• Computational Structural Engineering
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• v.10 no.4
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• pp.315-325
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• 1997

This paper describes the application of discretized continuum-type optimality criteria (DCOC) and the development of optimum design program for the multispan partially prestressed concrete beams. The cost of construction as objective function which includes the costs of concrete, prestressing steel, non-prestressing steel and formwork is minimized. The design constraints include limits on the maximum deflection, flexural and shear strengths, in addition to ductility requirements, and upper and lower bounds on design variables as stipulated by the design Code. Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables-effective depth, eccentricity of prestressing steel and non-prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. The self-weight of the structure is included in the equilibrium equation of the real system, as is the secondary effect resulting from the prestressing force. An iterative procedure and computer program for updating the design variables are developed. Two numerical examples of multispan PPC beams with rectangular cross-section are solved to show the applicability and efficiency of the DCOC-based technique.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.379-388
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• 2000

This paper describes the application of discretized continuum-type optimality criteria (DCOC) for design of the reinforced concrete T-beams. The cost of construction as objective function which includes the costs of concrete, reinforced steel and formwork is minimized. The design constraints include limits on the maximum deflection in a given span on bending and shear strengths and optimality criteria is given based on the well blown Kuhn-Tucker necessary conditions, followed by an iterative procedure for designs when the design variables are the depth and the steel ratio. The versatility of the DCOC technique has been demonstrated by considering numerical examples which have one and five span RC T-beams.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.485-490
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• 2000

This paper describes the application of discretized continuum-type optimality criteria (DCOC) for minimum-cost design of the reinforced concrete frame structures consisting of beams and columns. The cost of construction as objective function which includes the costs of concrete, reinforced steel and formwork is minimized. The design constraints include limits on the maximum deflection at a prescribed node, bending and shear strengths in beams, uniaxial bending strength of columns according to design codes(CEB/FIP, 1990). In the first stage, only beams with uniform cross-sectional parameters per span are considered. But the steel ratio is allowed to vary freely. The cross-sectional parameters and steel ratio in each column are assumed to be uniform for practical reasons. Optimality criteria is given based on the well known Kuhn-Tucker necessary conditions, followed by an iterative procedure for designs when the design variables are the depth and the steel ratio. The versatility of the DCOC technique has been demonstrated by considering numerical examples which have one-bay four-storey frame.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.176-183
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• 1999

This paper describes the application of discretized continuum-type optimality criteria (DCOC) for the reinforced concrete continuous beams. The cost of construction as objective function which includes the costs of concrete, reinforced steel, formwork is minimized. The design constraints include limits on the maximum deflection in a given span, on bending and shear strengths, optimality criteria is given based on the well known Kuhn-Tucker necessary conditions, followed by an iterative procedure for designs when the design variables are the depth and the steel ratio. The self-weight of the beam is included in the equilibrium equation of the real system. Two numerical examples of reinforced concrete continuous beams with rectangular cross-section are solved to show the applicability and efficiency for the DCOC-based technique

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.171-178
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• 1997

This paper describes the application of discretized continuum-type optimality criteria (DCOC) for the multispan partially prestressed concrete beams. The cost of construction as objective function which includes the costs of concrete, prestressing steel, non-prestressing steel and formwork is minimized. The design constraints include limits on the maximum deflection, flexural and shear strengths, in addition to ductility requirements, and upper and lower bounds on design variables as stipulated by the design code. Based on Kuhn-Tucker necessary conditions, the optimality criteria are explicitly derived in terms of the design variables-effective depth, eccentricity of prestressing steel and non-prestressing steel ratio. The prestressing profile is prescribed by parabolic functions. The self-weight of the structure is included in the equilibrium equation of the real system, as is the secondary effect resulting from the prestressing force. Two numerical examples of multispan PPC beams with rectangular cross-section are solved to show the applicability and efficiency fo the DCOC-based technique.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1561-1570
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• 1997

This study explores the treatment of the max-value cost function over a parameter interval in parametric optimization. To avoid the computational burden of the transformation treatment using an artificial variable, a direct treatment of the original max-value cost function is proposed. It is theoretically shown that the transformation treatment results in demanding an additional equality constraint of dual variables as a part of the Kuhn-Tucker necessary conditions. Also, it is demonstrated that the usability and feasibility conditions on the search direction of the transformation treatment retard convergence rate. To investigate numerical performances of both treatments, typical optimization algorithms in ADS are employed to solve a min-max steady-state response optimization. All the algorithm tested reveal that the suggested direct treatment is more efficient and stable than the transformation treatment. Also, the better performing of the direct treatment over the transformation treatment is clearly shown by constrasting the convergence paths in the design space of the sample problem. Six min-max transient response optimization problems are also solved by using both treatments, and the comparisons of the results confirm that the performances of the direct treatment is better than those of the tranformation treatment.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1256-1261
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• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.48-54
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• 2004

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. In practical applications, it is customary to transform the dynamic loads into static loads by dynamic factors, design codes, and etc. But the optimization results with the unreasonably transformed loads cannot give us good solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple loading conditions which are not costly to include in modem structural optimization. In this research, the proposed algorithm is applied to the optimization of flexible multibody dynamic systems. The equivalent static load is derived from the equations of motion of a flexible multibody dynamic system. A few examples that have been solved before are solved to be compared with the results from the proposed algorithm.