A Novel Hybrid Element Analysis for Piezoelectric-parent Material Wedges

Chen, Mengcheng; Ping, Xuecheng

doi:10.1007/s00466-006-0078-1

Cited by 14 publications

(2 citation statements)

References 33 publications

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“…To employ the FEM for such applications requires information on the asymptotic expansion in the vicinity of the crack so that the stress and electric displacement intensity factors can be evaluated accurately. However, the asymptotic solutions for the interface cracks are complex and often difficult to obtain analytically (Chen and Ping, 2007). Furthermore, the FEM necessitates the use of very fine meshes around the crack tips and leads to increased computational effort.…”

Section: Introductionmentioning

confidence: 99%

SBFEM for fracture analysis of piezoelectric composites under thermal load

Ooi

Song

et al. 2015

International Journal of Solids and Structures

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a b s t r a c tThis paper extends a semi-analytical technique, the so-called scaled boundary finite element method (SBFEM), to analyze fracture behaviors of piezoelectric materials and piezoelectric composites under thermal loading. In this method, only the boundary is discretized leading to a reduction of the spatial dimension by one. The temperature field in the domain is obtained using the SBFEM and expressed as a series of power functions of the radial coordinate. The resulting stress and electric displacement distribution along the radial direction is represented analytically. This permits the generalized stress and electric displacement intensity factors to be directly evaluated from the solution by following standard stress recovery procedures in the finite element method (FEM). Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.

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Section: Introductionmentioning

confidence: 99%

SBFEM for fracture analysis of piezoelectric composites under thermal load

Ooi

Song

et al. 2015

International Journal of Solids and Structures

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“…Since it is very hard to get analytical eigensolutions of complex crack forms, this method cannot directly deal with more complex fracture mechanics problems such as cracks in anisotropic materials, interface cracks, and cracks terminating at interfaces. In recent years, Chen and Ping 43–45 have developed a 2D hybrid crack‐tip singular element by using the numerical eigensolution of the singular stress field on the basis of the one‐dimensional (1D) finite element eigenanalysis method, which avoids difficulty in accessing exact analytical solutions for asymptotic displacement and stress fields. Ping et al 46,47 and Zhang et al 48 extended this singular element to three‐dimensional (3D) fracture mechanics problems.…”

Section: Introductionmentioning

confidence: 99%

A novel crack‐tip singular element for extended finite element analysis

Wang

Ping

Wang

et al. 2023

Fatigue Fract Eng Mat Struct

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The traditional extended finite element method (XFEM) is suitable for simulating crack growth, but the crack‐tip stress field analysis still depends on the enriched function. In this paper, based on the numerical eigensolution of the singular displacement and stress field together with the Hellinger–Reissner (H–R) variational principle, a novel crack‐tip singular element is established to replace the enriched element in the crack‐tip region in the traditional XFEM. The stress field inside the element adopts a series expression instead of only including the leading‐order terms. The element only requires Gaussian integration at the element boundary and avoids mesh refinement in the crack‐tip region. The element can be used to analyze cracks in anisotropic materials, interface cracks, and cracks terminating at the bimaterial interface. The numerical solutions of the singular stress field in various crack forms are presented through numerical examples, which proves the effectiveness and versatility of the novel crack‐tip singular element.

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