• Korean Journal of Mathematics
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• v.6 no.2
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• pp.195-203
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• 1998

In [3], we showed that overintegration may be needed to obtain the optimal $H^1$ error rate for the $p$ version. In this paper, we examine the convergence of the $p$ version in practice, and comment on the implementation of the $p$ version in commercial codes. Also, we give an example of a problem with extremely rough coefficients, for which overintegration is necessary to obtain the optimal $H^1$ convergence rate.

• Computational Structural Engineering
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• v.4 no.2
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• pp.77-85
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• 1991

A new finite element technology based on the p-version of E.F.M. is discussed with reference to its potential for application to stress intensity factor computations in linear elastic fracture mechanics, especially cracked cylindrical shells. It is shown that the p-version model is far better suited for computing the stress intensity factors than the conventional h-version models with the help of three test problems. The main advantage of this technology is that the accuracy of approximation can be established without mesh refinement or the use of special procedures such as crack-tip element and mixed variational approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.145-152
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• 1995

A general stiffener element which includes transverse shear deformation(TSD) is formulated using the p-version of finite element method. Hierarchic C"-shape functions, derived from Integrals of Legendre polynomials, are used to define the assembled stiffness matrix of the stiffener and plate on the basis of 5 D.0.F displacement fields. The stiffness matrix for the stiffener with respect to the local reference frame is transformed to the plate reference system by applying the appropriate transformation matrices in order to insure compatibility of displacements at the junction of the stiffener and plate. The transformation matrices which account for the orientation and the eccentricity effects of the stiffener with respect to the plate reference axes are used to find local behavior at the junction of the stiffener and the relative contributions of the plate and stiffener to the strength of the composite system. The results obtained by the p-version of the finite element method are compared with the results in literatures, especially those by the h-version software, MICROFEAP-II.P-II.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.429-436
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• 1999

The best available solution to predict the fatigue life of structural steels is the implementation of EPFM approach based on the principles and techniques of elasto plastic fracture mechanics. To predict the fatigue life, the conventional Paris law has been modified by substituting the range of J-value denoted by ΔJ for ΔK that is calculated by the proposed p-version model. The proposed P-version finite element model is formulated by the incremental theory of Plasticity that consists of the constitutive equation fur elastic-perfectly plastic materials, Tresca/von-Mises yield criteria, and associated flow rule. The experimental fatigue test is conducted with five UP(Center Clucked Panels) specimens to validate the accuracy of the p-version finite element model. Also, the results obtained by LTM approach have been compared with those by EPFM approach.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.153-159
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• 2005

We investigate the error estimates of the h and p versions of the finite element method for an elliptic problems. We present theoretical results showing the p version gives results which are not worse than those obtained by the h version in the finite element method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1991.04a
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• pp.15-19
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• 1991

An attempt has been made to generate a cured boundary by using a transfinite interpolation technique. In the following sections, it will be shown how to construct transfinite interpolants both in h-version and in p-version over polygonal and nonpolygonal regions. Numerirical test cases validate the applicability and superior capability with the help of several structural problem.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.1-8
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• 1992

This paper presents a p-version finite element approach for modeling the stress distribution around a circular hole in a finite strip subjected to membrane and flexural behaviors. Also, same problem with a crack emanating from a perforated tension strip was solved by virtual crack extension method. The p-version of the finite element method based on integrals of Legendre polynomials is shown to perform very well for modeling geometries with very steep stress gradients in the vicinity of a circular cutout. Here, the transfinite mapping technique for circular boundaries was used to avoid the discretization errors. The numerical results from the proposed scheme have a good comparison with those by Nisida, Howland, Newman etc. and the conventional finite element approach.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.10a
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• pp.38-45
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• 1994

P-version finite element model for the computation of stress intensity factors in two dimensional cracked panels by J-integral method is presented. The proposed model is based on high order theory and hierarchical shape function. The displacements fields are defined by integrals of Legendre polynomials which can be classified into three part such as basic mode, side mode, integral mode. The stress intensity factors are computed by J-integral method. The example models for validating the proposed p-version model are centrally cracked panel, single and double edged crack in a rectangular panel under pure Mode I. And the analysis results are compared with those by the h-version of FEM and empirical solutions in literatures. Very good agreement with the existing solution are shown.

• Computational Structural Engineering
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• v.9 no.1
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• pp.33-45
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• 1996

A general stiffener element which includes transverse shear deformation is formulated using the p-version finite element method. Hierarchic C/sup o/-shape functions, derived from Integrals of Legendre polynomials, are used to define the assembled stiffness matrix of the stiffener with respect to the local reference frame is transformed to the plate reference system by applying the appropriate transformation matrices in order to insure compatibility of displacements at the junction of the stiffener and plate. The transformation matrices which account for the orientation and the eccentricity effects of the stiffener with respect to the plate reference axes are used to find local behavior at the junction of the stiffener and the relative contributions of the plate and stiffener to the strength of the composite system. The results obtained by the p-version finite element method are comared with the results in literatures, especially those by the h-version finite element analysis program, MICROFEAP-II.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.5
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• pp.17-26
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• 2005

The objectives of this study are to determine the behavior of simply supported skew RC slabs subjected to a point load. The p-version nonlinear skew RC FE model has been used. Integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. In the nonlinear formulation of this model, the material model is based on the Kupfer's yield criterion, hardening rule, and crushing condition and layered model is used through the thickness. The cracking behavior is modeled by a smeared crack model and the fixed crack approach is adopted as the crack model. It is shown that the proposed model is able to adequately predict the deflection and ultimate load of nonlinear skew RC slabs with respect to steel arrangements and steel ratios.