Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

Meng, G.; Wang, Hui; Zhou, Li; Li, Feng

doi:10.1155/2015/638783

Cited by 10 publications

(5 citation statements)

References 42 publications

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“…The extended application of the weighted nonlocal divergence and gradient operators on tensor and vector fields, respectively, follows as in ( 8) and (10). In addition, as is with the unweighted nonlocal operators, adjoint operators can also be defined for the weighted nonlocal operators.…”

Section: Nonlocal Weighted Operatorsmentioning

confidence: 99%

“…A straightforward solution is the use of micromodels in which the resolution is refined until the model can explicitly resolve all important microstructural details. This solution strategy has been utilised to model microstructurally heterogeneous materials such as composites using numerical techniques such as the Finite-Element method [1][2][3][4], Finite-Difference Method [5][6][7][8], and meshless methods such as the Element-free Galerkin method [9][10][11][12] to name just a few. This method of enriching the model suffers from several drawbacks amongst which include the fact that the microstructural details that plays important role in the response of the material may exist over wide orders of magnitude and explicit resolution of the microstructure for some applications may require computational resources that is prohibitively expensive.…”

Section: Introductionmentioning

confidence: 99%

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A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

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Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.

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Section: Nonlocal Weighted Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

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“…Chen et al [25] analyzed the buckling problem of a functionally graded piezoelectric rectangular plate under non-uniform force load, thermal load and electrical load by an element-free Galerkin method. Meng et al [26] used the element-free Galerkin method to analyze the singular field at the crack tip of the FGPSs. Chuaqui and Roque [27] proposed a global interpolation element-free method for the FGPSs, and researched the static deformation of a functionally graded piezoelectric beam under mechanical and electrical loads.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of functionally graded piezoelectric bionic fishtail based on Hermite element-free method

Ma,

Zhou,

et al. 2024

Funct. Compos. Struct.

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Piezoelectric bionic fishtails have good flexibility, response speed, anti-interference ability, and have great application prospects in ocean exploration. However, the inherent drawbacks of the mechanical properties of traditional homogeneous piezoelectric materials significantly affect the propulsion performance and reliability of the piezoelectric bionic fishtails. To fill this gap, this paper develops a functionally graded piezoelectric bionic fishtail (FGPBF) by imitating the tail characteristics of groupers. The geometric structure and working principle of the FGPBF are introduced in detail. Based on the first-order shear deformation theory and Hermite element-free method, an element-free model for the FGPBF is established. The effects of gradient factor, substrate material, substrate thickness and electrical load on the propulsion performance of the FGPBF are addressed. The results show that the current results are in good agreement with the finite element results. The deformation of the FGPBF is negatively correlated with the thickness and stiffness of the substrate and linearly positively correlated with the electrical load. As the gradient factor increases, the deflection of the FGPBF first increases and then decreases. When the gradient factor is 2, the potential is 200 V, the dimensionless aluminum substrate thickness is 1, the propulsion performance of the FGPBF is improved by 28% compared to the homogeneous piezoelectric bionic fishtail.

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“…Later, Sladek et al (2015) researched the effect of conductivity on the fracture behavior of the FGPSs. An improved Galerkin meshless method has been developed by Meng et al (2015) to numerically analyze the FGPSs with cracks. Mikaeeli and Behjat (2016) applied an element-free Galerkin method to research a thick FGPP.…”

Section: Introductionmentioning

confidence: 99%

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

Ma,

Zhou,

et al. 2024

Journal of Intelligent Material Systems and Structures

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Functionally graded piezoelectric structures (FGPSs) have excellent electromechanical properties and are promising for engineering applications. However, the inhomogeneous material properties and piezoelectric effects create great difficulties in the mechanical analysis of the FGPSs. In this paper, a Hermite interpolation element-free Galerkin method (HIEFGM) is proposed for the numerical analysis of the FGPSs. The HIEFGM utilizes a set of nodes to represent the problem domain, which can ideally reflect the inhomogeneous material properties of the FGPSs. Firstly, the governing equations of the FGPSs are derived through the constitutive equation, equilibrium equation, and boundary conditions. Secondly, the approximating function of the field quantities is obtained by the improved moving least-square method and Hermite interpolation. The HIEFGM formulation of the FGPSs is obtained using the variational principle. Furtherly, the influence of weight function, scaling parameter, and node densities on the HIEFGM of the FGPSs is discussed in detail through a parameter study. Finally, the availability of present method is estimated by several examples with different configurations and boundary conditions. The influence of gradation exponent on the electromechanical responses of the FGPSs is analyzed. The results show that the present method has excellent accuracy and stability in analyzing the FGPSs. As the gradation exponent increases, the distribution of the field quantities of the FGPSs exhibits nonlinear characteristics. This work may provide an effective methodology for the analysis of the FGPSs, and contribute to the theoretical research and engineering application of the FGPSs.

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Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

Cited by 10 publications

References 42 publications

A computational homogenization framework for non-ordinary state-based peridynamics

A computational homogenization framework for non-ordinary state-based peridynamics

Numerical analysis of functionally graded piezoelectric bionic fishtail based on Hermite element-free method

Analysis of functionally graded piezoelectric structures by Hermite interpolation element-free Galerkin method

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