Recent advances in Japan in optimum mechanical and structural designs for dynamics

Finite Elements in Analysis and Design 14 (1993) 89-100 89 Elsevier

FINEL 308

Recent advances in Japan in optimum mechanical and structural designs for dynamics

Hiroshi Yamakawa

Department of Mechanical Engineering, Waseda Unicersity, 3-4-10kubo, Shinjuku, Tokyo 169, Japan

Abstract. A number of papers on optimum mechanical and structural designs have lately appeared in Japan. Those papers related to dynamics problems in the last decade (1983-1992) were classified and reviewed. Several sophisticated methods have been required, and have been developed, for the purposes of those optimizations. Some of the methods are introduced here briefly, by means of some examples. This review may provide some help for understanding the recent progress of the work in Japan.

Introduction

Computer analysis has recently been one of the inevitable tools for a number of designs of mechanical and structural systems. Efforts to synthesize structural systems have also been made, and called "structural synthesis". Structural synthesis aims to find the maximum efficiency, the minimum cost and other minimum or maximum objectives in a design, which is then known as an optimum design. The rapid developments in the hardware and software of computer systems have enabled us to obtain optimum designs for mechanical and structural systems with the aid of optimization techniques. Many software programs for sensitivity analysis and optimization have been added to most of the general purpose computer programs for structural analysis, and released to designers. In Japan, many studies on optimum designs have been made in the last decade, and several sophisticated methods have been developed and practical applications carried out. Here we shall restrict our interest to the studies on optimum designs for dynamics problems in mechanical and structural engineering in the last decade (1983-1992) in Japan, and make a brief review of them, because no other adequate review is available,

Classification of optimum designs for dynamics problems

More investigations on optimum designs have been made for statics problems than for dynamics problems in mechanical and structural systems. The difficulty and complexity of optimizations may increase considerably because design variables are not only functions in space variables but also in time variables. So it will be necessary, and convenient, to classify the past studies on optimizations related to dynamics problems. One group of classified results is shown in Table 1. Some aspects of optimizations for noise control were involved there. As shown in the Table, the problems are classified into two main categories, being problems in natural frequency analysis and in dynamic response analysis. Among the latter problems, some control problems were involved. In the Table, such notations as NF, DR, L, and NL are added for the later classifications.

0168-874X/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

90 11. Yamakawa / Optimum mechanical and structural designs

Table 1 Classification of optimum designs for dynamics problems

Type System Optimum designs

Natural frequency analysis (NF) Linear (L) Natural frequency control Vibrational modes control Damping controls etc.

Control of dynamic response Control of shocks Control of noise Simultaneous optimization of

structural/control systems

Dynamic response analysis (DR) Nonlinear (NL)

In the following, we review the relevant papers in mechanical and structural engineering. It is a little difficult to distinguish thoroughly the control problems from the optimum design problems for the dynamic state, but papers based only on the control theories will be excluded from this review.

Optimum designs for dynamics problems in mechanical engineering

A comparatively large number of papers have appeared in this field. Relevant papers will be reviewed here, mainly by referencing the Transactions of the Japan Society of Mechanical Engineers, since most of the papers have appeared there. The number of relevant papers amounts to more than 30 in the last decade (1983-1992), and a classification is given in Table 2. We now introduce the abstracts of the papers in each category shown in Table 2. The numbers in brackets following the sentences denote the references in the list in this Article.

Methodology

General method New methods for vibration isolation were developed by utilizing the nodal points and

anti-resonance points in vibrations [1,13]. The former method was to create a nodal point, isolated from vibrations, by using bending moments calculated in auxiliary elements. In the later study, the target peaks of resonance of the structure are removed by making the vibration mode coincide with the exciting point, which is based on the sensitivities of the resonance and anti-resonance points. An example for a plate is shown below, where the peak of the 4th resonance vanishes. Table 3 shows the modifications of the thickness of the plate and Figs. 1 and 2 show the compliance and corresponding modes respectively.

