Stress intensity factors for an inclined surface crack under biaxial stress state

Zeng, Zhao-Jing; Dai, Shu-Ho

doi:10.1016/0013-7944(94)90228-3

Cited by 34 publications

(4 citation statements)

References 6 publications

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“…Zhao-Jing & Shu-Ho [3] used the simplified model of King [2] and developed an analytical formulation to find the stress intensity factors for a rectangular plate with an inclined crack. Maruyama and Ichinomiya [4] showed the variation of natural frequency with angular orientation of narrow slits for clamped rectangular plates in their experiments.…”

Section: Introductionmentioning

confidence: 99%

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Gupta

Jain

Salhotra

et al. 2015

International Journal of Mechanical Sciences

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Section: Introductionmentioning

confidence: 99%

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Gupta

Jain

Salhotra

et al. 2015

International Journal of Mechanical Sciences

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“…Studies related to fundamental frequencies of intact isotropic plates with uniform and nonuniform thickness have been reported by researchers in references. [1][2][3][4][5] Sakata 6,7 has derived an estimated method for determining the fundamental frequencies of both simply supported and clamped, unidirectional linearly varying thickness orthotropic plate to investigate the effect of flexural stiffness on obtained frequencies. Further, Sakata in 8 has also reported an orthotropic rectangular plate with stepped thickness and discussed flexural stiffness's influence on the vibrational characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…Frequency parameter for an intact orthotropic plate with varying thickness in one axis.Frequency parameter d 1 ¼ xL2 …”

mentioning

confidence: 99%

Non-linear vibration analysis of specially orthotropic tapered micro-plates with arbitrary located crack: A non-classical analytical approach

Chandrakar

Jain

Gupta

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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The present work aims to study the non-linear vibrations in a cracked orthotropic tapered micro-plate. Linear and parabolic variation in the plate thickness is assumed in one as well as two directions. The partial crack is located in the centre, and it is continuous; this crack’s location is arbitrary and can be varied within the centre-line. Based on classical plate theory, the equilibrium principle is applied, and the governing equation of tapered orthotropic plate is derived. Additionally, the microstructure’s effect has been included in the governing equation using the non-classical modified couple stress theory. The simplified line spring model is used to consider the impact of partial crack on the plate dynamics and is incorporated using in-plane forces and bending moments. The introduction of Berger’s formulation brings the non-linearity in the model in terms of in-plane forces. Here, Galerkin’s method has been chosen for converting the derived governing equation into time-dependent modal coordinates, which uses an approximate solution technique to solve the non-linear Duffing equation. The crack is considered along the fibres and across the fibres to show the effect of orthotropy. Results are presented for an orthotropic cracked plate with non-uniform thickness. The effects of the variation of taper constants, crack location, crack length, internal material length scale parameter on the fundamental frequency are obtained for two different boundary conditions. The non-linear frequency response curves are plotted to show the effect of non-linearity on the system dynamics using the method of multiple scales, and the contribution of taper constants and crack parameters on non-linearity is shown with bending-hardening and bending-softening phenomenon. It has been found that vibration characteristics are affected by the taper parameters and fibre direction for a cracked orthotropic plate.

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“…Aksel and Erdogan 7 studied the accuracy of the LSM and proposed the crack compliance coefficients for any configuration and number of cracks. Zhao-Jing and Shu-Ho 8 presented an approximate analytical solution for an inclined surface cracked plate under biaxial stress. They derived the variation patterns of the stress intensity factors (SIFs) for cracks in the plates under loadings in the Modes II and Z of the fracture.…”

Section: Introductionmentioning

confidence: 99%

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

Ranjbaran

Seifi

2019

The Journal of Strain Analysis for Engineering Design

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This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

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Stress intensity factors for an inclined surface crack under biaxial stress state

Cited by 34 publications

References 6 publications

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Effect of microstructure on vibration characteristics of partially cracked rectangular plates based on a modified couple stress theory

Non-linear vibration analysis of specially orthotropic tapered micro-plates with arbitrary located crack: A non-classical analytical approach

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

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