MULTI-OBJECTIVE OPTIMIZATION OF THE INNER REINFORCEMENT FOR A VEHICLE'S HOOD CONSIDERING STATIC STIFFNESS AND NATURAL FREQUENCY

Choi, S.H.,Kim, S.R.,Park, J.Y.,Han, S.Y. The Korean Society of Automotive Engineers 2007 International journal of automotive technology Vol.8 No.3

A multi-objective optimization technique was implemented to obtain optimal topologies of the inner reinforcement for a vehicle's hood simultaneously considering the static stiffness of bending and torsion and natural frequency. In addition, a smoothing scheme was used to suppress the checkerboard patterns in the ESO method. Two models with different curvature were chosen in order to investigate the effect of curvature on the static stiffness and natural frequency of the inner reinforcement. A scale factor was employed to properly reflect the effect of each objective function. From several combinations of weighting factors, a Pareto-optimal topology solution was obtained. As the weighting factor for the elastic strain efficiency went from 1 to 0, the optimal topologies transmitted from the optimal topology of a static stiffness problem to that of a natural frequency problem. It was also found that the higher curvature model had a larger static stiffness and natural frequency than the lower curvature model. From the results, it is concluded that the ESO method with a smoothing scheme was effectively applied to topology optimization of the inner reinforcement of a vehicle's hood.

Discrete thickness optimization of an automobile body by using the continuous-variable-based method

Gang-Won Jang,Young-Min Choi,Gyoo-Jae Choi 대한기계학회 2008 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.22 No.1

Design optimization of an automobile body for dynamic stiffness improvement is presented. The thicknesses of plates consisting of a monocoque body of an automobile are employed as design variables for optimization whose objective is to increase the first torsional and bending natural frequencies. By allotting one design variable to each plate of the body, compared to previous works based on element-wise design variables, the design space of optimization can be reduced to a large extent. Because the present optimization is based on continuous-variable-based algorithms, considering manufacturability of the optimized result, the converged values of plate thicknesses should be approximated to commercially available discrete values. A new straightforward thickness discretization scheme considering design sensitivities and employing a subsequent reduced optimization problem is proposed. The validity of the proposed thickness discretization scheme is verified through numerical experiments.

Multi-objective Optimization of Machine Tool Spindle-Bearing System

Van-Canh Tong,Jooho Hwang,Jongyoup Shim,Jeong Seok Oh,Seong-Wook Hong 한국정밀공학회 2020 International Journal of Precision Engineering and Vol.21 No.10

In this study, a multi-objective optimization is performed for the design of a spindle-bearing system based on particle swarm optimization (PSO). Multiple objectives, such as natural frequencies, static stiff ness, and total friction torque are considered in this design optimization. Bearing preload and bearing locations are selected as the design variables. Pareto-optimal solutions are used to support the selection of optimal values of the design parameters. A finite element model is established for the analysis and design of the spindle system with four angular contact ball bearings. Two optimization processes are performed with the PSO technique. The first process involves the first two natural frequencies and friction torque of the spindle, whereas the second process focuses on the spindle’s static stiff ness and friction torque. The simulation results show noticeable improvement in the objectives compared with those of the primitive spindle. The experiments conducted on an actual spindle system fabricated with the optimal design demonstrate the benefits of the optimal design. The proposed design method is expected to be very useful in the design optimization of machine tool spindle systems subjected to various customer-oriented objectives.

Topology Optimization Scheme for Dynamic Stiffness Problems Using Harmony Search Method

이승민,한석영 한국정밀공학회 2016 International Journal of Precision Engineering and Vol.17 No.9

This paper suggests a new topology optimization scheme for natural frequency problems based on the harmony search (HS) method. The HS method is expected to be very effective since its topology optimization procedure is similar to the procedure for tuning the instruments found in an orchestra. To apply the HS method to dynamic topology optimization, an objective function is defined as a natural frequency, and the design domain is defined as harmony memory (HM) in the HS method. The harmony rate update rule is introduced to obtain a robust topology. Through a parametric study of the harmony memory considering rate (HMCR), pitch adjusting rate (PAR), and bandwidth (BW), the proper ranges of the search variables are determined and applied to numerical examples. Some examples are provided to examine the effectiveness of the HS method compared to the artificial bee colony algorithm (ABCA) in dynamic topology optimization. Properly selected parameters for the suggested algorithm with the harmony rate update rule provide a robust topology, a fast convergence rate and a stable optimization process. It can be effectively expanded to apply to shape and topological shape optimization algorithms.

유용방향법 최적화 알고리즘을 사용한 고유진동수에 대한 구조 최적설계 FEA 모듈 개발

조희근(Hee Keun Cho) 한국생산제조학회 2013 한국생산제조학회지 Vol.22 No.1

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.