Direct sensitivity identification and optimization methods based on experimental data were studied in [29]. Such characteristic matrices as mass, damping and stiffness and their sensitivities are identified by the proposed method directly, from the experimental data shown schematically in Fig. 3.

Three approximated optimization methods based on them were also presented. Figure 4 shows the progression of identification for sensitivities of the characteristic matrices. Figure 5 and Table 4 show a truss model and its optimized results. The optimum design methods for an air-spring vibration system, and for a plate and its vibration, were studied in [6,22].

H. Yamakawa / Optimum mechanical and structural designs

Table 2 Papers in mechanical engineering

91

Category Ref. Key words Type System

1. Methodology (a) General method

(b) Multi-objective method

(c) Pseudo-inverse matrix method

(d) New computer technology (fuzzy, neural network)

2. Support optimization

3. Rotating machinery

4. Random vibration and vibration to moving load

5. Robust structure

6. Simultaneous optimization

[1] vibration isolation, nodal point NF L [6] air spring, vibration isolation NF L [13] anti-resonance NF L [22] plate NF L [29] experimental sensitivity and optimization NF L

[3] Pareto optimization shaft NF L [5] multi-level optimization NF L [31] speed control hump DR L

[10] indeterminate shaft synthesis NF L [12] pseudo-inverse, substructure NF L [19] pseudo-inverse NF L

[30] fuzzy inference DR L [32] neural network, pipe support DR L

[14] optimal support NF L [15] optimal support NF L [16] optimal support NF L [32] pipe support, neural network DR L

[2] overhanging rotation machine NF L [4] self-optimizing support NF L [7] journal bearing NF L [8] operating curve DR L, NL [21] operating curve DR L, NL

[9] random load DR L [11] moving load DR L [26] moving load, energy criteria DR L [23] moving load DR L

[24] pipe conveying fluid DR L [28] robust structure NF, DR L, NL

[17] electro-mechanical system DR NL [26] flexible structure DR L [27] multi-goal programming DR L [34] fuzzy goal DR L

Multi-objective methods Multi-objective and multi-level methods were studied for manufacturing machines with the

related natural frequencies [3,5]. A multi-objective method for speed control humps for vehicles was studied [31].

Pseudo-inverse matrix me thod To a t ta in the desired values of objective funct ion, the pseudo- inverse matrix me thod or the

inverse me thod for a genera l matr ix can be used. This approach is not among the o p t i m u m design methods, bu t among a k ind of goal p rog ramming or satisfying methods . As a case of requi red na tu ra l f requencies and o ther objectives, this approach was s tudied in [10,12,19]. The use of the pseudo- inverse matr ix me thod and subs t ruc ture synthesis me thod was combined and s tudied in [19].

92 H. Yamakawa / Optimum mechanical and structural designs

Table 3

Thickness of the plate after design revision

Element Thickness (mm) Element Thickness (mm)

1 3.960 13 6.720

2 3.717 14 5.031

3 3.607 15 5.062

4 3.572 16 6.748 5 3.764 17 9.554 6 5.863 18 7.405

7 5.859 19 7.467

8 5.766 20 9.586

9 6.426 21 7.437

10 6.194 22 5.345

11 6.209 23 5.165 12 6.444 24 7.094

_-__ Original transfer function Modified transfer function

Original mode

Fig. 1. Compliance.

tlodified mode

Fig. 2. Changes in mode shape

H. Yamakawa / Optimum mechanical and structural designs 93

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. ~ ! ranster runctton[ Structure and Response trom II ' Experimental Data ] [

Fig. 3. Experimental sensitivity analysis.

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Fig. 5. Truss model.

