• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.51-64
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• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.17-23
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• 2001

The evaluation of a few of the smallest eigenpairs of large symmetric eigenvalue problem is of great interest in many physical and engineering applications. A deflation-preconditioned conjugate gradient(PCG) scheme for a such problem has been shown to be very efficient. In the present paper we provide the numerical stability of a deflation-PCG with partial shifts.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.342-349
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• 2008

A selection method of primary degrees of freedom in dynamic condensation for nonproportional damping structures is proposed. Recently, many dynamic condensation schemes for complex eigenanalysis have been applied to reduce the number of degrees of freedom. Among them, iterative scheme is widely used because accurate eigenproperties can be obtained by updating the transformation matrix in every iteration. However, a number of iteration to enhance the accuracy of the eigensolutions may have a possibility to make the computation cost expensive. This burden can be alleviated by applying properly selected primary degrees of freedom. In this study, which method for selection of primary degrees of freedom is best fit for the iterative dynamic condensation scheme is presented through the results of a numerical experiment. The results of eigenanalysis of the proposed method is also compared to those of other selection schemes to discuss a computational effectiveness.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.4
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• pp.432-446
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• 1996

A stochastic Hamilton variational principle(SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. In addition to, a method to analyse stochastic design sensitivity for structural dynamics is present. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element codes. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The algorithms developed can readily be adapted to existing deterministic finite element codes. The numerical results for stochastic analysis by proceeding approach of cantilever, 2D-frame and 3D-frame illustrates in this paper.

• Steel and Composite Structures
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• v.4 no.1
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Smart Structures and Systems
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• v.18 no.4
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• pp.733-754
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• 2016

Structural optimization involves a large number of structural analyses. When optimizing large structures, these analyses require a considerable amount of computational time and effort. However, there are specific types of structure for which the results of the analysis can be achieved in a much simpler and quicker way thanks to their special repetitive patterns. In this paper, frequency constraint optimization of cyclically repeated space trusses is considered. An efficient technique is used to decompose the large initial eigenproblem into several smaller ones and thus to decrease the required computational time significantly. Some examples are presented in order to illustrate the efficiency of the presented method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.1
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• pp.85-99
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• 2008

The dynamic response analysis for large structures using finite element method requires a large amount of computational resources. This paper presents an efficient vibration analysis procedure by combining node-based substructuring reduction method with a response analysis scheme for structures with undamped, proportional or nonproportional damping. The iterative form of substructuring reduction scheme is derived to reduce the full eigenproblem and to calculate the dynamic responses. In calculating the time response, direct integration scheme is used because it can be applied directly to the reduced model. Especially for the non proportional damping matrix, the transformation matrices defined in the displacement space are used to reduce the system. The efficiency and the effectiveness of the present method are demonstrated through the numerical examples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.34-41
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• 2001

Most of the eigenvalue analysis methods for the undamped or proportionally damped systems use the well-known Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is to be used for large structures. However, in the case of the non-proportionally damped systems such as the soil-structure interaction system, the structural control system and the composite structures, no counterpart of the Sturm sequence property for undamped systems has been developed yet. Hence, when some important modes are missed for those systems, it may leads to poor results in dynamic analysis. In this paper, a technique for calculating the number of eigenvalues inside the open disk of arbitrary radius for the eigenproblem with the damping matrix is proposed by applying Chen's algorithm and Gleyse's theorem. To verify the applicability of the proposed method, two numerical examples are considered.