3D BEM for the general piezoelectric solids

Denda, Mitsunori; Wang, C.-Y.

doi:10.1016/j.cma.2009.04.014

Cited by 12 publications

(2 citation statements)

References 22 publications

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“…The BEM principally requires reduced surface discretizations, and may be regarded as an appealing alternative to the FEM for elastostatic problems (see for example, Banerjee and Henry (1992), Chen and Lin (2010), Cruse (1969), Denda and Wang (2009), Masters and Ye (2004), Milroy et al (1997), Mittelstedt and Becker (2006), Pan and Yuan (2000), Turco and Aristodemo (1998), Wang and Denda (2007), and Wu and Stern (1991), for 3D problems). As the BEM requires no domain discretization, fewer unknowns are needed to be stored.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical method with a system of decoupled ordinary differential equations for three-dimensional elastostatic problems

Khaji

Khodakarami

2012

International Journal of Solids and Structures

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Keywords:3D elastostatic problems Semi-analytical method Diagonal coefficient matrices Chebyshev polynomials Subparametric elements Clenshaw-Curtis quadrature Decoupled ordinary differential equations a b s t r a c tIn this paper, a new semi-analytical method is presented for modeling of three-dimensional (3D) elastostatic problems. For this purpose, the domain boundary of the problem is discretized by specific subparametric elements, in which higher-order Chebyshev mapping functions as well as special shape functions are used. For the shape functions, the property of Kronecker Delta is satisfied for displacement function and its derivatives, simultaneously. Furthermore, the first derivatives of shape functions are assigned to zero at any given node. Employing the weighted residual method and implementing Clenshaw-Curtis quadrature, coefficient matrices of equations' system are converted into diagonal ones, which results in a set of decoupled ordinary differential equations for solving the whole system. In other words, the governing differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. To evaluate the efficiency and accuracy of the proposed method, which is called Decoupled Scaled Boundary Finite Element Method (DSBFEM), four benchmark problems of 3D elastostatics are examined using a few numbers of DOFs. The numerical results of the DSBFEM present very good agreement with the results of available analytical solutions.

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Section: Introductionmentioning

confidence: 99%

A semi-analytical method with a system of decoupled ordinary differential equations for three-dimensional elastostatic problems

Khaji

Khodakarami

2012

International Journal of Solids and Structures

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“…The generalized displacement vector contains the displacements and the electric potential . Using effective coefficients (elastic coefficients , piezoelectric coefficients , and dielectric coefficients ) and average state values (stress Cauchy tensor , strain tensor , electrical displacements , and electric fields ), the constitutive equations for homogeneous material can be expressed as [12][13][14] = − ,…”

Section: Boundary Element Formulationmentioning

confidence: 99%

A Simplified Scheme for Piezoelectric Anisotropic Analysis in Human Vertebrae Using Integral Methods

Duarte

Thoeni

Garzón‐Alvarado

et al. 2018

Mathematical Problems in Engineering

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This paper outlines a computational model for the analysis of the piezoelectric behaviour of the vertebral body remodelling process. Particular attention is paid to the algorithms for the simulation of the stress energy density for each point of the geometry and the distribution of the density in the bone. In addition, the model takes into account the piezoelectric effect and the anisotropy (transversal isotropy) of the bone. A model for internal anisotropic piezoelectric bone remodelling of a human vertebra is discussed in detail. The model consists of the implementation of an algorithm which includes the elastic and electric variables in a single equation using boundary element method. The presented results show a good agreement with biological data and the model does not include any electric additional charge.

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Hybrid fundamental-solution-based FEM for piezoelectric materials

Cao

Qin

2012

Comput Mech

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3D BEM for the general piezoelectric solids

Cited by 12 publications

References 22 publications

A semi-analytical method with a system of decoupled ordinary differential equations for three-dimensional elastostatic problems

A semi-analytical method with a system of decoupled ordinary differential equations for three-dimensional elastostatic problems

A Simplified Scheme for Piezoelectric Anisotropic Analysis in Human Vertebrae Using Integral Methods

Hybrid fundamental-solution-based FEM for piezoelectric materials

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