• Computational Structural Engineering
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• v.11 no.1
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• pp.191-204
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• 1998

The general formulation for free vibration and stability analysis of unsymmetric thin-wared space frames is presented in case where the shear deformation effects are neglected. The kinetic and total potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including warping deformation and second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated, and load-correction stiffness matrices for off-axis distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.

• Computational Structural Engineering
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• v.11 no.1
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• pp.171-178
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• 1998

The added viscoelastic dampers increase damping and stiffness of buildings and results in so called non-classical or non-proportional damping problem. In this system the eigenvectors of the undamped system may not diagonalize the damping matrix, and the system is generally analyzed by converting the equation of motion into a 2n first order state-space form. As this approach is complex and time-consuming compared to the classically damped problem, the system is often analyzed by neglecting the off-diagonal terms in the damping matrix. In this paper the theoretical background of the approximate approach is studied, and the vibration characteristics of a three-story shear building with a viscoelastic damper are investigated using the exact and approximate method. It is found that the approximate method may produce good result when the additional damping is small, but as the damping increases the error also increase.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.1
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• pp.65-73
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• 1987

An efficient plate bending finite element has been developed using higher-order inplane displacement profiles of the plate. The 6-noded, 21-d.o.f. triangular element including shear deformation effect has been derived from the plate-like continuum by the Galerkin's weighted residual method. Square plate examples were tested with selected element meshes and several aspect ratios for their static behavior under uniformly distributed load. The result of the example tests indicated consistently good performance of the present higher-order plate bending element in comparison with the thin and thick plate solution and other existing finite element solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.445-454
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• 1991

In this thesis, Mindlin plate element with nine nodes and three degrees-of-freedom at each node is formulated and is employed in eigen-analysis of a rectangular plates in order to alleviate locking phenomenon of eigenvalues. Eigenvalues and their modes may be locked if conventional $C_{0}$-isoparametric element is used. In order to reduce stiffness locking phenomenon, two methods (1, the general reduced and selective integration, 2, the new element that use of modified shape function) are studied. Additionally in order to reduce the error due to mass matrix, two mass matrixes (1, Gauss-Legendre mass matrix, 2, Gauss-Lobatto mass matrix) are considered. The results of eigen-analysis for two models (the square plate with all edges simply-supported and all edges built-in), computed by two methods for stiffness matrix and by two mass matrixes are compared with theoretical solutions and conventional numerical solutions. These comparisons show that the performance of the two methods with Gauss-Lobatto mass matrix is better than that of the conventional plate element. But, by considering the spurious rigid body motions, the element which employs modified shape function with full integration and Gauss-Lobatto mass matrix can elevate the accuracy and convergence of numerical solutions.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.2
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• pp.109-116
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• 2010

It is important to make a mechanical structure precisely and reasonably in predicting the dynamic characteristics, controlling the vibration, and designing the structure dynamics. In finite element analysis model updating is appropriate as the design parameter is used to analyze the dynamic system. The errors can be contained from the physical parameters and the element modeling. From the dynamic test, more precise dynamic characteristics can be obtained. In this paper, model updating algorithm is developed using frequency difference between experiment and calculation. Modal frequencies are obtained by experiment and finite element analysis for beams with various cross section and shapes which have added masses and holes in the middle. For plates with and without groove, experiment and analyses are carried out by applying free boundary conditions as well. Mass and stiffness matrices are updated by comparing test and analytical modal frequencies. The result shows that the updated frequencies become closer to the test frequencies in case that both matrices are updated. An improved analytical model is obtained by changing model parameters such that the discrepancy between test and finite element frequencies is minimized. For beam and plate models updating of mass and stiffness matrices can improve the dynamical behavior of the model by acting on the physical parameters such as masses and stiffness.