F i g u r e 6 s h o w s an H - s h a p e d s t r u c t u r e c o m p o s e d o f t h r e e s u b s t r u c t u r e s . T h e 8 th a n d 9 th

n a t u r a l f r e q u e n c i e s w e r e c o n s i d e r e d to c o i n c i d e , a n d to h a v e t h e v a l u e o f 340 Hz . T h e r e s u l t s

o b t a i n e d by t h e m e t h o d a r e s h o w n in Fig. 7, by e x p r e s s i n g t h e t r a n s f e r f u n c t i o n s .

Table 4 Optimization results

Significant figure 16 3 Modification ratio (%) 1 10 Iteration 127 338

Element 1 (m 2) 7.12 × 10- 5 8.08 × 10-5 Element 2 1.00× 10 -4 4.01 × 10 -5 Element 3 1.90 × 10-4 2.76 x 10-4 Element 4 4.08 × 10-5 4.78 × 10-5 Element 5 1.00× 10 -4 4.52× 10 -5 Element 6 7.51 × 10 -5 9.65 x 10 -5 Element 7 1.00× 10 -4 5.57× 10 -5 Element 8 1.43 × 10-4 2.40 × 10-4 Element 9 7.98 × 10 -5 7.35 × 10 -5 Element 10 1.00× 10 -4 4.52x 10 -5


( ( ( / \

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~ ' \ / \ / \ / / ~b'"q / I \VI c om~. 2 \ A ' : A rell ion b

A r e g J o f l a

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Fig . 6. H - s h a p e d s t r u c t u r e .

Application of new computer technologies Lately, the new computer technologies such as AI, fuzzy reasoning, neural networks and

genetic algorithms have been intensively applied to various optimum designs. However, a few papers can be found for dynamics problems in the decade in Japan [30,32,33]. One shows the application of fuzzy reasoning to the optimum dynamic design of a beam. Others include studies on the optimum allocations of pipe supports by using neural networks and a simultaneous optimization, which will be introduced again in the sections on Support optimization and Simultaneous optimization.

Support optimization

A series of studies was made to find the optimum locations of supports for beam and plate structures with maximum fundamental frequencies, by using sensitivities [14-16]. The optimal allocations of pipe supports subjected to seismic loads were studied [17]. The problem of optimum design to minimize the dynamic response was simulated by neural networks, called the Boltzmann Machine, and solved. The pipe system was modelled as a mass-spring system with multiple degrees of freedom, and the support as the spring-damper shown in Fig. 8. Figure 9 shows a matrix expressing the allocation (A-E) of the support elements ($1-$5). The optimum allocation was determined by the neural network. Figure 10 shows the convergence of the energy of the network.

- - - - - t l l ~ r l l e n i l l trlnsfer l ~ c f i ~ sf l r l l l M l l l i l ~ An l lv f i ( I f f r l ~ f e r f ~ t i e n I f er l | I r , l l l l l f e

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Fig. 8. Pipe and support models.

ci

Rotating machinery

Optimum designs of rotating machines, with a view to avoiding the vibration near the critical speeds, were studied by considering the overhanging shaft [2], self-optimizing shaft [4] and journal bearing [7].

Optimum operating curves for rotating shaft systems were studied so as to reduce the transient vibrations when passing through the critical speeds [8,21]. A step-by-step dynamic analysis and sensitivity analysis were utilized. An example of the optimum operating curve and the envelopes of transient vibrations near the critical speed are shown in Fig. 11.

Random vibration and vibration subjected to a moving load

The design methods for optimum shapes of structures subjected to random loads and moving loads have been studied [9,11,20,23]. Methods based on vibration energy were developed [9,20] and step-by-step sensitivity analysis was utilized for the methods [11,23].

Robust structure

Optimal and robust shapes of pipes conveying fluid were studied by making use of the adjoint variational principle and the Lagrange multiplier method [24]. A general method to design robust structures was presented [28].

