoelectric materials subjected to mechanical load and electric field. The model combines Biot's theory of poroelasticity and the classical theory of piezoelectric material wherein it is assumed that piezoelectric coupling exists only with the solid phase of the porous medium. This model is used to analyze the stress and electric wave generated in bone and porous Lead-Zirconate-Titanate (PZT) due to high frequency pulse loading. The governing partial differential equations are solved in the frequency domain by transforming them into a polynomial eigenvalue structure. This approach permits… More >

Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional… More >

H. Nguyen-Van¹, N. Mai-Duy², T. Tran-Cong³

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 209-222, 2008, DOI:10.3970/cmes.2008.023.209

Abstract This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated.… More >

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 >

Kuang-Chong Wu¹, Shyh-Haur Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 147-156, 2007, DOI:10.3970/cmes.2007.020.147

Abstract A formulation for two-dimensional self-similar anisotropic elastodyamics problems is generalized to piezoelectric materials. In the formulation the general solution of the displacements is expressed in terms of the eigenvalues and eigenvectors of a related eight-dimensional eigenvalue problem. The present formulation can be used to derive analytic solutions directly without the need of performing integral transforms as required in Cagniard-de Hoop method. The method is applied to derive explicit dynamic Green's functions. Some analytic results for hexagonal 6mm materials are also derived. Numerical examples for the quartz are illustrated. More >