Radial basis reproducing kernel particle method for piezoelectric materials

Zhang, Ting; Wei, Gaofeng; Jian, Ma; Gao, Hongfen

doi:10.1016/j.enganabound.2017.10.020

Cited by 22 publications

(1 citation statement)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Li and Zhou (2017) presented a meshless approach with Galerkin weak form to analyze the fracture problem for the piezoelectric materials by introducing the singular term into the approximation function. Zhang et al (2018) used the radial basis function to reduce the error of the numerical results of reproducing kernel particle approach for piezoelectric materials. Considering the transverse shear deformations and von Ka´rma´n geometric relation, Sahoo (2019) derived a nonlinear model of laminated beam with piezoelectric patch using the element-free Galerkin method.…”

Section: Introductionmentioning

confidence: 99%

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Zhou

Xue

2022

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

Piezoelectric materials have played an important role in industry due to a number of beneficial properties. However, most numerical methods for the piezoelectric materials need mesh, in which the mesh generation and remeshing are prominent difficulties. This paper proposes a Hermite interpolation element-free Galerkin method (HIEFGM) for piezoelectric materials, where the Hermite approximate approach and interpolation element-free Galerkin method (IEFGM) are combined. Based on the constitutive equation, geometric equation, and Galerkin integral weak form, the HIEFGM formulation for piezoelectric materials is established. In the proposed method, the problem domain is discretized by many nodes rather than the meshes, so the pre-processing of numerical computation is simplified. Furthermore, a new approximation technique based on the moving least squares method and Hermite approximate approach is used to derive the approximation function of field quantities. The derived approximation function has the Kronecker delta property and considers the field quantity normal derivatives of boundary nodes, which avoids the problem of imposing the essential boundary conditions and improves the accuracy of meshless approximation. The effects of the scaling factor, node density, and node arrangement on the accuracy of the proposed method are investigated. Numerical examples are given for assessing the proposed method and the results uniformly demonstrate the proposed method has excellent performance in analyzing piezoelectric materials.

show abstract

Section: Introductionmentioning

confidence: 99%