• Journal of Korean Society of Steel Construction
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• v.21 no.4
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• pp.433-442
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• 2009

In this paper, new three-dimensional vibration data for the solid cylinders of the N-sided polygonal cross-section with V-notches or sharp cracks are presented, and a Ritz procedure is employed, which incorporates a mathematically complete set of algebraic-trigonometric polynomials in conjunction with an admissible set of edge functions that explicitly model the tri-axial stress singularities that exist along a terminus edge of the V-notch. Convergence studies demonstrate the necessity of adding the edge functions to achieve the accurate frequencies and mode shapes of N-sided polygonal cylindrical solids with stress singularities.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.631-635
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• 1996

Stress singularities appear at the interface edge in dissimilar materials also under thermal loading. First, these singularities then an interface meets a free side surface with an arbitrary angle are studied for a two-dimensional problem. The singular properties under thermal loading are made clear and the concrete singular field are obtained. Secondly, the dependence of stress field on elastic constants in axisymmetric dissimilar materials are. discussed. That is, it is shown that three elastic constants mutually independent are necessary, in general, to characterize the stress field of axisymmetric dissimilar materials, although Dunders' parameters defined for two-dimensional dissimilar materials have been often applied correspondingly also to axisymmetric problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.101-112
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• 1994

The measurement of residual stress distribution of $Si_3N_4/SUS304$ joint was performed on 23 specimens with the same joint condition using PSPC type X-ray stress measurement system and the two-dimensional elastoplastic analysis using finite element method was also attempted. As results, residual stress distribution near the interface on the ceramic side of the joint was revealed quantitatively. Residual stress on the ceramic side of the joint was turned out to be tensional near the interface, maximum along the edge, varying in accordance with the condition of the joint and variance to be most conspicuous for the residual stress normal to the interface characterized by the stress singularities. In the vicinity of the interface, the high stress concentration occurs and residual stress distributes three-dimensionally. Therefore, the measured stress distribution differed remarkably from the result of the two-dimensional finite-element analysis. Especially at the center of the specimen near the interface, the residual stress, $\sigma_{x}$ obtained from the finite element analysis was compressive, whereas measurement using X-ray yielded tensile $\sigma_{x}$. Here we discuss two dimensional superposition model the discrepancy between the results from the two dimensional finite element analysis and X-ray measurement.

• Structural Engineering and Mechanics
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• v.43 no.3
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• pp.321-336
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• 2012

As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of three-dimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.