• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.1-6
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• 2002

David Gavid [3] proved that in many familiar cases the upper semi-finite topology on the set of closed subsets of a space is the largest topology making the coincidence function continuous, when the collection of functions is given the graph topology. Considering G-spaces and taking the coincidence set to consist of points where orbits coincidence, we obtain G-version of many of his results.

• Structural Engineering and Mechanics
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• v.33 no.3
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• pp.285-306
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• 2009

In the literature the problem of the topology optimization of the structure is usually solved for one, clearly described from the mechanical point of view material. Generally the topology optimization answers the question of the distribution of this mentioned above material within the design domain. Finally, material-voids distribution it is obtained. In this paper, for the structure mainly strengthened or sometimes weakened by the inclusions, the variation approach of the topology optimization problem is formulated. This multi material approach may be useful for the design process of various mechanical or civil engineering structures which need to be more "refined" and more "optimal" than they can be using previous topology optimization procedures of optimization one material structures.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.603-608
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• 2008

It is well known that the topology optimization for plastic problem is not easy since the iterative analyses to evaluate the objective and cost function with respect to the design variation are very time-consuming. The finite element limit analysis is an efficient tool which is possible to predict collapse modes and sequential collapse loads of a structure considering not only large deformation but also plastic material behavior with moderate computing cost. In this paper, the optimum topology of a structure considering large and plastic deformation is obtained using the finite element limit analysis. To verify the constructed optimization code, topology optimizations of some typical problems are performed and the optimal topologies by elastic design and plastic design are compared.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.2
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• pp.224-229
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• 2010

This paper presents a reliability-based topology optimization (RBTO) using bi-directional evolutionary structural optimization (BESO). An actual design involves uncertain conditions such as material property, operational load and dimensional variation. Deterministic topology optimization (DTO) is obtained without considering of uncertainties related to the uncertainty parameters. However, the RBTO can consider the uncertainty variables because it has the probabilistic constraints. In this paper, the reliability index approach (RIA) is adopted to evaluate the probabilistic constraint. RBTO based on BESO starting from various design domains produces a similar optimal topology each other. Numerical examples are presented to compare the DTO with the RBTO.

• Journal of the Optical Society of Korea
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• v.19 no.1
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• pp.13-21
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• 2015

In recent years energy consumption has become a main concern for network development, due to the exponential increase of network traffic. Potential energy savings can be obtained from a load-adaptive scheme, in which a day can be divided into multiple time periods according to the variation of daily traffic patterns. The energy consumption of the network can be reduced by selectively turning off network components during the time periods with light traffic. However, the time segmentation of daily traffic patterns affects the energy savings when designing multiperiod logical topology in optical wavelength routed networks. In addition, turning network components on or off may increase the overhead of logical topology reconfiguration (LTR). In this paper, we propose two mixed integer linear programming (MILP) models to design the optimal logical topology for multiple periods in IP-over-WDM networks. First, we formulate the time-segmentation problem as an MILP model to optimally determine the boundaries for each period, with the objective to minimize total network energy consumption. Second, another MILP formulation is proposed to minimize both the overall power consumption (PC) and the reconfiguration overhead (RO). The proposed models are evaluated and compared to conventional schemes, in view of PC and RO, through case studies.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.245-254
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• 2017

In this paper, deployment dynamics of large-scale flexible solar arrays with deployable mast is investigated. The adopted solar array system is introduced firstly, then kinematic description and kinematic constraint equations are deduced, and finally, dynamics equation of the system is established by the Jourdain velocity variation principle and a new method to deal with topology changes of the deployable mast is introduced. The dynamic behavior of the system is studied in detail. Simulation results indicate that the proposed model is effective to describe the deployment dynamics of the solar arrays and that the introduced method is applicable for topology changes.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.6
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• pp.77-82
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• 2008

This paper presents a Reliability-Based Topology Optimization(RBTO) using the Evolutionary Structural Optimization(ESO). An actual design involves some uncertain conditions such as material property, operational load and dimensional variation. The Deterministic Topology Optimization(DTO) is obtained without considering the uncertainties related to the uncertainty parameters. However, the RBTO can consider the uncertainty variables because it has the probabilistic constraints. In order to determine whether the probabilistic constraints are satisfied or not, simulation techniques and approximation methods are developed. In this paper, the reliability index approach(RIA) is adopted to evaluate the probabilistic constraints. In order to apply the ESO method to the RBTO, sensitivity number is defined as the change in the reliability index due to the removal of the ith element. Numerical examples are presented to compare the DTO with the RBTO.

• Computational Structural Engineering
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• v.9 no.3
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• pp.169-177
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear programming formulation of the topology problem is presented. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.4
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• pp.529-538
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• 2010

This paper presents a reliability-based topology optimization (RBTO) based on bidirectional evolutionary structural optimization (BESO). In design of a structure, uncertain conditions such as material property, operational load and dimensional variation should be considered. Deterministic topology optimization (DTO) is performed without considering the uncertainties related to the design variables. However, the RBTO can consider the uncertainty variables because it can deal with the probabilistic constraints. The reliability index approach (RIA) and the performance measure approach (PMA) are adopted to evaluate the probabilistic constraints in this study. In order to apply the BESO to the RBTO, sensitivity number for each element is defined as the change in the reliability index of the structure due to removal of each element. Smoothing scheme is also used to eliminate checkerboard patterns in topology optimization. The limit state indicates the margin of safety between the resistance (constraints) and the load of structures. The limit State function expresses to evaluate reliability index from finite element analysis. Numerical examples are presented to compare each optimal topology obtained from RBTO and DTO each other. It is verified that the RBTO based on BESO can be effectively performed from the results.