• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.303-309
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• 2007

For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. In this paper we focus on both first and second order paraxial boundary conditions(PBCs) in the framework of variational approximations which are based on paraxial approximations of the scalar and elastic wave equations. We propose a penalty function method for the treatment of PBCs and apply these into finite element analysis. The numerical verification of the efficiency is carried out through comparing PBCs with Lysmer-Kuhlemeyer's boundary conditions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.2
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• pp.153-160
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• 2008

In this study, we propose a new three-node hybrid-mixed curved beam element with the relaxed-equiribrium stress functions for static analysis. The proposed element considering shear deformation is based on the Hellinger-Reissner variational principle. The stress functions are carefully chosen from three important considerations: (i) all the kinematic deformation modes must be suppressed, and (ii) the spurious constraints must be removed in the limiting behaviors via the field-consistency, and (iii) the relaxed equilibrium conditions could be incorporated because it might be impossible to select the stress functions and parameters to fully satisfy both the equiribrium conditions and the suppression of kinematic deformation modes in the three-node curved beam hybrid-mixed formulation. Numerical examples confirm the superior and stable behavior of the proposed element regardless of slenderness ratio and curvature. Besides, the proposed element shows the outstanding performance in predicting the stress resultant distributions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.365-371
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• 1998

In the present study, we attempted to add the incompatible functions as additional variable terms to the conventional u-p formulation. It is derived from the four-field generalized variational principle that encompasses velocity, pressure, velocity strains and stress fields as independent interpolated variables. As a severe test of the present formulation, we have investigated the driven cavity with the corner velocity singularity like leaky lid. Through the test, the present element performs very well without unstable oscillation of pressure distribution.

• The Journal of the Acoustical Society of Korea
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• v.8 no.5
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• pp.51-58
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• 1989

The finite element method is usually formulated by utilizing the variation principle. In this paper, we introduce the approximate equation of finite element from Helmholtz eqation by means of the Galerkin method, which provides the best approximation of those methods known as the method of weighted residuals, and a numerical simulation based of the finite element method is applied to analysing the acoustic modes and the pattern of sound radiation in two and three dimensional sound fields. Beside the numerical calculations, the acoustic modes and the sound pressure level are mesured by scale model experiments. The finite element analysis of the model shows very good agreement with the mesured results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.5
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• pp.55-62
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• 2003

Subdomain-interface variational formulation is presented to solve a class of dynamic contact problems of composite structures. The penalty method is used for imposing inequality constraints on contact surfaces and for connecting finite element subdomains that satisfy interface compatibility conditions. As a result, any complex-shaped domain can be easily divided into independently modeled subdomains without considering the conformity of meshes on interfaces. Some advantageous features of the present method are shown through a set a numerical studies with a developed computer code.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.37-49
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• 2000

This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.119-129
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• 2004

A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

• Journal of Aerospace System Engineering
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• v.17 no.1
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• pp.24-32
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• 2023

This paper studied HART II in descending flight using rotorcraft analysis code based on geometrically exact beam (GEB) model. The present GEB model expressed by a mixed variational formulation could capture the geometrically nonlinear behavior of the blade without arbitrary assumptions. In previous results, correlation of airloads with structural moments for HART II was not as good as blade deflections. However, in present results, predictions of airloads and structural loads are fairly correlated with measured data.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.165-172
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• 2003

In this study, a new and efficient harmonic axisymmetric shell element for static and dynamic analysis Is proposed. The present element considering shear strain is based on a modified mixed variational principle in which the independent unknowns are only the Quantities prescribable at the shell edges. Unlike existing hybrid-mixed axisymmetric shell elements, the present element introduces additional nodeless degrees for displacement field Interpolation In order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and the nodeless degrees are condensed out by the Guyan reduction. Through several numerical examples, the hybrid-miked shell element with the additional nodeless degrees and the consistent stress parameters is shown to be efficient and yield very accurate results for static and vibration analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.2 s.72
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• pp.151-160
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• 2006

In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and introduces additional nodeless degrees for displacement field interpolation in order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.