S 1 S? S 3 $4 $5 A 01 O 0 00 O~ ~ 0

c~ ~ ~ CW~o

I,D lE 1 0 0 0 0 0 O0 0 0

r . . . . . . . . . . . . . . . . . . . .

uA O 0 O O 00 10 O O I ' ~ ~C) oo oo oo 'lC 0 0 0 0 0 0 0 0 0 1 U2 D ,~9-O-'(~O 00 00 O 0 E 00 00 01 O 0 0 0

12 34 56 78 91(3

Fig. 9. Allocation matrix of support elements.

i 1 |

t g , , e

Fig. 10. Convergence of network energy.

96 1f. Yamakawa / Optimum mechanical and structural designs

3

0

. . . . i n i t i a l ope ra t ing O p t i l n l operat inj~/

" ,3 sb - - ' ~ s Time t see

i n i t i a l

o p t i u u n / \ operating // \

'~ ~i SO ~'.S Time t sec

Fig. 11. Optimum driving curve and dynamical response.

Root Tip

Control On DIn] .. '- ,,, ~---~v3,0MPa

Root Tip

Cot~|rol Off

DI i ~ : P a

Root "tip Fig. ]2. Stress distribution along span.

Simultaneous optimization

Simultaneous optimization of structural and control systems are of interest these days, even in Japan. The general method for simultaneous optimization of nonlinear mechanical and control systems has been presented, and applied to the design of flexible robot ann and control systems [17]. Some methods of simultaneous optimization of structural and control systems were based on linear structural analysis and optimal regulator design methods, but several new aspects were added to the simultaneous designs [26,27,33,34]. A simultaneous structural/control design synthesis of a wing with an active control system was treated in [35]. The target programming problem with nonlinear multi-fuzzy goals was solved by the sequen- tial linear approximation method, and a requirement to ensure the stability of the control system was also involved there. Figures 12 and 13 show the optimum shapes of the wing and the history of the mass, maximum stress and gain during the optimization respectively.

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=~ 0.5

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i \ ...... ~ arch rise ratio 0 : i . . - ' " " • "

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15 10 15 20 I 15 Jo collision speed v m/s

Fig. 14. Results of S + U design.

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Optimum designs for dynamics problems in structural engineering

Fewer papers have appeared in this field than in the mechanical field, though many papers have appeared for statics problems. For example, looking through the journal of structural engineering of the Japan Society of Civil Engineers over these five years, only four papers have appeared [35-38].

Two symposiums on system optimization were held by the subcommittee of Structural Optimization in the Japan Society of Civil Engineers. One was in 1989, the other in 1991, and proceedings were issued. The relevant papers were listed in [39-48]. Among them, two studies are introduced briefly here. An optimum impact-resistant design of steel arch for the Sabo dam was studied in [46]. The arch weight was minimized, while satisfying simultaneously both constraints of the allowable stress for the sand and the energy criterion for the large lock. Figure 14 shows the results of the optimum design.

58.84 kN m a s s

6.118~k~

19.61 kN

(a)

58.84 kN 58.84 kN 58.84 kN mass mass | mass

/ I I l l / / I I //

Load i ng condition a (b) Loadin~ condition b Fig. 15. Static loading.

98

Table 5 Optimal

tl. Yamakawa / Optimum mechanical and structural designs

design for 10-member truss

Mass excitation Design Member Static

group numbers loadings h = 0.30 h = 0.20 h = 0.10 h = 0.05 h = 0.02

b 1 1,2 8.125 cm 2 9.099 cm e 10.038 cm: 13.727 cm 2 17.812 cm 2 21.616 cm 2 b e 3,4 7.149 7.589 8.000 8.894 9.750 10.627 b 3 5 0.336 0.250 0.154 0.100 0.100 0.100 b 4 6 2.204 2.200 2.253 2.223 2.026 2.983 b s 7,8 5.189 6.109 7.023 8.862 10.628 12.133 b 6 9,10 5.431 6.369 7.356 9.486 11.265 12.701

