• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.3
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• pp.267-275
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• 2009

This paper presents the p-convergent coupling element on the basis of the ESSE(equivalent single layer shell element) and the PLLE(partial-linear layerwise element) to analyze laminated composite plates. The ESSE is formulated by the degenerated shell theory, on the other hand, the assumption of the PLLE is piecewise linear variation of the in-plane displacement and a constant value of lateral displacement across the thickness. The proposed finite element model is based on p-convergence approach. The integrals of Legendre polynomials and Gauss-Lobatto technique are chosen to interpolate displacement fields and to implement numerical quadrature, respectively. This study has been focused on the verification of p-convergent element. For this purpose, various finite element multiple models associated with the combination of ESSE and PLLE elements are tested to show numerical stability. The simple examples such as a cantilever beam subjected vertical load and a plate with tension are adopted to evaluate the performance of proposed element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.189-196
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• 2009

This paper presents the subparametric finite element model formulated by partial-linear layerwise theory for the analysis of laminate composites. The proposed model is based on refined approximations of two dimensional plane for orthotropic thick laminate plate as well as thin case. Three dimensional problem can be reduced to two dimensional case by assuming piecewise linear variation of in-plane displacement and a constant value of out-of-plane displacement across the thickness. The integrals of Legendre polynomials are chosen to define displacement fields and Gauss-Lobatto numerical integration is implemented in order to directly obtain maximum values occurred at the nodal points of each layer without other extrapolation techniques. The validity and characteristics of the proposed model have been tested by using orthotropic multilayered plate problem as compared to the values available in the published references. In this study, the convergence test has been carried out to determine the optimal layer model in terms of central deflection and stresses. Also, the distribution of displacements and stresses across the thickness has been investigated as the number of layer is increased.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5A
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• pp.649-656
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• 2008

The enhancement of the service life of damaged or cracked structures is a major issue for researchers and engineers. The hierarchic void element based on the integrals of Legendre polynomials is used to characterize the fracture behaviour of unpatched crack as well as repaired crack with bonded composite patches by computing the stress intensity factors and stress contours at the crack tip. Since the equivalent single layer approach is adopted in this study, the proposed element is necessary to represent a discontinuous crack part as a continuum body with zero stiffness. Thus the aspect ratio of this element to represent the crack should be extremely slender. The sensitivity of numerical solution with respect to energy release rate, displacement and stress has been tested to show the robustness of zero stiffness element as the aspect ratio is increased up to 2000. The stiffness derivative method and displacement extrapolation method have been applied to calculate the stress intensity factors of Mode I problem. It is noted that the proposed hierarchical void element can be one of alternatives to analyze the patched crack problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.491-499
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• 2002

A p-version finite element model based on degenerate shell element is proposed tot the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted tot in the sense of yon Karman hypothesis. The material model is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized lot anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed P-version finite element model is demonstrated through several comparative points of iew in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic tone.

• Journal of Korean Tunnelling and Underground Space Association
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• v.6 no.4
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• pp.327-343
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• 2004

During tunnel construction, ground failures often occur due to existence of weak zones, such as faults, joints, and cavities, ahead of tunnel face. It is hard to detect effectively weak zones, which can lead underground structure to fail after excavation and before supporting, by using conventional characterization methods. In this study, an enhanced analytical method of predicting weak zones ahead of tunnel face is developed to overcome some problems in the conventional geophysical exploration methods. The analytical method is based on Coulomb's and Gauss' laws with considering the characteristics of electric fields subjected to rock mass. Using the developed method, closed form solutions are obtained to detect a spherical shaped zone and an oriented fault ahead of tunnel face respectively. The analytical results suggest that the presence of weak zones and their sizes, location, and states can be accurately predicted by combining a proper inversion process with resistance measured from several electrodes on the tunnel face. It appears that the skin depth or resistivity in rock mass is affected by the diameter of tunnel face, natural electric potential and noises induced by experimental measurement and spatial distribution of uncertain properties. The developed analytical solution is verified through experimental tests. About 1800 concrete blocks of 5cm by 5cm by 5cm in size are prepared and used to model a joint rock mass around tunnel face. Weak zones are simulated ahead of tunnel face with a material which has relatively higher conductivity than concrete blocks. Experimental results on the model test show a good agreement with analytical results.