• Structural Engineering and Mechanics
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• v.76 no.6
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• pp.799-821
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• 2020

The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.349-354
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• 1992

In this paper, a modal analysis is applied for a hung Euler-Bernoulli beam with a lumped mass. We first derive the equations of motion using the Hamilton's principle. Then regarding the tension of beam as constant, we characterize the eigenfrequencies and the feature of eigenfunctions. The approximation employed here is corresponding that the lumped mass is sufficiently large than that of beam. Finally we compare the eigenfrequencies derived here with those obtained based on the Southwell's method.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.419-432
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• 2007

Double-diffusive convection inside a triangular porous cavity is studied numerically. Galerkin finite element method is adopted to derive the discrete form of the governing differential equations. The first-order backward Euler scheme is used for temporal discretization with the second-order Adams-Bashforth scheme for the convection terms in the energy and species conservation equations. The Boussinesq-Oberbeck approximation is used to calculate the density dependence on the temperature and concentration fields. A parametric study is performed with the Lewis number, the Rayleigh number, the buoyancy ratio, and the shape of the triangle. The effect of gravity orientation is considered also. Results obtained include the flow, temperature, and concentration fields. The differences induced by varying physical parameters are analyzed and discussed. It is found that the heat transfer rate is sensitive to the shape of the triangles. For the given geometries, buoyancy ratio and Rayleigh numbers are the dominating parameters controlling the heat transfer.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.65-72
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• 1998

From the Boltzmann equation with BGK approximation, a gas-kinetic BGK scheme is developed and methods for its efficient calculation, using the convergence acceleration techniques, are presented in a framework of an implicit time integration. The characteristics of the original gas-kinetic BGK scheme are improved in order for the accurate calculation of viscous and heat convection problems by considering Osher's linear subpath solutions and Prandtl number correction. Present scheme applied to various numerical tests reveals a high level of accuracy and robustness and shows advantages over flux vector splittings and Riemann solver approaches from Euler equations.

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.571-574
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• 2005

This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems in the sense of the above by using Euler approximation.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1004-1007
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• 1992

In this paper, we present a solution to the PID tuning problem by optimizing a GPC(General Predictive Control) criterion. The PID structure is ensured by constraning the parameters to a feasible set defined by the discrete-time Euler approximation of the ideal continuous-time PID controller. The algorithm is ectended by incorporating heuristic rules for selection of the significant design parameters. The algorithm has been successfully tested and some results are prewented.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.7-17
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• 1990

The objective of this paper is to provide a method of optimizing are as of the members as well as shape of both truss and arch structures. The design process includes satisfaction of stress and Euler buckling stress constraints for truss and combined stress constraints for arch structures. In order to reduce the number of detailed finite element analysis, the Force Approximation Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the structure with information from the approximate structural analysis. Numerical examples are performed and compared with other methods to demonstrate the efficiency and reliability of the Force Approximation Method for shape optimization. It is shown that the number of finite element analysis is greatly reduced and that it leads to a highly efficient method of shape optimization of structures.

• Journal of the Korea Computer Graphics Society
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• v.5 no.1
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• pp.27-33
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• 1999

In this paper, we propose an efficient technique for the animation of flexible thin objects. Mass-spring model was employed to represent the flexible objects. Till now, many techniques have used the mass-spring model to generate plausible animation of soft objects. A straight-forward approach to the animation with mass-spring model is explicit Euler method, but the explicit Euler method has serious disadvantage that it suffers from 'instability problem'. The implicit integration method is a possible solution to overcome the instability problem. However, the most critical flaw of the implicit method is that it involves a large linear system. This paper presents a fast animation technique for mass-spring model with approximated implicit method. The proposed technique stably updates the state of n mass-points in O(n) time when the number of total springs are O(n). We also consider the interaction of the flexible object and air in order to generate plausible results.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.1
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• pp.201-216
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• 2013

Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.