Analysis of a Crack in a Finite Thermopiezoelectric Plate under Heat Flux

Tsamasphyros, G.; Song, Zhongxiao

doi:10.1007/s10704-005-5421-6

Cited by 13 publications

(7 citation statements)

References 11 publications

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“…is consistent with that in Tsamasphyros and Song (2005) in the first two significant digits. The difference in the dominant value K II = @T @ŷ between the present result and that in Tsamasphyros and Song (2005) is 2.4%.…”

Section: Elementsupporting

confidence: 88%

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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: Elementsupporting

confidence: 88%

“…The difference in the dominant value K II = @T @ŷ between the present result and that in Tsamasphyros and Song (2005) is 2.4%. Due to the symmetric loading and geometric conditions, the normal stress singularity at the crack tip vanishes, i.e., K I ¼ K IV ¼ 0.…”

Section: Elementcontrasting

confidence: 66%

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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“…Therefore, the supplementary functions ψ k is introduced in Eq. (27) having the representations [17].…”

Section: Electric and Mechanical Field Solutions Without Thermal Fluxmentioning

confidence: 99%

The General Solution for a Finite Thermopiezoelectric Plate Containing a Hole and a Crack

Tsamasphyros

Song

2006

Arch Appl Mech

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By application of complex variables and conformal transformation, the general solution to multiply connected domains of two dimensions is constructed in terms of multiple Laurent series for thermopiezoelectric materials. Three typical boundaries, i.e., a rectangular contour, a curvilinear hole, and a line crack are considered in the paper. Though the Green's function of an arbitrarily shaped hole still remains unknown for anisotropic materials, the approximate solutions both for thermal and electro-mechanical fields are obtained in explicit form by the least square method. The accuracy of the approximation are investigated upon each boundary contours. It is found that the local error on the crack surface diminishes below 10 −7 % by adopting only 20 terms of related power series. For a rectangular plate, the precision is enhanced up to the level of 99.99% on its boundary contour by adding the supplementary function, due to the rectangular corners, into the complex solution. Considering that the singular character of a crack is retained in the solution, the stress and electric displacement intensity factors influenced by the hole width and plate size are exhibited herein.

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“…Boundary value problems for coupled fields are complex, thus analytical methods can be only applied to simple problems of thermo-piezoelectricity, e.g. [26], [27] and [32]. The analysis and design process of smart engineering structures with integrated piezoelectric actuators or sensors requires powerful calculation tools.…”

Section: Introductionmentioning

confidence: 99%