T. Lahmer¹, J. Ilg², R. Lerch²

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.2, pp. 105-126, 2015, DOI:10.3970/cmes.2015.106.105

Abstract In the recent years many publications appeared putting emphasis on the simulation-based identification of piezoelectric material parameters from electrical or mechanical measurements and combinations of them. By experience, one is aware of the importance of a single input parameter. However, it is not yet fully understood and in particular quantified to which extend missing knowledge in the single parameters (parameter uncertainty) influences the quality of the model's prognosis. In this paper, we adapt and apply variance-based sensitivity measures to models describing the piezoelectric effect in the linear case and derive global information about the single input parameter's sensitivities. More >

J. Sladek^1,2, V. Sladek¹, E. Pan³, D.L. Young⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 273-296, 2014, DOI:10.3970/cmes.2014.099.273

Abstract This paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It is noted that the stresses… More >

Xiaoming Zhang¹, Xingxin Xu^1,2, Yuqing Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.100.001

Abstract Orthogonal polynomial approach has been used to deal with the wave propagation in structures that have finite dimension in only one direction, such as horizontally infinite flat plates, axially infinite hollow cylinders. In order to solve wave propagation in two-dimensional piezoelectric rod with rectangular cross section, i.e. the piezoelectric plate with finite dimensions in two directions, an extended orthogonal polynomial approach is proposed in this paper. For validation and illustration purposes, the proposed approach is applied to solving the wave propagation in a square steel rod. The results obtained are in good agreement with the results from the semi-analytical finite… More >

Ying Xu¹, Shuling Hu¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.5, pp. 397-408, 2013, DOI:10.3970/cmes.2013.091.397

Abstract Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. In this paper, the flexoelectric effect is taken into account to investigate the electrostatic potential distribution in a bent flexoelectric semiconductive nanowire, and the numerical solution is obtained by using the finite difference method. The effect of donor concentration on the electrostatic potential are also investigated. The results show that, the flexoelectricity increases the value of the voltage on the cross section. The flexoelectric effect is varied with the size, i.e. when the radius of the nanowire is small the flexoelectric effect is significant. It is also… More >

Mohsen Sadeghbeigi Olyaie¹, Mohammad Reza Razfar², Edward J. Kansa³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.1, pp. 43-88, 2011, DOI:10.3970/cmes.2011.075.043

Abstract This paper presents integration of reliability analysis with topology optimization design for a linear mircroactuator, including multitude cantilever piezoelectric bimorphs. Each microbimoph in the mechanism can be actuated in both axial and flexural modes simultaneously. We consider quasi-static and linear conditions, and the smoothed finite element method (S-FEM) is employed in the analysis of piezoelectric effects. Since microfabrication methods are used for manufacturing this type of actuator, uncertainty variables become very important. Hence, these variables are considered as constraints during our topology optimization design process and reliability based topology optimization (RBTO) is conducted. To avoid the overly-stiff behavior in FEM… More >

Chih-Ping Wu^1,2, Jian-Sin Wang², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 1-38, 2009, DOI:10.3970/cmes.2009.052.001

Abstract A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. In the present formulation, the shape function for the reproducing kernel (RK) interpolation function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of this DRK interpolation, the essential boundary conditions can be… More >

H. Nguyen-Van¹, N.Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 65-96, 2008, DOI:10.3970/cmes.2008.036.065

Abstract A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized using the stabilized conforming nodal… More >

J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 273-300, 2008, DOI:10.3970/cmes.2008.034.273

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each node is surrounded by a… More >

B. Yang², V. K. Tewary³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 165-178, 2006, DOI:10.3970/cmes.2006.015.165

Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has been developed previously for efficient… More >

F. Han¹, E. Pan¹, A.K. Roy², Z.Q. Yue³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.1, pp. 15-30, 2006, DOI:10.3970/cmes.2006.014.015

Abstract In this paper, an analytical solution is presented to study the response of piezoelectric, transversely isotropic, functionally graded, and multilayered half spaces to uniform circular surface loadings (pressure or negative electric charge). The inhomogeneous material is exponentially graded in the vertical direction and can have multiple discrete layers. The propagator matrix method and cylindrical system of vector functions are used to first derive the solution in the transformed domain. In order to find the responses in the physical-domain, which are expressed in one-dimensional infinite integrals of the Bessel function products, we introduced and adopted an adaptive Gauss quadrature. Two piezoelectric… More >