• Proceedings of the KSME Conference
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• 2000.11a
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• pp.464-469
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• 2000

In order to analyze effectively the discontinuous parts such as holes or notches included in mechanical structures by the finite element method, a singular finite element for orthotropic materials. is proposed. This singular element is formulated by the Trefftz method and the hybrid variational principles, which the displacements and stresses are simultaneously assumed using the Trefftz functions. Through several numerical tests, it is shown that the proposed singular element is very efficient for the accurate stress analysis of the various types of discontinuous parts.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.163-171
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• 1996

For the effective analysis of two dimensional plane problems, Treffiz finite elements and cavity elements have been proposed. These element matrix equaitons were formulated on the basis of hybrid variational principle and Treffiz function sets derived consitstently from the complex theoy of plane elasticity. In order to suggest the accuracy chatacteristics of the proposed Treffiz elements typical plane problems were analyzed and these results were compared with ones obtained by using the conveintional displacement type elements. The accuracy of the proposed elements is less sensitive to the element size and shape than the conventional displacement type elements. These elements, being able to be formed with multi-nodes, give the convenient modeling of an analytic domain. The cavity elements give the comparatively exact values of stress concentration factors of stress intensity factors and can be effectively used for the analysis of mechanical stuctures containing various cavities.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.1018-1025
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• 1999

For the effective analysis of two dimensional plane problems with geometrical discontinuities, singular finite element has been proposed. The element matrix equation was formulated on the basis of hybrid variational principle and Trefftz function sets derived consistently from the complex theory of plane elasticity by introducing a conformal mapping function. In order to suggest the accuracy characteristics of the proposed singular finite element, typical plane problems were analyzed and these results were compared with exact solutions. The singular finite element gives the comparatively exact values of stress concentration factors or stress intensity factors and can be effectively used for the analysis of mechanical structures containing various geometrical discontinuities.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.5
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• pp.442-449
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• 2009

A two-dimensional cross-section analysis program based on the finite element method has been developed for composite blades with solid, thin-walled and compound cross-sections. The weighted-modulus method is introduced to determine the laminated composite material properties. The shear center and the torsion constant for any given section are calculated according to the Trefftz' definition and the St. Venant torsion theory, respectively. The singular value problem of cross-section stiffness properties faced during the section analysis has been solved by performing an eigenvalue analysis to remove the rigid body mode. Numerical results showing the accuracy of the program obtained for stiffness, offset and inertia properties are compared in this analysis. The current analysis results are validated with those obtained by commercial software and published data available in the literature and a good correlation has generally been achieved through a series of validation study.

• Advances in aircraft and spacecraft science
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• v.3 no.3
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• pp.317-330
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• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.