• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.373-379
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• 2001

There is a big issue to generate 3D hexahedral finite element (FE) model, since a process to divide the whole domain into several simple-shaped sub-domains is required before generating a continuous mesh with mapped mesh generators. In general, it is nearly impossible to set up proper division numbers interactively to keep mesh connectivity between sub-domains on a complicated arbitrary-shaped domain. If mesh continuity between sub-domains is not required in an analysis, this complicated process can be omitted. Element-free Galerkin method (EFGM) can accept discontinuous meshes, which only requires nodal information. However it is difficult to choose a reasonable influenced domain in moving least squares scheme with non-uniformly distributed nodes in discontinuous FE models. A new FE scheme fur discontinuous mesh is proposed in this paper by applying improved EFGM with some modification to derive FE approximated function in discontinuous parts. Its validity is evaluated on linear elastic problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.55-68
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• 2007

First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.12
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• pp.1180-1187
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• 2007

In the present work, topology optimization method using adaptive inner-front level set method is presented. In the conventional level set based topology optimization method, there exists an incapability for inner-front creation during optimization process. In this regard, as a new attempt to avoid and to overcome the limitation, an inner-front creation algorithm is proposed. In the inner-front creation algorithm, the strain energy density of a structure along with volume constraint is considered. Especially, to facilitate the inner-front creation process during the optimization process, the inner-front creation map which corresponds to the discrete valued function of strain energy density is constructed. In the evolution of the level set function during the optimization process, the least-squares finite element method (LSFEM) is employed. As an application to shell structures, the lightweight design of doubly curved shell and segmented mirror is carried out.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.446-451
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• 2007

An Improved finite element model updating method to address the numerical difficulty associated with ill-conditioning and rank-deficiency. These difficulties frequently occur in model updating problems, when the identification of a larger number of physical parameters is attempted than that warranted by the information content of the experimental data. Based on the standard Bounded Variables Least-squares (BVLS) method, which incorporates the usual upper/lower-bound constraints, the proposed method is equipped with new constraints based on the correlation coefficients between the sensitivity vectors of updating parameters. The effectiveness of the proposed method is investigated through the numerical simulation of a simple framed structure by comparing the results of the proposed method with those obtained via pure BVLS and the regularization method. The comparison indicated that the proposed method and the regularization method yield approximate solutions with similar accuracy.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.12 s.255
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• pp.1626-1633
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• 2006

In the present paper, in the context of the meshless interpolation of a moving least squares (MLS) type, a novel method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The support domains for the shape functions in the MLS approximation are defined from the primary nodes, and the secondary nodes use the same support domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and moved without an additional mesh. Several numerical examples are presented to illustrate the effectiveness of the present method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.67-74
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• 2023

A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy's momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.

• Structural Monitoring and Maintenance
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• v.9 no.2
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• pp.157-177
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• 2022

In this paper, an innovative finite element updating method is presented based on the variation wavelet transform coefficients of Auto/cross-correlations function (WTCF). The Quasi-linear sensitivity of the wavelet coefficients of the WTCF concerning the structural parameters is evaluated based on incomplete measured structural responses. The proposed algorithm is used to estimate the structural parameters of truss and plate models. By the solution of the sensitivity equation through the least-squares method, the finite element model of the structure is updated for estimation of the location and severity of structural damages simultaneously. Several damage scenarios have been considered for the studied structure. The parameter estimation results prove the high accuracy of the method considering measurement and mass modeling errors.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.411-420
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• 2009

This study presents an extended finite difference method based on moving least squares(MLS) method for solving potential problems with interfacial boundary. The approximation constructed from the MLS Taylor polynomial is modified by inserting of wedge functions for the interface modeling. Governing equations are node-wisely discretized without involving element or grid; immersion of interfacial condition into the approximation circumvents numerical difficulties owing to geometrical modeling of interface. Interface modeling introduces no additional unknowns in the system of equations but makes the system overdetermined. So, the numbers of unknowns and equations are equalized by the symmetrization of the stiffness matrix. Increase in computational effort is the trade-off for ease of interface modeling. Numerical results clearly show that the developed numerical scheme sharply describes the wedge behavior as well as jumps and efficiently and accurately solves potential problems with interface.

• Journal of the Korean Institute of Navigation
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• v.25 no.4
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• pp.461-469
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• 2001

The purpose of this paper is the optimum modification of dynamic characteristics of stiffened plate structure including the number of stiffener. This paper shows the optimum structural modification method by dynamic sensitivity analysis and quasi-least squares method and considers it's validity. In the method of the optimization, finite element method, sensitivity analysis and optimum structural modification method are used. The change of natural frequency and total weight are made to be an objective function. Thickness of plate, the number of stiffener and cross section moment of stiffener become a design variable. The dynamic characteristics of stiffened plate structure is analyzed using finite element method. Next, rate of change of dynamic characteristics by the change of design variable is calculated using the sensitivity analysis. Then, amount of change of design variable is calculated using optimum structural modification method. It is shown that the results are effective in the optimum modification for dynamic characteristics of the stiffened plate structure including the number of stiffener.

• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.83-94
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• 2023

An accurate and highly efficient inverse element labelled iPCB is developed based on the inverse finite element method (iFEM) for real-time shape estimation of plane-curved structures (such as arch bridges) utilizing onboard strain data. This inverse problem, named shape sensing, is vital for the design of smart structures and structural health monitoring (SHM) procedures. The iPCB formulation is defined based on a least-squares variational principle that employs curved Timoshenko beam theory as its baseline. The accurate strain-displacement relationship considering tension-bending coupling is used to establish theoretical and measured section strains. The displacement fields of the isoparametric element iPCB are interpolated utilizing nonuniform rational B-spline (NURBS) basis functions, enabling exact geometric modelling even with a very coarse mesh density. The present formulation is completely free from membrane and shear locking. Numerical validation examples for different curved structures subjected to different loading conditions have been performed and have demonstrated the excellent prediction capability of iPCBs. The present formulation has also been shown to be practical and robust since relatively accurate predictions can be obtained even omitting the shear deformation contributions and considering polluted strain measures. The current element offers a promising tool for real-time shape estimation of plane-curved structures.