• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.2
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• pp.221-230
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• 2000

Sweep geometric models are based on the notion of moving a curve, surface or solid along some path. Sweeping allows definition of prismatic shell surfaces in a simple way, This paper describes an application of sweep geometric models for the optimization of prismatic shells. This geometric model is integrated with finite element formulations. A nine-node degenerated shell element is adopted to calculate the response of prismatic shells. Several examples we presented to demonstrate the process of optimization. From numerical examples, it is observed that sweep geometric models provide an efficient and reliable way of obtaining optimal solutions for a large class of prismatic shell structures.

• Steel and Composite Structures
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• v.30 no.5
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• pp.483-492
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• 2019

In the current study, the influence of the initial lateral (sweep) shape and the cross-sectional twist imperfection on the lateral torsional buckling (LTB) response of doubly-symmetric steel I-beams was investigated. The material imperfection (residual stress) was not considered. For this objective, standard European IPN 300 beam with different unbraced span was numerically analyzed for three imperfection cases: (i) no sweep and no twist (perfect); (ii) three different shapes of global sweep (half-sine, full-sine and full-parabola between the end supports); and (iii) the combination of three different sweeps with initial sinusoidal twist along the beam. The first comparison was done between the results of numerical analyses (FEM) and both a theoretical solution and the code lateral torsional buckling formulations (EC3 and AISC-LRFD). These results with no imperfection effects were then separately compared with three different shapes of global sweep and the presence of initial twist in these sweep shapes. Besides, the effects of the shapes of initial global sweep and the inclusion of sinusoidal twist on the critical buckling load of the beams were investigated to unveil which parameter was considerably effective on LTB response. The most compatible outcomes for the perfect beams was obtained from the AISC-LRFD formulation; however, the EC-3 formulation estimated the $P_{cr}$ load conservatively. The high difference from the EC-3 formulation was predicted to directly originate from the initial imperfection reduction factor and high safety factor in its formulation. Due to no consideration of geometric imperfection in the AISC-LFRD code solution and the theoretical formulation, the need to develop a practical imperfection reduction factor for AISC-LRFD and theoretical formulation was underlined. Initial imperfections were obtained to be more influential on the buckling load, as the unbraced length of a beam approached to the elastic limit unbraced length ($L_r$). Mode-compatible initial imperfection shapes should be taken into account in the design and analysis stages of the I-beam to properly estimate the geometric imperfection influence on the $P_{cr}$ load. Sweep and sweep-twist imperfections led to 10% and 15% decrease in the $P_{cr}$ load, respectively, thus; well-estimated sweep and twist imperfections should considered in the LTB of doubly-symmetric steel I-beams.

• Journal of the Korea Computer Graphics Society
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• v.21 no.1
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• pp.13-21
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• 2015

We present a robust GPU algorithm constructing a sweep volume boundary for a triangular mesh model. Sweeping geometric entities of a triangular mesh object is first approximated to a set of triangles, the envelope of which becomes the outer boundary of the sweep volume. We find the envelope by computing the arrangement of the triangle set and extracting its outmost boundary. To ensure robustness of the algorithm, we adopt random perturbation of sweep vertices and the interval arithmetic using multi-level precisions. The algorithm is implemented to perform most computation on GPU, and as a result it runs two orders of magnitude faster than other algorithms.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.7 s.250
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• pp.603-611
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• 2006

This paper presents the response surface optimization method using three-dimensional Wavier-Stokes analysis to optimize the blade shape of an axial flow fan. Reynolds-averaged Wavier-Stokes equations with $k-{\epsilon}$ turbulence model are discretized with finite volume approximations using the unstructured grid. Regression analysis is used for generating response surface, and it is validated by ANOVA and t-statistics. Four geometric variables, i.e., sweep and lean angles at mean and tip respectively were employed to improve the efficiency. The computational results are compared with experimental data and the comparisons show generally good agreements. As a main result of the optimization, the total efficiency was successfully improved. Also, detailed effects of sweep and lean on the axial flow fan are discussed.

