• Title/Summary/Keyword: Dynamic structural optimization

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Topological optimized design considering dynamic problem with non-stochastic structural uncertainty

  • Lee, Dong-Kyu;Starossek, Uwe;Shin, Soo-Mi
    • Structural Engineering and Mechanics
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    • v.36 no.1
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    • pp.79-94
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    • 2010
  • This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

Dynamic sensitivity analysis and optimum design of aerospace structures

  • Gu, Yuanxian;Kang, Zhan;Guan, Zhenqun;Jia, Zhiwen
    • Structural Engineering and Mechanics
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    • v.6 no.1
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    • pp.31-40
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    • 1998
  • The research and applications of numerical methods of design optimization on structural dynamic behaviors are presented in this paper. The emphasis is focused on the dynamic design optimization of aerospace structures, particularly those composed of composite laminate and sandwich plates. The methods of design modeling, sensitivity analysis on structural dynamic responses, and the optimization solution approaches are presented. The numerical examples of sensitivity analysis and dynamic structural design optimization are given to demonstrate the effectiveness of the numerical methods.

Nonlinear Dynamic Response Structural Optimization of an Automobile Frontal Structure Using Equivalent Static Loads (등가정하중법을 이용한 차량 전면 구조물의 비선형 동적 반응 구조최적설계)

  • Yoon, Shic;Jeong, Seong-Beom;Park, Gyung-Jin
    • Proceedings of the KSME Conference
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    • 2008.11a
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    • pp.1156-1161
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    • 2008
  • Nonlinear dynamic analysis is generally used in automobile crash analysis and structural optimization considering crashworthiness uses the results of nonlinear dynamic analysis. Automobile crash optimization has high nonlinearity and difficulty in calculating sensitivity. Recently the equivalent static load (ESL) method has been proposed in order to overcome these difficulties. The ESL is the static load set generating the same displacement field as the nonlinear dynamic displacement field at each time step in dynamic analysis. From various researches regarding the ESL method, it has been proved that the ESL method is fairly useful. The ESL method can mathematically optimize a crash optimization problem through nonlinear analysis and well developed static optimization. The ESL is applied to nonlinear dynamic structural optimization of the automobile frontal impact problem. An automobile bumper is optimized. The mass of the structure is minimized while some constraints are satisfied.

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Mathematical Proof for Structural Optimization with Equivalent Static Loads Transformed from Dynamic Loads (동하중에서 변환된 등가정하중에 의한 최적화 방법의 수학적 고찰)

  • Park, Gyung-Jin;Kang, Byung-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.2
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    • pp.268-275
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    • 2003
  • 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. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate 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 leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

Structural dynamic optimization with probability constraints of frequency and mode

  • Chen, Jian-Jun;Che, Jian-Wen;Sun, Huai-An;Ma, Hong-Bo;Cui, Ming-Tao
    • Structural Engineering and Mechanics
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    • v.13 no.5
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    • pp.479-490
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    • 2002
  • The structural dynamic optimization problem based on probability is studied. Considering the randomness of structural physical parameters and the given constraint values, we develop a dynamic optimization mathematical model of engineering structures with the probability constraints of frequency, forbidden frequency domain and the vibration mode. The sensitivity of structural dynamic characteristics based on probability is derived. Two examples illustrate that the optimization model and the method applied are rational and efficient.

Structural Shape Optimization under Static Loads Transformed from Dynamic Loads (동하중으로부터 변환된 등가정하중을 통한 구조물의 형상최적설계)

  • Park, Ki-Jong;Lee, Jong-Nam;Park, Gyung-Jin
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.1262-1269
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    • 2003
  • In structural optimization, static loads are generally utilized although real external forces are dynamic. Dynamic loads have been considered in only small-scale problems. Recently, an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed. The transformation is conducted to match the displacement fields from dynamic and static analyses. The algorithm can be applied to large-scale problems. However, the application has been limited to size optimization. The present study applies the algorithm to shape optimization. Because the number of degrees of freedom of finite element models is usually very large in shape optimization, it is difficult to conduct dynamic response optimization with the conventional methods that directly threat dynamic response in the time domain. The optimization process is carried out via interfacing an optimization system and an analysis system for structural dynamics. Various examples are solved to verify the algorithm. The results are compared to the results from static loads. It is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid even for very large-scale problems such as shape optimization.

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Structural Shape Optimization under Static Loads Transformed from Dynamic Loads (동하중으로부터 변환된 등가정하중을 통한 구조물의 형상최적설계)

  • Park, Ki-Jong;Lee, Jong-Nam;Park, Gyung-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.8
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    • pp.1363-1370
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    • 2003
  • In structural optimization, static loads are generally utilized although real external forces are dynamic. Dynamic loads have been considered in only small-scale problems. Recently, an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed. The transformation is conducted to match the displacement fields from dynamic and static analyses. The algorithm can be applied to large-scale problems. However, the application has been limited to size optimization. The present study applies the algorithm to shape optimization. Because the number of degrees of freedom of finite element models is usually very large in shape optimization, it is difficult to conduct dynamic response optimization with the conventional methods that directly threat dynamic response in the time domain. The optimization process is carried out via interfacing an optimization system and an analysis system for structural dynamics. Various examples are solved to verify the algorithm. The results are compared to the results from static loads. It is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid even for very large-scale problems such as shape optimization.

Structural Dynamic Optimization Using a Genetic Algorithm(GA) (유전자 알고리즘(GA)을 이용한 구조물의 동적해석 및 최적화)

  • 이영우;성활경
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.5
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    • pp.93-99
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    • 2000
  • In many dynamic structural optimization problems, the goal is to reduce the total weight of the structure without causing the resonance. Up to now, gradient informations(i.e., design sensitivity) have been used to achieve the goal. For some class of dynamic problems, especially coalescent eigenvalue Problems with multiobjective optimization, the design sensitivity analysis is too much complicated mathematically and numerically. Therefore, this article proposes a new technique fur structural dynamic modification using a mode modification method with Genetic Algorithm(GA). In GA formulation, fitness is defined based on penalty function approach. Design variables are iteratively improved by using genetic algorithm. Two numerical examples are shown, (ⅰ) a cantilevered plate, and (ⅱ) H-shaped structure. The results demonstrate that the proposed method is highly efficient.

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Optimization of Flexible Multibody Dynamic Systems Using Equivalent Static Load Method (등가정하중을 이용한 유연다물체 동역학계의 구조최적설계)

  • 강병수;박경진
    • 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.

Structural Design Optimization of a Micro Milling Machine for Minimum Weight and Vibrations (마이크로 밀링 머신의 저진동.경량화를 위한 구조 최적설계)

  • Jang, Sung-Hyun;Kwon, Bong-Chul;Choi, Young-Hyu;Park, Jong-Kweon
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.18 no.1
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    • pp.103-109
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    • 2009
  • This paper presents structural design optimization of a micro milling machine for minimum weight and compliance using a genetic algorithm with dynamic penalty function. The optimization procedure consists of two design stages, which are the static and dynamic design optimization stages. The design problem, in this study, is to find out thickness of structural members which minimize the weight, the static compliance and the dynamic compliance of the micro milling machine under several constraints such as dimensional constraints, maximum compliance limit, and safety factor criterion. Optimization results showed a great reduction in the static and dynamic compliances at the spindle nose of the micro milling machine in spite of a little decrease in the machine weight.