• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.833-845
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• 2015

Natural frequencies of the structural systems should be far away from the excitation frequency in order to avoid or reduce the destructive effects of dynamic loads on structures. To accomplish this goal, a structural optimization on size and shape has been performed considering frequency constraints. Such an optimization problem has highly nonlinear property. Thus, the quality of the solution is not independent of the optimization technique to be applied. This study presents the performance evaluation of the recently proposed meta-heuristic algorithm called Teaching Learning Based Optimization (TLBO) as an optimization engine in the weight optimization of the truss structures under frequency constraints. Some examples regarding the optimization of trusses on shape and size with frequency constraints are solved. Also, the results obtained are tabulated for comparison. The results demonstrated that the performance of the TLBO is satisfactory. Additionally, TLBO is better than other methods in some cases.

• Steel and Composite Structures
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• v.12 no.6
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• pp.541-548
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• 2012

This paper deals with the applicability of extended layerwise optimization method (ELOM) for frequency optimization of laminated composite plates. The design objective is the maximization of the fundamental frequency of the laminated plates. The fibre orientations in the layers are considered as design variables. The first order shear deformation theory (FSDT) is used for the finite element solution of the laminates. Finally, the numerical analysis is carried out to show the applicability of extended layerwise optimization algorithm of laminated plates for different parameters such as plate aspect ratios and boundary conditions.

• Architectural research
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• v.12 no.1
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• pp.39-47
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• 2010

This paper describes a topology optimization technique which can maximize the fundamental frequency of the structures. The fundamental frequency maximization is achieved by means of the minimization of modal strain energy as an inverse problem so that the strain energy based resizing algorithm is directly used in this study. The strain energy to be minimized is therefore employed as the objective function and the initial volume of structures is used as the constraint function. Multi-frequency problem is considered by the introduction of the weight which is used to combine several target modal strain energy terms into one scalar objective function. Several numerical examples are presented to investigate the performance of the proposed topology optimization technique. From numerical tests, it is found to be that the proposed optimization technique is extremely effective to maximize the fundamental frequency of structure and can successfully consider the multi-frequency problems in the topology optimization process.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.1
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• pp.63-69
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• 2013

In order to find the optimum design of structures that have characteristic natural frequency range, a numerical optimization method to solving eigenvalue problems is a widely used approach. However in the most cases, it is difficult to decide the accurate thickness and shape of structures that have allowable natural frequency in design constraints. Parallel analysis algorithm involving the feasible direction optimization method and Rayleigh-Ritz eigenvalue solving method is developed. The method is implemented by using finite element method. It calculates the optimal thickness and the thickness ratio of individual elements of the 2-D plane element through a parallel algorithm method which satisfy the design constraint of natural frequency. As a result this method of optimization for natural frequency by using finite element method can determine the optimal size or its ratio of geometrically complicated shape and large scale structure.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.248-251
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• 2006

This paper provides the basic theory and numerical results of shell design optimization considering the appearance of close natural frequencies in optimization process. In this study the fundamental natural frequency to be maximized is considered as the objective function and the initial volume of structures is used as the constraint function. In addition, the constraints related to natural frequency is also adopted to avoid the natural frequency closeness phenomenon during the optimization iteration. The Coon's patch is used to represent the shape and thickness distribution of shells. A degenerated shell finite element is adopted to calculate the fundamental natural frequency of the shells. The SQP available in the optimizer DoT is used to search optimum solution. From numerical results, the introduction of the frequency constraint into shell design optimization can deeply affect on the final optimum shape of shells although it is likely to be used to avoid the frequency closeness phenomenon.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.10
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• pp.135-142
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• 2019

Ant colony optimization(ACO) technique is utilized in truss size optimization with frequency constraints. Total weight of truss to be minimized is considered as the objective function and multiple natural frequencies are adopted as constraints. The modified traveling salesman problem(TSP) is adopted and total length of the TSP tour is interpreted as the weight of the structure. The present ACO-based design optimization procedure uses discrete design variables and the penalty function is introduced to enforce design constraints during optimization process. Three numerical examples are carried out to verify the capability of ACO in truss optimization with frequency constraints. From numerical results, the present ACO is a very effective way of finding optimum design of truss structures in free vibration. Finally, we provide the present numerical results as future reference solutions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.1
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• pp.84-91
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• 2013

Ultrasonic flip-chip bonding needs a precise bonding tool which delivers ultrasonic energy into chip bumps effectively to use the selected resonance mode and frequency of the horn structure. The bonding tool is excited at the resonance frequency and the input and output ports should locate at the anti-nodal points of the resonance mode. In this study, we propose new design method with topology optimization for ultrasonic bonding tools. The SIMP(solid isotropic material with penalization) method is used to formulate topology optimization and OC(optimal criteria) algorithm is adopted for the update scheme. MAC(modal assurance criterion) tracking is used for the target frequency and mode. We fabricate two prototypes of ultrasonic tools which are based on 3D optimization models after reviewing 2D and 3D topology optimization results. The prototypes are satisfied with the ultrasonic frequency and vibration amplitude as the ultrasonic bonding tools.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.181-190
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• 2019

Topology optimization of structures seeking the best distribution of mass in a design space to improve the structural performance and reduce the weight of a structure is one of the most comprehensive issues in the field of structural optimization. In addition to structures stiffness as the most common objective function, frequency optimization is of great importance in variety of applications too. In this paper, an efficient multi-objective Bi-directional Evolutionary Structural Optimization (BESO) method is developed for topology optimization of frequency and stiffness in continuum structures simultaneously. A software package including a Matlab code and Abaqus FE solver has been created for the numerical implementation of multi-objective BESO utilizing the weighted function method. At the same time, by considering the weaknesses of the optimized structure in single-objective optimizations for stiffness or frequency problems, slight modifications have been done on the numerical algorithm of developed multi-objective BESO in order to overcome challenges due to artificial localized modes, checker boarding and geometrical symmetry constraint during the progressive iterations of optimization. Numerical results show that the proposed Multiobjective BESO method is efficient and optimal solutions can be obtained for continuum structures based on an existent finite element model of the structures.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.10a
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• pp.410-415
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• 2000

In this paper feasible direction method which is one of the optimization method is adopted to natural frequency optimization. In order to find the optimum design of structures that have characteristic natural frequency range, a numerical optimization method to solving eigenvalue problems is a widely used approach. However most cases, it is difficult to decide the accurate thickness and shape of structures that have allowable natural frequency in design constraints. Parallel analysis algorithm involving the feasible direction optimization method and Rayleight-Ritz eigenvalue solving method is developed. The method is implemented by using finite element method. It calculated the optimal thickness and the thickness ratio of each element of 2-D plane element through the parallel algorithm method which satisfy the design constraint of natural frequency.

• Journal of the Korean Society for Nondestructive Testing
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• v.29 no.6
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• pp.579-585
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• 2009

The multifrequency eddy current testing(ECT) have been proposed various frequency mixing algorithms. In this study, we compare these approaches to frequency mixing of ECT signals from steam generator tubes; time-domain optimization, discrete cosine transform-domain optimization. Specifically, in this study, two different frequency mixing algorithms, a time-domain optimization method and a discrete cosine transform(DCT) optimization method, are investigated using the experimental signals captured from the ASME standard tube. The DCT domain optimization method is computationally fast but produces larger amount of residue.