• Advances in aircraft and spacecraft science
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• v.7 no.4
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• pp.353-369
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• 2020

This paper presents the flutter analysis and optimum design of axially functionally graded box beam cantilever wing section by considering various geometric and material parameters. The coupled dynamic equations of the continuous model of wing system in terms of material and cross-sectional properties are formulated based on extended Hamilton's principle. By expressing the lift and pitching moment in terms of plunge and pitch displacements, the resultant two continuous equations are simplified using Galerkin's reduced order model. The flutter velocity is predicted from the solution of resultant damped eigenvalue problem. Parametric studies are conducted to know the effects of geometric factors such as taper ratio, thickness, sweep angle as well as material volume fractions and functional grading index on the flutter velocity. A generalized surrogate model is constructed by training the radial basis function network with the parametric data. The optimized material and geometric parameters of the section are predicted by solving the constrained optimal problem using firefly metaheuristics algorithm that employs the developed surrogate model for the function evaluations. The trapezoidal hollow box beam section design with axial functional grading concept is illustrated with combination of aluminium alloy and aluminium with silicon carbide particulates. A good improvement in flutter velocity is noticed by the optimization.

• 유체기계공업학회:학술대회논문집
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• 2004.12a
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• pp.578-582
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• 2004

This paper presents the response surface optimization method using three-dimensional Navier-Stokes Analysis to optimize the shape of a axial flow fan. Reynolds-averaged Navier-Stokes equations with k-$\epsilon$ turbulence model are discretized with finite volume approximations. Regression analysis is used for generating response surface, and it is validated by ANOVA. Five geometric variables, i.e., distribution of sweep angle at mean and tip, lean angle at mean and tip, and spanwise location of mean were employed to optimize the efficiency. The computational results are compared with experiment data. As a main result of the optimization, the efficiency was successfully improved.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2690-2695
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• 2007

This work presents numerical optimization for design of a blade stacking line of a low speed axial flow fan with a fast and elitist Non-Dominated Sorting of Genetic Algorithm (NSGA-II) of multi-objective optimization using three-dimensional Navier-Stokes analysis. Reynolds-averaged Navier-Stokes (RANS) equations with ${\kappa}-{\varepsilon}$ turbulence model are discretized with finite volume approximations and solved on unstructured grids. Regression analysis is performed to get second order polynomial response which is used to generate Pareto optimal front with help of NSGA-II and local search strategy with weighted sum approach to refine the result obtained by NSGA-II to get better Pareto optimal front. Four geometric variables related to spanwise distributions of sweep and lean of blade stacking line are chosen as design variables to find higher performed fan blade. The performance is measured in terms of the objectives; total efficiency, total pressure and torque. Hence the motive of the optimization is to enhance total efficiency and total pressure and to reduce torque.

• International Journal of Air-Conditioning and Refrigeration
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• v.16 no.1
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• pp.1-8
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• 2008

Numerical optimization for design of a blade stacking line of a low speed axial flow fan with a fast and elitist Non-Dominated Sorting of Genetic Algorithm(NSGA-II) of multi-objective optimization using three-dimensional Navier-Stokes analysis is presented in this work. Reynolds-averaged Navier-Stokes(RANS) equations with ${\kappa}-{\varepsilon}$ turbulence model are discretized with finite volume approximations and solved on unstructured grids. Regression analysis is performed to get second order polynomial response which is used to generate Pareto optimal front with help of NSGA-II and local search strategy with weighted sum approach to refine the result obtained by NSGA-II to get better Pareto optimal front. Four geometric variables related to spanwise distributions of sweep and lean of blade stacking line are chosen as design variables to find higher performed fan blade. The performance is measured in terms of the objectives; total efficiency, total pressure and torque. Hence the motive of the optimization is to enhance total efficiency and total pressure and to reduce torque.