• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.1
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• pp.39-45
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• 1989

Many mechanical systems including ships and/or offshore structures have poor dynamic response characteristics such as undesirable natural frequencies and undesirable mode shapes. It is mandatory to redesign the structure. In this paper a procedure for the dynamic redesign of an undamped structural system is presented. The method which uses a penalty function with a penalty term containing error in equilibrium for a given vibration mode may have a shortcoming. This method includes unconstrained eigenvector degrees of freedom as unknowns. In the work developed here, only constrained mode shape changes are used in the solution procedure, resulting in a reduction of the unnecessary calculations. Among the set of equations which characterizes the redesign of the structural systems, the under constrained problem is discussed here and formulated as an optimization problem, with an optimal criterion such as minimum change or minimum structural weight of the system. Four simple numerical applications illustrate the efficiency of the method. The method can be applied to the vibration problems of ships and/or offshore structures with an implementation of the commercial FE codes.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.603-625
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• 2019

Main cable configurations under final dead load and in the unloaded state and critical construction parameters (e.g. unstrained cable length, unstrained hanger lengths, and pre-offsets for tower saddles and splay saddles) are the core considerations in the design and construction control of a suspension bridge. For the purpose of accurate calculations, it is necessary to take into account the effects of cable strands over the anchor spans, arc-shaped saddle top, and tower top pre-uplift. In this paper, a method for calculating the cable configuration under final dead load over a main span, two side spans, and two anchor spans, coordinates of tangent points, and unstrained cable length are firstly developed using conditions for mechanical equilibrium and geometric relationships. Hanger tensile forces and unstrained hanger lengths are calculated by iteratively solving the equations governing hanger tensile forces and the cable configuration, which gives careful consideration to the effect of hanger weight. Next, equations for calculating the cable configuration in the unloaded state and pre-offsets of saddles are derived from the cable configuration under final dead load and the conditions for unstrained cable length to be conserved. The equations for the main span, two side spans and two anchor spans are then solved simultaneously. In the proposed methods, coupled nonlinear equations are solved by turning them into an unconstrained optimization problem, making the procedure simplified. The feasibility and validity of the proposed methods are demonstrated through a numerical example.

• Journal of Korea Water Resources Association
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• v.45 no.12
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• pp.1213-1226
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• 2012

Evolutionary algorithms, which are frequently used in an automatic calibration of watershed runoff simulation models, are unconstrained optimization algorithms. An additional method is required to impose constraints on those algorithms. The purpose of the study is to modify the SCE-UA (shuffled complex evolution-University of Arizona) to impose constraints by a penalty function and to improve performance of the automatic calibration module of the SWMM (storm water management model) linked with the SCE-UA. As indicators related to peak flow are important in watershed runoff event simulation, error of peak flow and error of peak flow occurrence time are selected to set up constraints. The automatic calibration module including the constraints was applied to the Milyang Dam Basin and the Guro 1 Pumping Station Basin. The automatic calibration results were compared with the results calibrated by an automatic calibration without the constraints. Error of peak flow and error of peak flow occurrence time were greatly improved and the original objective function value is not highly violated in the automatic calibration including the constraints. The automatic calibration model with constraints was also verified, and the results was excellent. In conclusion, the performance of the automatic calibration module for watershed runoff event simulation was improved by application of the penalty function to impose constraints.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.73-84
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• 1993

In this research, configuration design optimization of plane truss structure has been tested by using decomposition technique. In the first level, the problem of transferring the nonlinear programming problem to linear programming problem has been effectively solved and the number of the structural analysis necessary for doing the sensitivity analysis can be decreased by developing stress constraint into member stress approximation according to the design space approach which has been proved to be efficient to the sensitivity analysis. And the weight function has been adopted as cost function in order to minimize structures. For the design constraint, allowable stress, buckling stress, displacement constraint under multi-condition and upper and lower constraints of the design variable are considered. In the second level, the nodal point coordinates of the truss structure are used as coordinating variable and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, unconstrained optimal design problems are easy to solve. The decomposition method which optimize the section areas in the first level and optimize configuration variables in the second level was applied to the plane truss structures. The numerical comparisons with results which are obtained from numerical test for several truss structures with various shapes and any design criteria show that convergence rate is very fast regardless of constraint types and configuration of truss structures. And the optimal configuration of the truss structures obtained in this study is almost the identical one from other results. The total weight couldbe decreased by 5.4% - 15.4% when optimal configuration was accomplished, though there is some difference.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.3
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• pp.39-55
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• 1992

In this research, a Three Level Decomposition technique has been developed for configuration design optimization of truss structures. In the first level, as design variables, behavior variables are used and the strain energy has been treated as the cost function to be maximized so that the truss structure can absorb maximum energy. For design constraint of the optimal design problem, allowable stress, buckling stress, and displacement under multi-loading conditions are considered. In the second level, design problem is formulated using the cross-sectional area as the design variable and the weight of the truss structure as the cost function. As for the design constraint, the equilibrium equation with the optimal displacement obtained in the first level is used. In the third level, the nodal point coordinates of the truss structure are used as coordinating variable and the weight has been taken as the cost function. An advantage of the Three Level Decomposition technique is that the first and second level design problems are simple because they are linear programming problems. Moreover, the method is efficient because it is not necessary to carry out time consuming structural analysis and techniques for sensitivity analysis during the design optimization process. By treating the nodal point coordinates as design variables, the third level becomes unconstrained optimal design problems which is easier to solve. Moreover, by using different convergence criteria at each level of design problem, improved convergence can be obtained. The proposed technique has been tested using four different truss structures to yield almost identical optimum designs in the literature with efficient convergence rate regardless of constraint types and configuration of truss structures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.95-109
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• 1993

In this study, the optimal configuration of arch structure has been tested by a decomposition technique. The object of this study is to provide the method of optimizing the shapes of both two hinged and fixed arches. The problem of optimal configuration of arch structures includes the interaction formulas, the working stress, and the buckling stress constraints on the assumption that arch ribs can be approximated by a finite number of straight members. On the first level, buckling loads are calculated from the relation of the stiffness matrix and the geometric stiffness matrix by using Rayleigh-Ritz method, and the number of the structural analyses can be decreased by approximating member forces through sensitivity analysis using the design space approach. The objective function is formulated as the total weight of the structures, and the constraints are derived by including the working stress, the buckling stress, and the side limit. On the second level, the nodal point coordinates of the arch structures are used as design variables and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, the problem of optimization can be reduced to unconstrained optimal design problem which is easy to solve. Numerical comparisons with results which are obtained from numerical tests for several arch structures with various shapes and constraints show that convergence rate is very fast regardless of constraint types and configuration of arch structures. And the optimal configuration or the arch structures obtained in this study is almost the identical one from other results. The total weight could be decreased by 17.7%-91.7% when an optimal configuration is accomplished.