• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.1
• /
• pp.153-160
• /
• 2001

A general procedure for the design sensitivity analysis of structural dynamic problems has been presented in frame of the FRF-based substructuring formulation. For a system response function, the proposed method gives a parametric design sensitivity formula in terms of the partial derivatives of the connection element properties and the transfer matrix of the subsystems. The derived design sensitivity formula is applied to an engine mount system. An interior noise problem in the passenger car is analyzed using the FRF-based substructuring method and the proposed formulation is adopted to study the response variations with respect to the dynamic characteristics of the engine mounts and the bushes. To obtain the FRFs, a finite element model is built for the engine mount structures, and test data is used for the trimmed body including cabin cavity. The comparison of sensitivities derived by the proposed method and the finite difference method shows that the proposed method is efficient and accurate. The proposed sensitivity analysis method indicates effectively the most sensitive location to the interior noise among the engine mounts and the bushes.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.461-477
• /
• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2000.11a
• /
• pp.194-200
• /
• 2000

Researches on the FRF-based substructuring method have been mainly focused on vibratory response analysis. Present study is concerned about the application of the method to the dynamic stress analysis of a compressor mounting bracket in a passenger car. This is performed by using reaction forces that can be obtained by the FRF-based substructuring method. The air-conditioner system, composed of a compressor, a bracket and a test jig, is analyzed by using the FRF-based substructuring method. The experimental and numerical FRFs are combined to calculate the system responses and reaction forces at the connection point. The dynamic reaction forces plugged into the bracket FE model to compute the compute the stresses of the bracket. Dynamic stresses by the present method are compared with those from FE model. The comparison shows possibility of practical usage of the method for the real problem.

• Structural Engineering and Mechanics
• /
• v.4 no.5
• /
• pp.553-568
• /
• 1996

Finite element stiffness matrix methods are presented for finding natural frequencies (or buckling loads) and modes of repetitive structures. The usual approximate finite element formulations are included, but more relevantly they also permit the use of 'exact finite elements', which account for distributed mass exactly by solving appropriate differential equations. A transcendental eigenvalue problem results, for which all the natural frequencies are found with certainty. The calculations are performed for a single repeating portion of a rotationally or linearly (in one, two or three directions) repetitive structure. The emphasis is on rotational periodicity, for which principal advantages include: any repeating portions can be connected together, not just adjacent ones; nodes can lie on, and members along, the axis of rotational periodicity; complex arithmetic is used for brevity of presentation and speed of computation; two types of rotationally periodic substructures can be used in a multi-level manner; multi-level non-periodic substructuring is permitted within the repeating portions of parent rotationally periodic structures or substructures and; all the substructuring is exact, i.e., the same answers are obtained whether or not substructuring is used. Numerical results are given for a rotationally periodic structure by using exact finite elements and two levels of rotationally periodic substructures. The solution time is about 500 times faster than if none of the rotational periodicity had been used. The solution time would have been about ten times faster still if the software used had included all the substructuring features presented.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.2
• /
• pp.267-274
• /
• 2002

Using a flexible rotating beam test bed, experimental verification of a flexible multibody dynamic simulations for a rotating beam model has been carried out. The test bed consists of a flexible arm, harmonic driver reducer, AC servo motor and DSP board with PC. The mechanical ports of the test bed has been designed using 3D CAD program. For the simulation model, mass and moment of inertia of each part of the flexible rotating beam test bed are also obtained from 3D CAD model. In the flexible multibody dynamic simulations, the substructuring model has been established to capture nonlinear effects of the flexible rotating beam. Through the experimental verification, substructuring model provides better results than those from the linear model in the high speed rotation.

• 한국전산유체공학회:학술대회논문집
• /
• 2004.03a
• /
• pp.83-90
• /
• 2004

Substructuring methods are usually used in finite element structural analyses. In this study a multi-level substructuring algorithm is developed and proposed as a possible candidate for incompressible fluid solves. Finite element formulation for incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et.al.[5]. The present algorithm consists of four stages such as a gathering stage, a condensing stage, a solving stage and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At highest level, each subdomain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each subdomain has been replaced by a sequential static condensation. The global algebraic system arising feom the assembly of each subdomains is solved using Conjugate Gradient Squared(CGS) method. In this case, pre-conditioning techniques usually accompanied by iterative solvers are not needed.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.04a
• /
• pp.50-57
• /
• 1999

Structural analysis of large-scale structures involving large amount of computational load and data storage requires high-performance computing resources. We have previously developed PC-level distributed structural analysis algorithms based on substructuring technique where each personal computer assigned to a slave node has been involved in the computations for single substructures. Recently, it has been proved by the authors that the performance of distributed structural analysis algorithm can be further enhanced by changing substructuring schemes. Therefore a new distributed structural analysis algorithm with one PC to multiple substructures scheme is presented in this paper. The algorithm is implemented on the network of multiple personal computers and applied to structural analysis of two dimensional frame structures.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.602-606
• /
• 2000

A general procedure for the design sensitivity analysis of structural dynamic problems has been presented in frame of the FRF-based substructuring formulation. In the procedure, the direct differentiation method is used for the sensitivity formula. For a system response function, the proposed method gives a parametric design sensitivity formula in terms of the partial derivatives of the connection element properties and the transfer matrix of the subsystems. The derived design sensitivity formula is applied to a numerical example. The comparison of sensitivities derived by the proposed method and the finite difference method shows that the proposed method is efficient and accurate.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1998.04a
• /
• pp.373-380
• /
• 1998

Generally the excessive caused by isolated sources in localized to members closely located to the vibration sources. In this case it may not be economical to model the whole structure to obtain the responses of a specific member. In this study, a substructuring technique has been used for local vibration of a framed structure. The boundary conditions of members selected are determined by condensing the degrees of freedom of the remaining members. Fixed and hinged boundary condition are also assumed for comparison. According to the results, the substructuring technique is quite efficient in predicting the responses of a structure on which the vibration source in located, but is not very reliable for the members located for away from the source.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.6
• /
• pp.743-749
• /
• 2007

Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large size problems, but, originally, it was designed to calculate only the smallest eigenvalues. In this paper, an updated version of AS is proposed to calculate the interior eigenvalues over a specified range by using a shift value, which is referred to as the shifted AS. Numerical experiments demonstrate that the proposed method has better efficiency to compute numerous interior eigenvalues for the finite element models of structural problems than a Lanczos-type method.