Mass 148.67 kg 167.48 kg 186.41 kg 234.23 kg 280.65 kg 324.54 kg Displacement

(Node) 0.365 cm (1) 0.5t2 cm (1) 0.640 cm (1) 0.846 cm (2) 0.988 cm (2) 1.089 cm (2) Natural freq. (lst) 3.45 Hz 3.67 Hz 3.88 Hz 4.43 Hz 4.91 Hz 5.29 Hz

According to a seismic design for a circuit breaker system, the design system is confirmed safe if it withstands a duration of three periods of sinusoidal ground acceleration. The optimal design procedure was developed and an optimization algorithm was presented for the structures, subjected to 3 cycles of resonant excitation under this concept. Figure 15 shows a ten member truss and Table 5 the results of optimal designs.

Concluding remark

Recent advances in optimum structural and mechanical designs in Japan over the last decade were reviewed here. It is hoped that this article may help understanding of the advances in the fields in Japan, although not all relevant papers have been fully reviewed.

References

[1] K. SETO, "A study on vibrational isolation by utilizing the vibrational modes (lst Report), Trans. JSME 49 (439C), pp. 341-350, 19083 (in Japanese).

[2] A. SUEOKA, H. TAMURA, Y. TSUDA and H. YAMAZAKI, "Optimum design of rotating machines of overhanging type (lst Report)", Trans. JSME 49 (441C), pp. 772-778, 1983 (in Japanese).

[3] M. YOSHIMURA, T. HAMADA, K. YURA and K. HITOMI, "Multi-objective optimum design of mechanical and structural systems (Pareto optimization on main shaft system of manufacturing machine)", Trans. JSME, 49 (445C), pp. 1606-1613, 1983 (in Japanese).

[4] Y. IWATA and K. NONAMI, "Vibration control of rotating shaft with self-optimizing support systems", Trans. JSME, 49 (446C), pp. 1897-1903, 1983 (in Japanese).

[5] M. YOSHIMURA, T. HAMADA, K. YURA, K. NOIKE and K. HITOMI, "Multi-level optimization of mechanical and structural system", Trans. JSME, 50 (452C), pp. 724-732, 1984 (in Japanese).

[6] S. KOYANAGI, "Overall optimum design methods of the air spring vibration isolation system", Trans. JSME 52 (478C), pp. 1758-1763, 1986 (in Japanese).

[7] T. IWATUBO, M. SADO and R. KAWAI, "The optimum design for a rotating shaft supported by journal bearings (3rd Report, Normalization of the reference function and consideration of uncertainty of design constants), Trans. JSME 52 (483C), pp. 2828-2833, 1986 (in Japanese).

[8] H. YMAKAWA, Y. N1SHIOKA and Y. SuzurJ, "A study on the optimum operating curve for rotating systems under consideration of the effect of limited power supply", Trans. JSME 52 (484C), pp. 3108-3114, 1986 (in Japanese).

[9] Y. TADA and Y. KUSAaA, "Optimum design of structures subjected to random loads (Optimization by approximate sensitivity), Trans. JSME 54 (498C), pp. 490-498, 1988 (in Japanese).

[10] S. NAKAGIRI and K. Suzvrd, "Indeterminate shift synthesis of vibration eigenvalue and eigenvector by the use of finite element method", Trans. JSME 54 (499C), pp. 523-528, 1988 (in Japanese).

[11] J. HINO and T. YOSHXMURA, "An optimum dynamic design for beams subject to a moving load", Trans. JSME 54 (499C), pp. 781-786, 1988 (in Japanese).

[12] M. OKUMA, M. NANPE, S. PARK and A. NAGAMATSU, "Technique of structural dynamic optimization (lst


Report, Use of mathematical pseudo inverse method and substructure synthesis method)", Trans. JSME 54 (504C), pp. 1753-1761, 1988 (in Japanese).

