• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.759-777
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• 2013

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated ad minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used a the design variable. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such ad the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.419-424
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• 1999

In this paper, the comparison of the first order approximation schemes such as SLP (sequential linear programming), CONLIN(convex linearization), MMA(method of moving asymptotes) and the second order approximation scheme, SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore, when it is considered with the expense of computation, MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem, it was applied to the helicopter tail boom considering column buckling and local wall buckling constraints. It is concluded that MMA can be a very efficient approximation scheme from simple problems to complex problems.

• Journal of the Korean Society for Railway
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• v.9 no.1 s.32
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• pp.50-56
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• 2006

This paper presents a mathematical model of the long-term track tamping scheduling problem in the Korean highspeed railway system. The presented model encompasses various operational field constraints, moreover improves a state-of-the-art model in extending the feasible space. We show the model is sized up to intractable scale, then propose another approximation model that is possible to handle with the present computer system and commercial optimization package, directly. The aggregated index, lot, is selected, considering the resolution of the planning horizon as well as scheduling purpose. Lastly, this paper presents two test results for the approximation model. The results expose the approximation model to quite promising in deploying it into an operational software program for the long-term track tamping scheduling problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1102-1109
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• 2006

In this paper, the polarization of piezoelectric materials is considered to improve actuation since the piezoelectric polarization has influences on the performance of the actuator. The topology design of compliant mechanism can be formulated as an optimization problem of material distribution in a fixed design domain and continuous approximation of material distribution (CAMD) method has demonstrated its effectiveness to prevent the numerical instabilities in topology optimization. The optimization problem is formulated to maximize the mean transduction ratio subject to the total volume constraints and solved using a sequential linear programming algorithm. The effect of CAMD and the performance improvement of actuator are confirmed through Moonie actuator and PZT suspension design.

• 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.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.91-98
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• 1994

An efficient optimization procedure combining the frequency approximation technique and the component-mode synthesis method is proposed for the structural dynamic optimization of the large structures subject to prescribed natural frequency constraints. Frequency constraints are approximated by using the first-order sensitivities with respect to both design parameters and their reciprocals. The component-mode synthesis method proposed by the authors in Ref.[8] is used for the repetitive detail finite-element analysis and sensitivity analysis. The validity of the proposed optimization procedure is confirmed through the numerical implementation of some examples. The presented approximation technique requires much smaller number of repetitive analysis than that using the sensitivities with respect to design parameters only, and further improvement in the numerical efficiency is achieved by the adoption of the introduced component-mode synthesis.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.8
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• pp.398-402
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• 2002

The ELD computation has been based upon the so-called B-coefficient which uses a quadratic approximation of system loss as a function of generation output. Direct derivation of system loss sensitivity based on the Jacobian-based method was developed in early 1970s', which could eliminate the dependence upon the approximate loss formula. However, both the B-coefficient and the Jacobian-based method require a complicated Procedure for calculating the system loss sensitivity included in the constraints of the optimization problem. In this paper, an ELD formulation in which only the bus power equations are defined as the constraints has been introduced. Derivation of the partial derivatives of the system loss with respect to the generator output and calculation of the penalty factors for individual generators are not required anymore in proposed method. A comprehensive solution procedure including calculation of the Jacobians and Hessians of the formulation has been presented in detail. Proposed ELD formulation has been tested on a sample system and the simulation indicated a satisfactory result.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.168-174
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• 2000

A biarc is a curve connecting two circular arcs with the constraints of tangent continuity so that it can represent the free form currie approximately connecting several biarcs with the tangent continuity. Since a biarc consists of circular arcs, the offset curve of the curve represented by biarcs can be easily obtained. Besides. if the tool path is represented by biarcs, the efficiency of machining is improved and the amount of data is decreased. When approximating a curve with biarcs, the location of the point where two circular arcs meet each other plays an important part in determining the shape of a biarc. In this thesis, the optimum point where two circular arcs meet is calculated using the tangent information of the curve to approximate so that it takes less calculation time to approximate due to the decrease of the number of iterations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.3
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• pp.259-266
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• 2011

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.