• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.225-239
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• 2005

Applications of the Trefftz boundary element method (BEM) to anti-plane electroelastic problems are presented in this paper. Both direct and indirect methods with domain decomposition are discussed in details. Each crack is treated as semi-infinite thin slit defined in a subregion, for which a particular solution of the anti-plane problem, satisfying exactly the crack-face condition, is derived. The stress intensity factors defined at each crack tip can be directly computed from the coefficients of the particular solution. The performance of the proposed formulation is assessed by two examples and comparison is made with results obtained by other approaches. The Trefftz boundary element approach is demonstrated to be suitable for the analysis of the anti-plane problem of piezoelectric materials.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.855-859
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• 2004

We develop a new four-node flat shell element which is accurate, efficient, and suitable to be used on general purpose. The new element has a hybrid Trefftz element with drilling degrees of freedom as a membrane part. We define the two independent displacement field: the internal displacement field that satisfies governing equations in the domain a priori and the boundary displacement field that is usually used as a conventional finite element method. The hybrid Trefftz variational formulation connects these two displacement fields on the boundary of the domain. To add drilling degrees of freedom, we introduce the Allman's quadratic displacement field to the boundary displacement field. As a result, our flat shell element has 6 degrees of freedom per a node. We also use the well-known DKMQ plate bending element for the plate part of the proposed element. The DKMQ element satisfies Mindlin-Reissner‘s plate theory along the edge of the element and gives proper behavior regardless of the thickness. A series of numerical experiments shows that the performance of the new element such as accuracy, rate of convergence, robustness to mesh quality, and so on.

• 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.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.402-407
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• 2008

We suggest a linear elastic flat shell element based on the HT(hybrid Trefftz) method. We formulate the membrane part of the proposed element as an HT plane element with the drilling DOF. For the bending part, we developed a thick HT plate element that can represent transverse shear deformations accurately. Because we derive both the membrane and the bending parts consistently using the HT functional, we can easily construct the triangular and the quadrilateral elements in a unified way. In addition, warping of quadrilateral element is compensated by force and moment equilibrium equations. We evaluate the performance of the new element in terms of accuracy and convergence.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.439-451
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• 2009

The paper deals with the problem related to the modelling of riveted assemblies for crashworthiness analysis of full-scale complete aircraft structures. Comparisons between experiments and standard FE computations on high-energy accidental situations onto aluminium riveted panels show that macroscopic plastic strains are not sufficiently localised in the FE shells connected to rivet elements. The main reason is related to the structural embrittlement caused by holes, which are currently not modelled. Consequently, standard displacement FE models do not succeed in initialising and propagating the rupture in sheet metal plates and along rivet rows as observed in the experiments. However, the literature survey show that it is possible to formulate super-elements featuring defects that both give accurate singular strain fields and are compatible with standard displacement finite elements. These super-elements can be related to the displacement model of the hybrid-Trefftz principle of the finite element method, which is a kind of domain decomposition method. A feature of hybrid-Trefftz finite elements is that they are mainly used for elastic computations. It is thus proposed to investigate the possibility of formulating a hybrid displacement finite element, including the effects of a hole, dedicated to crashworthiness analysis of full-scale aeronautic structures.

• 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.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.655-678
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• 1996

The paper reports on alternative hybrid/mixed formulations being developed by the Structural Analysis Research Group of Institute Superior T$\acute{e}$cnico. These formulations open the scope and increase the power of the finite element method by allowing different fields to be independently approximated, within certain consistency criteria, and by enhancing the use of a wide range of approximation functions. They have been applied to the analysis of 2-D problems, laminar structures and solids, using different constitutive relations, both in quasi-static and dynamic regimes. The fundamental properties of the formulations are identified and assessed and their performance is illustrated using simple, linear applications.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.10 no.2
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• pp.77-85
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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 arbitrary cross-section profiles and material distributions. The modulus weighted approach is used to take into account the non-homogeneous material characteristics of advanced blades. The CLPT (Classical Lamination Plate Theory) is applied to obtain the effective moduli of the composite laminate. The location of shear center for any given cross-sections are determined according to the Trefftz' definition while the torsion constants are obtained using the St. Venant torsion theory. A series of benchmark examples for beams with various cross-sections are illustrated to show the accuracy of the developed cross-section analysis program. The cross section cases include thin-walled C-channel, I-beam, single-cell box, NACA0012 airfoil, and KARI small-scale blades. Overall, a reasonable correlation is obtained in comparison with experiments or finite element analysis results.