[13] I. KAJIWARA, M. OOKUMA, A. NAGAMATSU and K. SETO, "A technique of structural dynamic optimization using resonance and anti-resonance sensitivities", Trans. JSME 54 (505C), pp. 2084-2091, 1988 (in Japanese).

[14] Y. NARITA, "Optimal vibration support of continuous systems (1st Report, Search algorithm for optimal location)", Trans. JSME 54 (507C), pp. 2605-2609, 1988 (in Japanese).

[15] Y. NARITA and E. TAKAHASHI, "Optimal vibration support of continuous systems (2nd Report, Application to continuous beams of variable cross section)", Trans. JSME 55 (510C), pp. 281-285, 1989 (in Japanese).

[16] Y. NARITA, "Optimal vibration support of continuous systems (3rd Report, Maximization of difference between adjacent frequencies)", Trans. JSME 55 (513C), pp. 1168-1172, 1989 (in Japanese).

[17] H. YAMAKAWA, "A study on a unified method for the dynamic analysis of electro-mechanical systems and the optimum design and the optimum control methods based on it (1st Report, The basic idea of the unified method and the optimum design and the optimum control method)", Trans. JSME 55 (519C), pp. 2777-2783, 1989 (in Japanese).

[18] I. KAJIWARA and A. NAGAMATSU, "A structural optimization method considering time history response", Trans. JSME 56 (522C), pp. 391-397, 1990 (in Japanese).

[19] M. IWAHARA and A. NAGAMATSU, "Technique of structural dynamic optimization (2nd Report, Expansion of mathematical pseudo-inverse method to inequality behaviour constraint)", Trans. JSME 56 (523C), pp. 612-618, 1990 (in Japanese).

[20] Y. TADA, R. MATSUMOTO and K. KUSAKA, "Optimum shape design of structures subjected to moving loads (Strain energy and kinetic energy criteria), Trans. JSME 56 (527C), pp. 1733-1738, 1990 (in Japanese).

[21] H. YAMAKAWA and S. MURAKAMI, "A study on the optimum operating curve for rotating systems under consideration of the effect of limited power supply (2rid Report)", Trans. JSME 56 (527C), pp. 1739-1744, 1990 (in Japanese).

[22] K. INOUE, M. KATO and K. OHNUrO, "Optimum design of a plate based on the minimization of the vibration energy", Trans. JSME 56 (529C), pp. 2361-2366, 1990 (in Japanese).

[23] J. H1NO, S. HASH1MOTO and T. YOSHIMURA, "Discrete optimal design for a beam subject to a moving load", Trans. JSME 56 (530C), pp. 2610-2614, 1990 (in Japanese).

[24] Y. SEGUCHI, M. TANAKA and S. TANAKA, "Optimal and robust shapes of a pipe conveying fluid", Trans. JSME 56 (530C), pp. 2615-2622, 1990 (in Japanese).

[25] I. TAKAHASHI and Y. NARITA, "Optimal support spacing for vibration of continuous, orthotropic plates of variable thickness under in-plane forces, Trans. JSME 56 (531C), pp. 2841-2844, 1990 (in Japanese).

[26] T. IWATSUBO, M. IKEDA, S. KAWAMURA and K. ADACrtI, "Development of simultaneous optimum design of structural and control systems of flexible structures", Trans. JSME 57 (534C), pp. 407-412, 1991 (in Japanese).

[27] Y. TADA, R. MATSUMOTO and M. NAGAI, "Optimum structural design considering vibration control", Trans. JSME 57 (537C), pp. 1557-1561, 1991 (in Japanese).

[28] H. YAMAKAWA and M. MIYASHITA, "A study on robust structures (1st Report: Concept of robust structure and its design method), Trans. JSME 57 (544C), pp. 3913-3918, 1991 (in Japanese).

[29] H. YAMAKAWA and Y. TUBOKURA, "A study on direct sensitivity identification of structures by experimental data and optimum design based on the sensitivities", Trans. JSME 58 (546C), pp. 376-381, 1992 (in Japanese).