Vibration analysis and optimization of functionally graded carbon nanotube reinforced doubly-curved shallow shells

Zakia Hammou,Zakia Guezzen,Fatima Z. Zradni,Zouaoui Sereir,Abdelouahed Tounsi,Yamna Hammou 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.2

In the present paper an analytical model was developed to study the non‐linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non‐linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

Damage assessment of beams from changes in natural frequencies using ant colony optimization

Aditi Majumdar,Ambar De,Damodar Maity,Dipak Kumar Maiti 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.3

A numerical method is presented here to detect and assess structural damages from changes in natural frequencies using Ant Colony Optimization (ACO) algorithm. It is possible to formulate the inverse problem in terms of optimization and then to utilize a solution technique employing ACO to assess the damage/damages of structures using natural frequencies. The laboratory tested data has been used to verify the proposed algorithm. The study indicates the potentiality of the developed code to solve a wide range of inverse identification problems in a systematic manner. The developed code is used to assess damages of beam like structures using a first few natural frequencies. The outcomes of the simulated results show that the developed method can detect and estimate the amount of damages with satisfactory precision.

Damage assessment of beams from changes in natural frequencies using ant colony optimization

Majumdar, Aditi,De, Ambar,Maity, Damodar,Maiti, Dipak Kumar Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.3

A numerical method is presented here to detect and assess structural damages from changes in natural frequencies using Ant Colony Optimization (ACO) algorithm. It is possible to formulate the inverse problem in terms of optimization and then to utilize a solution technique employing ACO to assess the damage/damages of structures using natural frequencies. The laboratory tested data has been used to verify the proposed algorithm. The study indicates the potentiality of the developed code to solve a wide range of inverse identification problems in a systematic manner. The developed code is used to assess damages of beam like structures using a first few natural frequencies. The outcomes of the simulated results show that the developed method can detect and estimate the amount of damages with satisfactory precision.

링 보강 원통셸의 고유진동수 최적화에 관한 연구

장진건(Jin-Geon Chang),이영신(Young-Shin Lee),양태호(Tae-Ho Yang) 대한기계학회 2012 大韓機械學會論文集A Vol.36 No.3

보강 원통셸의 기본 고유 진동수를 최적화하기 위해서, 보강재의 개수를 1 개에서 5 개까지 보강된 원통셸에 대한 시뮬레이션을 수행하였다. 고유 진동수에 대한 최적화를 시뮬레이션하기 위해서 ANSYS 11.0 을 사용하였다. 최적화 방법으로 Subproblem Approximation Method 를 이용하였다. 최적화의 설계 함수로는 T-형 링 보강재의 기하형상이며, 제한 함수로는 보강에 따른 추가 부피가 10 % 이내로 제한하였다. 목적함수는 기본 고유진동수를 최대화하는 것이다. 최적 설계에 대한 성능 지표는 비보강 원통셸과 보강원통셸의 고유진동수와 부피의 비로서 정의하였다. 최적 성능 지수는 3 개의 보강재를 사용한 원통셸에서 나타났다. For the optimization of the fundamental natural frequency of stiffened cylindrical shells, simulations were performed for cylindrical shells that were stiffened with between one and five ring stiffeners. ANSYS 11.0 was used to simulate the optimization for the natural frequency. The Subproblem Approximation Method was applied as the optimization method. The design function of the optimization was the geometry of the T-shaped ring stiffener, and the constraint function was the maximum additional volume, constrained to a 10% increase. The objective function of the optimization was chosen to maximize the fundamental natural frequency. The performance index for optimal design was defined as the ratio of the natural frequency to the volume of the unstiffened and stiffened shells. The optimal performance index was obtained for the shell stiffened with three rings.

고유진동수 제약조건을 고려한 프레임 구조물의 최적화

김봉익(Bong-Ik Kim),이성대(Seong-Dae Lee) 한국해양공학회 2010 韓國海洋工學會誌 Vol.24 No.6

We present the minimum weight optimum design of cross sectional for frame structures subject to natural frequency. The optimum design in this paper employ discrete and continuous design variables and Genetic Algorithms. In this paper, Genetic Algorithms is used in optimization process, and be used the method of Elitism and penalty parameters in order to improved fitness in the reproduction process. For 1-Bay 2-Story frame structure, in examples, continuous and discrete design variables are used, and W-section (No.1~No.64), from AISC, discrete data are used in discrete optimization. In this case, Exhaustive search are used for finding global optimum Continuous variables are used for 1-Bay 7-Story frame structure. Two typical frame structure optimization examples are employed to demonstrate the availability of Genetic Algorithms for solving minimum weight optimum of frame structures with fundamental and multi frequency.