• Steel and Composite Structures
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• v.45 no.4
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• pp.579-590
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• 2022

One of the biggest problems in structural steel calculation is the design of structures using the lowest possible material weight, making this a slow and costly process. To achieve this objective, several optimization methods have been developed and tested. Nevertheless, a method that performs very efficiently when applied to different problems is not yet available. Based on this assumption, this work proposes a hybrid metaheuristic algorithm for geometric and dimensional optimization of space trusses, called Simulated Squirrel Search Algorithm, which consists of an association of the well-established neighborhood shifting algorithm (Simulated Annealing) with a recently developed promising population algorithm (Squirrel Search Algorithm, or SSA). In this study, two models are tried, being respectively, a classical model from the literature (25-bar space truss) and a roof system composed of space trusses. The structures are subjected to resistance and displacement constraints. A penalty function using Fuzzy Logic (FL) is investigated. Comparative analyses are performed between the Squirrel Search Algorithm (SSSA) and other optimization methods present in the literature. The results obtained indicate that the proposed method can be competitive with other heuristics.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.12
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• pp.1811-1820
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• 2010

Most components in the real world show nonlinear response. The nonlinearity may arise because of contact between the parts, nonlinear material, or large deformation of the components. Structural optimization considering nonlinearities is fairly expensive because sensitivity information is difficult to calculate. To overcome this difficulty, the equivalent load method was proposed for nonlinear response optimization. This method was originally developed for size and shape optimization. In this study, the equivalent load method is modified to perform topology optimization considering all kinds of nonlinearities. Equivalent load is defined as the load for linear analysis that generates the same response field as that for nonlinear analysis. A simple example demonstrates that results of the topology optimization using equivalent load are very similar to the numerical results. Nonlinear response topology optimization is performed with a practical example and the results are compared with those of conventional linear response topology optimization.

• Smart Structures and Systems
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• v.25 no.5
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• pp.605-617
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• 2020

The existence of damages in structures causes changes in the physical properties by reducing the modal parameters. In this paper, we develop a two-stages approach based on normalized Modal Strain Energy Damage Indicator (nMSEDI) for quick applications to predict the location of damage. A two-dimensional IsoGeometric Analysis (2D-IGA), Machine Learning Algorithm (MLA) and optimization techniques are combined to create a new tool. In the first stage, we introduce a modified damage identification technique based on frequencies using nMSEDI to locate the potential of damaged elements. In the second stage, after eliminating the healthy elements, the damage index values from nMSEDI are considered as input in the damage quantification algorithm. The hybrid of Teaching-Learning-Based Optimization (TLBO) with Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) are used along with nMSEDI. The objective of TLBO is to estimate the parameters of PSO-ANN to find a good training based on actual damage and estimated damage. The IGA model is updated using experimental results based on stiffness and mass matrix using the difference between calculated and measured frequencies as objective function. The feasibility and efficiency of nMSEDI-PSO-ANN after finding the best parameters by TLBO are demonstrated through the comparison with nMSEDI-IGA for different scenarios. The result of the analyses indicates that the proposed approach can be used to determine correctly the severity of damage in beam structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.233-238
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• 2008

In this paper, a shape design optimization method for linearly elastic problems is developed using isogeometric approach. In many design optimization problems for practical engineering models, initial raw data usually come from a CAD modeler. Then, designers should convert the CAD data into finite element mesh data since most of conventional design optimization tools are based on finite element analysis. During this conversion, there are some numerical errors due to geometric approximation, which causes accuracy problems in response as well as design sensitivity analyses. As a remedy for this phenomenon, the isogeometric analysis method can be one of the promising approaches for the shape design optimization. The main idea of isogeometric approach is that the basis functions used in analysis is exactly the same as the ones representing the geometry. This geometrically exact model can be used in the shape sensitivity analysis and design optimization as well. Therefore the shape design sensitivity with high accuracy can be obtained, which is very essential for a gradient-based optimization. Through numerical examples, it is verified that the shape design optimization based on an isogeometic approach works well.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.155-162
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• 2014

Using an isogeometric approach, a continuum-based shape design optimization method is developed for steady state power flow problems at high frequencies. In case the isogeometric method is employed to the shape design optimization, the NURBS basis functions used in CAD geometric modeling are directly utilized to embed the exact geometry into the computational framework so that the design parameterization for shape optimization is much easier than that in the finite element method and consequently provides the enhanced smoothness of design perturbations. Thus, exact geometric models can be used in both the response and the shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be expected. Through numerical examples, the developed isogeometric sensitivity is compared with finite difference one to provide excellent agreement. Also, it turns out that the proposed method works very well in the shape optimization problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.4
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• pp.684-695
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• 1992

The present study is concerned with the analysis of three-dimensional sheet metal forming process by the upper-bound method. For the analysis a systematic approach is necessary for the expression of geometric configuration of the deforming workpiece. In the present paper geometric configuration is constructed by three unit surfaces which are defined by sweeping the vertical section curves and boundary curve. The principal components of strain increment during the process is calculated directly from the change of geometric configuration for an arbitrary triangular element. The corresponding solution is found through optimization of the total energy consumption with respect to some parameters assumed in the velocity field and geometric profile. In order to verify the effectiveness of the present method, hydrostatic bulging of a rectangular disphragm is analyzed and the computation by the present method for the geometric shape renders the good result. From the comparison of the present results with the existing experimental results and elastic-plastic finite element solutions, good agreements have been obtained for the pressure curves, polar membrane strains and pressure distributions. The present method can thus be further applied to the analysis of other three-dimensional sheet metal forming processes.

• The Mathematical Education
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• v.60 no.4
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• pp.543-554
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• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.5
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• pp.9-17
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• 2005

In the early stage of helicopter design, an optimal configuration is usually determined after a numerous parametric study about the aerodynamic performance due to geometric variation. In order to improve the aerodynamic performance of a shrouded tail rotor, optimization of the tip clearance gap between blade and shroud, the blade planform shape, and the arrangement of blade spacing is required. In the present study, the aerodynamic performance characteristics of a shrouded tail rotor due to geometric variation was investigated by using an inviscid compressible unstructured mesh flow solver for rotary wings.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.523-537
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• 2011

A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.

• 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.