[30] J. HINO, S. TASAKA and T. YOSHIMURA, "A study for optimum dynamic design of a beam by using fuzzy inference", Trans. JSME 58 (548C), pp. 1048-1053, 1992 (in Japanese).

[31] K. MAEMORI and K. SAKAMOTO, "Multi-objective optimum design of speed control humps for vehicles (in the case of humps with elasticity)", Trans. JSME 58 (548C), pp. 1055-1059, 1992 (in Japanese).

[32] F. HARA, "Optimization of pipe-support allocation by neural network", Trans. JSME 58 (550C), pp. 1728-1734, 1992 (in Japanese).

[33] S. SuzuKi, "Multi-goal programming for structure/control design synthesis with fuzzy goals", Trans. JSME 58 (555C), pp. 3246-3252, 1992 (in Japanese).

[34] I. KAJ~WARA et al., "Optimum design of vibration control system using modal analysis and sensitivity analysis", Trans. JSME 58 (552C), p. 2365, 1992 (in Japanese).

[35] Y. KIKUTA, K. MATSUI and Y. N1NOBE, "Dynamic sensitivity analysis for structural systems", Trans. Struct. Eng., 33A, p. 703, 1987.

[36] T. HOSHIKAWA, S. KATSUKI and T. hDA, "A study on the optimal design of a steel pipe circular arch under impact load", Trans. Struct. Eng., 36A, p. 451, 1990.

[37] T. OKABAYASHI, W. TAKESHITA and A. IWAMI, "Optimum design of dynamic dampers for vibration control of stiffened arch bridge under a moving vehicle", Trans. Struct. Eng. 38A, p. 703, 1992.

[38] K. ENOMOTO, Y. NnNOBE, K. MATSUI, Y. KIKUTA and M. YAJIMA, "Characteristic in sensitivity coefficients of eigenvalues and eigenvectors of framed structures", Trans. Struct. Eng. 33A, p. 703, 1987.

[39] N. ISmKAWA, T. HOSHIKAWA, S. KAxsura and T. hDA, "A study on the optimal rise ratio of a circular arch under


impact loading", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 29-34, 1989.

[40] I. KAJIWARA, A. NAGAMATSU and K. SExo, "New theory for elimination of resonance peak and optimum design of optical servosystem", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 41-50, 1989.

[41] J. ONODA and N. WATANABE, "'An attempt for an integrated optimization of flexible space structure and its controller", Subcommittee of Structural optimization, Committee of structural Engineering, Japan Society of Civil Engineers, pp. 117-122, 1989.

[42] H. YAMAKAWA, "A study on a simultaneous optimization problem of structural and control systems", Subcom- mittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 29-34, 1989.

[43] I. KAJIWARA and A. NAGAMATSU, "Optimum design of structure and control systems", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 45-54, 1991.

[44] S. SuzuKi and S. YONEZAWA, "Structure optimization of an aircraft with an active control system", Subcommit- tee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 141-148, 1991.

[45] M. IWAHARA and A. NAGAMATSU, "A method for car body design optimization", Subcommittee of Structural, Optimization Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 175-180, 1991.

[46] N. ISHIKAWA, K. YAMAMOTO, S. SUZUKI and T. IIDA, "A fundamental study on the optimal impact-resistant design of steel arch type Sabo dam", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 199-204, 1991.

[47] Y.K. KJKUTA, K. MATSUI and Y. NnNOBE, "Optimal design of structures subject to 3 cycles of resonant excitation", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 211-216, 1991.

[48] M. hDA, "Optimum strong-motion station-array geometry for earthquake source studies", Subcommittee of Structural Optimization, Committee of Structural Engineering, Japan Society of Civil Engineers, pp. 211-216, 1991.

Documents

Recent advances in Japan in optimum mechanical and structural designs for dynamics