• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.183-194
• /
• 2003

We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given.

• Structural Engineering and Mechanics
• /
• v.15 no.4
• /
• pp.451-462
• /
• 2003

In this paper, a new block iterative algorithm is presented by using the special feature of the continuous Riccati equation in the optimal shape control. Because the real-time control require that the CPU time should be as short as possible, an appropriate modal control algorithm is sought. The computing cost is less than the one of the all state feedback control. A numerical example is given to illustrate the algorithm.

• Journal of Korean Society of Transportation
• /
• v.13 no.3
• /
• pp.67-86
• /
• 1995

It requires the detector system which can collect highly reliable traffic data in order to perform the real-time traffic signal control. This study is to decide the optimal shape of inductive loop for the real-time traffic signal control .This loop is located at the stopline in the signalized intersection for DS(Degree of Saturation) control. In order to find out the optimal shape of loop, 6types of experiments were performed . The results of the basic experiments of loops are as follows ; -the optimal number of turns for loop is 3 turns. -the impedance values of the loop detectors are similar to that of NEMA standards -the 1.8${\times}$4.5M loop is excellent for sensitivity in actual detection range of car length comparing to other shape of inductive loops. At the experimental of establishments of the optimal loop shape, it found that 1.8 4.5M loop has the highest values of $\DeltaL$ comparing to other types of loops, It means that the range of Lead-in cable length of this loop. And this loop is highly reliable in occpupancy time. Conclusivley, the 1.8${\times}$4.5M inductive loop is the optimal solution as a stop line loop detector for real -time traffic signal control.

• Korean Journal of Mathematics
• /
• v.25 no.3
• /
• pp.405-435
• /
• 2017

We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.

• Journal of Urban Science
• /
• v.7 no.1
• /
• pp.55-61
• /
• 2018

Long bridges, such as suspension bridges and diagonal bridges, are complex phenomena that show different behaviors depending on the shape and rigidity of the cross sections, such as wind vibrations and liquid vibrations from earthquakes in liquid storage containers. This is called the lower skirt on the lower side of the bridge, and the installation of lower skirt is effective for release and vortex vibrations caused by rapid winds, and that increases the stability of the wind resistance of the bridge. Optimal shape and installation of the lower skirt is also essential to make maximum wind speed effect of the lower skirt. Therefore, this study proposes a numerical analysis method to control the vibration of a bridge by calculating the optimal installation angle of an optimal lower skirt according to the optimal control theory and this study evaluates the impact on the optimal control system by minimizing the dominance equation with an evaluation function,which is an indicator for evaluating the optimal control theory state.

• Smart Structures and Systems
• /
• v.5 no.3
• /
• pp.241-260
• /
• 2009

Shape control of flexible structures using piezoelectric materials has attracted much attention due to its wide applications in controllable systems such as space and aeronautical engineering. The major work in the field is to find a best control voltage or an optimal placement of the piezoelectric actuators in order to actuate the structure shape as close as possible to the desired one. The current research focus on the investigation of static shape control of intelligent shells using spatially distributed piezoelectric curve beam actuators. The finite element formulation of the piezoelectric model is briefly described. The piezoelectric curve beam element is then integrated into a collocated host shell element by using nodal displacement constraint equations. The linear least square method (LLSM) is employed to get the optimum voltage distributions in the control system so that the desired structure shape can be well matched. Furthermore, to find the optimal placement of the piezoelectric curve beam actuators, a genetic algorithm (GA) is introduced in the computation model as well as the consideration of the different objective functions. Numerical results are given to demonstrate the validity of the theoretical model and numerical algorithm developed.

• Smart Structures and Systems
• /
• v.10 no.6
• /
• pp.573-591
• /
• 2012

In this study, a procedure to design an optimal LCVA that maximizes the equivalent damping ratio added to the primary structure subjected to along-wind excitation is proposed. That design procedure does not only consider the natural frequency and damping ratio of the LCVA, but also the proportion of the U-shaped liquid, which is closely related to the participation ratio of the liquid mass in inertial force. In addition, constraints to ensure the U-shape of the liquid are considered in the design process, so that suboptimal solutions that violate the optimal tuning law partly are adopted as a candidate of the optimal LCVA. The proposed design procedure of the LCVA is applied to the control of the 76-story benchmark building, and the optimal proportions of the liquid shape under various design conditions are compared.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.8 no.3
• /
• pp.52-58
• /
• 1999

In this study, the growth-strain method was used for shape optimization. The adequate value of growth ratio in the method was used the value obtained by volume control. And the linear PID control theory was applied to control internal stresses by stresses required by a designer. The effect of the values of $K_{P}$, $K_{I}$, and $K_{D}$ was investigated and the adequate values of $K_{P}$, $K_{I}$, and $K_{D}$ were determined empirically. Finally, a shape optimal design system was built up by the improved the growth-strain method with a commercial software I-DEAS. The effectiveness and practicality of the developed shape optimal design system was verified by some examples.les.les.les.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.9
• /
• pp.1337-1343
• /
• 2004

Shape optimization was performed to obtain a precise shape of cutouts including the internal shape of cutouts in a laminated composite plate by three dimensional modeling using solid element. Volume control of the growth-strain method was implemented and the distributed parameter chosen as Tsai-Hill fracture index for shape optimization. It makes Tsai-Hill failure index at each element uniform in laminated composites under the predetermined volume a designer requires. Shapes optimized by Tsai-Hill failure index were compared with those of the initial shapes for the various load conditions and cutouts. The following conclusions were obtained in this study; (1) It was found that growth-strain method was applied efficiently to shape optimization of three dimensional cutouts in a laminate composite, (2) The optimal shapes of the various load conditions and cutouts were obtained, (3) The maximum Tsai-Hill failure indices of the optimal shapes were remarkably reduced comparing with those of the initial shapes.

• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.1-23
• /
• 2001

This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. by introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. The existence of optima solutions for the penalized problem will be shown. Next, by employing Lagrange multipliers method and the material derivatives, we derive the shape gradient for the minimization problem of the shape functional which represents the viscous drag.