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Optimization of laminated composite structures under nonlinear dynamic loading using the equivalent static load method

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Abstract

As the application of composite materials increases, analysis and optimum design for various dynamic loads as well as static loads are required. In this paper, we present an optimal design study using the equivalent static load method for laminated composite structures subjected to various nonlinear dynamic loads. First, the dynamic analysis of the laminate composite structure was performed using the finite element method. Next, the equivalent static load at each time step was calculated using the calculated dynamic response, and the static response optimization of the composite structure was performed by applying the calculated equivalent static load as a multi-load condition. Then, optimal design was performed by minimizing mass or maximizing strength by designing stacking thickness and stacking angle as design variables by applying various dynamic loads for the three different composite material structures. As a result of the optimization, the results of the conventional dynamic response optimization method, the error of less than 0.1 %, and the convergence speed up to 18 times were shown, and it was verified that the convergence speed was excellent while ensuring the accuracy of the solution.

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Abbreviations

u :

X-directional displacement components

v :

Y-directional displacement components

w :

Z-directional displacement components

u o :

X-directional displacement within the plane

v o :

Y-directional displacement within the plane

w o :

Z-directional displacement within the plane

σ :

Stress vector

ε :

Strain vector

\(\left\{ {\bar Q} \right\}\) :

Elasticity matrix

[K] :

Stiffness matrix

[M] :

Mass matrix

{F} :

Force vector

u D (b, t):

Displacement vector of the structure based on the time calculated in the dynamic analysis

f D (t):

Dynamic load over time

f ESL (s):

Equivalent static load under the load condition, s

u ESL (b, s):

Static displacement vector generated by multiple equivalent static loads

b :

Design vatiables

p :

The number of design variables

q :

The number of inequality constraints

r :

The number of equality constraints

h ks (b j ) :

Equality constraint

g js (p i ) :

Inequality constraint

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Acknowledgments

This research was supported by National Research Foundation of Korea (NRF) grant funded by the Korea government, the Ministry of Science, ICT & Future Planning (No. 2019R1A2C 1090228), the Technology Innovation Program (20012518) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) and Konkuk University Researcher Fund in 2019.

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Authors and Affiliations

  1. Graduate School of Mechanical Design and Production Engineering, Konkuk University, 120 Neung dong-ro, Gwangjin-gu, Seoul, 05029, Korea

    Yijae Choi, Jaemin Moon, Jinhwan Park, K. Kim & S. J. Ma

  2. LG Energy Solution, 188 Munji-ro, Yuseong-gu, Daejeon, 34122, Korea

    Seungmin Song

  3. Ho Chi Minh City University of Technology and Education, No 1 Vo Van Ngan Street, Linh Chieu Ward, Thu Duc District, Ho Chi Minh City, Vietnam

    Mai Duc Dai

  4. School of Mechanical Engineering, Konkuk University, 120 Neung dong-ro, Gwangjin-gu, Seoul, 05029, Korea

    Chang-Wan Kim

Authors
  1. Yijae Choi
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  2. Jaemin Moon
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  3. Jinhwan Park
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  4. Seungmin Song
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  5. Mai Duc Dai
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  6. K. Kim
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  7. S. J. Ma
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  8. Chang-Wan Kim
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Corresponding author

Correspondence to Chang-Wan Kim.

Additional information

Yijae Choi received the B.S. degree in Mechanical Engineering, Konkuk University, Seoul, Republic of Korea, in 2019. She is currently working toward the M.S. degree in Mechanical Design and Production Engineering at Konkuk University, Seoul, Republic of Korea. Her research interests include multi-physics analysis.

Chang-Wan Kim received the B.S. degree in Mechanical Engineering, Hanyang University, Republic of Korea, in 1987. He received the M.S. degree in Mechanical Engineering from Pohang University of Science and Technology (POSTECH), Republic of Korea, in 1993. He received the Ph.D. degree in Aerospace and Engineering Mechanics from University of Texas at Austin, Texas, USA, in 2004. He is currently a Professor of Department of Mechanical Engineering, Konkuk University, Seoul, Korea. His research interests include vibration and noise analysis, multi-body dynamics, optimal design, and multi-physics analysis.

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Choi, Y., Moon, J., Park, J. et al. Optimization of laminated composite structures under nonlinear dynamic loading using the equivalent static load method. J Mech Sci Technol 35, 4105–4113 (2021). https://doi.org/10.1007/s12206-021-0822-7

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  • DOI: https://doi.org/10.1007/s12206-021-0822-7

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