Finite element analysis of piezoelectric corner configurations and cracks accounting for different electrical permeabilities

Chen, Mengcheng; Ping, Xuecheng

doi:10.1016/j.engfracmech.2006.08.008

Cited by 15 publications

(6 citation statements)

References 30 publications

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“…It can be proved that according to the characteristic matrixes A and B of anisotropy defined in (16) and (17), we have…”

Section: The Materials Characteristic Matrix Of Anisotropicmentioning

confidence: 99%

“…According to (16) and (17) Substituting matrix B into (28) and (29), with the application of the modified Müller method SRAM, the characteristic eigenvalues of different V-notch angles 2 are showed in Table 2. 1 and 2 are the first and second eigenvalues, respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Though many researchers studied the V-notch problem of isotropy material [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], there are seldom studies about the Vnotch problem of anisotropy material. This paper presents a novel systematic strategy to calculate the V-notch problem of anisotropy material.…”

Section: Introductionmentioning

confidence: 99%

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The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

Tian

Yuan

et al. 2013

Mathematical Problems in Engineering

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This paper presents a novel way to calculate the characteristic solutions of the anisotropy V-notch plane problem. The material eigen equation of the anisotropy based on the Stroh theory and the boundary eigen equation of the V-notch plane problem are studied separately. A modified Müller method is utilized to calculate characteristic solutions of anisotropy V-notch plane problem, which are employed to formulate the analytical trial functions (ATF) in the associated finite element method. The numerical examples show that the proposed subregion accelerated Müller method is an efficient method to calculate the solutions of the equation involving the complex variables. The proposed element ATF-VN based on the analytical trial functions, which contain the characteristic solutions of the anisotropy V-notch problem, presents good performance in the benchmarks.

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“…It can be proved that according to the characteristic matrixes A and B of anisotropy defined in (16) and (17), we have…”

Section: The Materials Characteristic Matrix Of Anisotropicmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

Tian

Yuan

et al. 2013

Mathematical Problems in Engineering

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“…Chen and Sze (2001) proposed a hybrid finite element with asymptotic expansion to determine the stress exponents and stress distributions of bonded bimaterial Vnotches. On the basis of this work, Sze et al (2001) and Chen and Ping (2007) developed the approach further and used it for the analyses of singular electro-elastic fields around a V-notch of piezoelectric material. By the same method, Ping et al (2008) analyzed the singular stress fields of V-notched anisotropic plates.…”

Section: Introductionmentioning

confidence: 99%

A new boundary element approach of modeling singular stress fields of plane V-notch problems

Niu

Chen

et al. 2009

International Journal of Solids and Structures

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a b s t r a c tIn this paper, a new boundary element (BE) approach is proposed to determine the singular stress field in plane V-notch structures. The method is based on an asymptotic expansion of the stresses in a small region around a notch tip and application of the conventional BE in the remaining region of the structure. The evaluation of stress singularities at a notch tip is transformed into an eigenvalue problem of ordinary differential equations that is solved by the interpolating matrix method in order to obtain singularity orders (degrees) and associated eigen-functions of the V-notch. The combination of the eigen-analysis for the small region and the conventional BE analysis for the remaining part of the structure results in both the singular stress field near the notch tip and the notch stress intensity factors (SIFs).Examples are given for V-notch plates made of isotropic materials. Comparisons and parametric studies on stresses and notch SIFs are carried out for various V-notch plates. The studies show that the new approach is accurate and effective in simulating singular stress fields in V-notch/crack structures.

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“…On the basis of stress asymptotic expansion near a V-notch tip, Seweryn (2002) obtained the singular stress field by taking two or three dominating stress eigen-functions as analytical constrains on the stress field in the notch tip region and the remaining area of the notched structure modeled by the conventional FEM. Chen and Sze (2001); Chen and Ping (2007); Ping et al (2008) proposed a hybrid finite element with asymptotic expansion to determine the stress exponents and stress distributions of bonded bimaterial V-notches. Because the stress singularity orders and associated eigenvectors of the displacement and stress at the two-dimensional V-notch tip region have been determined by means of the interpolating matrix method proposed by Niu et al (2009a), the stresses at V-notch tip regions can be expressed as the linear combination of the series expansion including two singular terms and several non-singular terms.…”

Section: Introductionmentioning

confidence: 99%

Effect of non-singular stress on the brittle fracture of V-notched structure

2012

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The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

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Finite element analysis of piezoelectric corner configurations and cracks accounting for different electrical permeabilities

Cited by 15 publications

References 30 publications

The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

A new boundary element approach of modeling singular stress fields of plane V-notch problems

Effect of non-singular stress on the brittle fracture of V-notched structure

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