• Composites Research
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• v.28 no.4
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• pp.204-211
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• 2015

This paper presents a theory related to a two-dimensional linear cross-sectional analysis, recovery relationship and a one-dimensional nonlinear beam analysis for composite wing structure with initial twist. Using VABS including a related theory, the design process of the composite rotor blade has been described. Cross-sectional analysis was performed at cutting point including all the details of geometry and material. Stiffness matrix and mass matrix were linked to each section to make 1D beam model. The 3D strain distributions within the structure were recovered based on the global behavior of the 1D beam analysis and visualize numerical results.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.2
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• pp.87-96
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• 1999

To analyze the dynamic behavior of structure, direct integration and mode superposition may be utilized in time domain analysis. As finite number of frequencies can give relatively exact solutions, mode superposition is preferable in analyzing structural behavior. In non-linear analysis, however, mode superposition is seldom used since time-varying element stiffness changes stiffness matrix, and the change of stiffness matrix leads to the change of essential constants - natural frequencies and mode shapes. In spite of these difficulties, there are some attempts to adopt mode superposition because of low cost compared to direct integration, but the result is not satisfactory. In this paper, a method using mode superposition in non-linear analysis is presented by separating local element stiffness from global stiffness matrix with the difference between linear and non-linear restoring forces to the external force vectors included. Moreover, the hysteresis model changing with the relative deformation in each floor makes it possible to analyze non-linear behavior of structure. The proposed algorithm is applied to shear beam model and the maximum displacement is compared with the result using direct integration method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.2
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• pp.165-178
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• 2000

The simplified model for 3-dimensional analysis of vehicle-bridge interactions is presented in this study. By using the analysis model which includes the eccentricity of axle loads and the effect of the torsional forces acting on the bridge, the more accurate analysis results of the behavior of the bridge can be obtained. The equations of kinetic energy, potential energy and damping energy are expressed by degrees of freedom of the vehicle and the bridge. And then by applying Lagrange's equations of motion, the equations of motion of the vehicle and the bridge are obtained. By deriving the equations of forces acting on the bridge considering the vehicle-bridge vertical interactions and also by identifying the position of vehicle as time goes by, mass matrix, stiffness matrix, damping matrix and load vector of vehicle-bridge system are constructed in accordance with the position of vehicles. Then using Newmark's β-method(average acceleration), the equations of motion for the total vehicle bridge system are solved.

• Journal of Korean Society of Steel Construction
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• v.28 no.5
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• pp.337-344
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• 2016

In this study, a form-finding method of tensegrity systems by using the force density method combined with the stiffness matrix method was presented. Numerous studies have been made on form-finding methods of the tensegrity systems. However, these methods are limited in the tensegrity systems with multiple null space of the equilibrium matrix. The proposed method can uniquely define a single integral feasible set of force densities for the structures. In order to draw maximum natural frequency that can lead a maximum stiffness of the tensegrity systems, a constrained maximization problem is formulated in the genetic algorithm. Several numerical examples are presented to prove dfficiency in searching for self-equilibrium congifurations of tensegrity systems with multiple self-stress states. A good performance of the proposed method has been shown in the results.

• Computational Structural Engineering
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• v.5 no.3
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• pp.119-126
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• 1992

Most civil engineering structures such as bridges, power plants, and offshore platforms are apt to suffer structural damages over their service lives caused by adverse loadings, such as earthquakes, wind and wave forces. Accumulation of structural damages over a long period of time might cause catastrophic structural failure. Therefore, a methodology for monitoring the structural integrity is essential for assuring the safety of the existing structures. A method for the damage assessment of structures by the second order inverse modal perturbation technique is presented in this paper. Perturbation equation consists of a matrix equation involving matrices of structural changes(stiffness and mass matrix changes) and matrices of modal property changes(natural frequency and mode shape changes). The damages of a structure are represented as changes in the stiffness matrix. In this study, a second order perturbation equation is formulated for the damage assessment of structures, and solved by an iterative procedure. The effectiveness of the proposed method has been investigated through a series of example analysis. The estimated results for the structural damage indicated that the present method yields resonable estimates for the structural changes.