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Exploration of static and free vibration resistance topologically optimal beam structure shapes using density design variables.

재료밀도 설계변수를 이용한 정적 및 자유진동 저항 위상최적 보의 형상 탐색에 관한 연구

  • Lee, Dongkyu (Department of Architectural Engineering, Sejong University) ;
  • Shin, Soo Mi (Research Institute of Industrial Technology, Pusan National University)
  • 이동규 (세종대학교 건축공학과) ;
  • 신수미 (부산대학교 생산기술연구소)
  • Received : 2024.02.06
  • Accepted : 2024.02.22
  • Published : 2024.03.15

Abstract

This study numerically compares optimum solutions generated by element- and node-wise topology optimization designs for free vibration structures, where element-and node-wise denote the use of element and nodal densities as design parameters, respectively. For static problems optimal solution comparisons of the two types for topology optimization designs have already been introduced by the author and many other researchers, and the static structural design is very common. In dynamic topology optimization problems the objective is in general related to maximum Eigenfrequency optimization subject to a given material limit since structures with a high fundamental frequency tend to be reasonable stiff for static loads. Numerical applications topologically maximizing the first natural Eigenfrequency verify the difference of solutions between element-and node-wise topology optimum designs.

Keywords

Acknowledgement

이 논문은 2022년도 정부(과학기술정보통신부)의 제원으로 한국연구재단(NRF-2022R1A2 C1003776)에 의해 수행되었습니다.

References

  1. M.P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Vol.71(2), pp.197-224, 1988. DOI:https://www.sciencedirect.com/science/article/abs/pii/0045782588900862?via%3Dihub https://doi.org/10.1016/0045-7825(88)90086-2
  2. S.L. Vatanabe, G.H. Paulino, E.C.N. Silva, Design of functionally graded piezocomposites using topology optimization and homogenization - Toward effective energy harvesting mate- rials. Computer Methods in Applied Mechanics and Engineering, Vol.266, pp.205-218, 2013. DOI:https://doi.org/10.1016/j.cma.2013.07.003
  3. R. Tavakoli, Optimal design of multiphase composites under elastodynamic loading. Computer Methods in Applied Mechanics and Engineering, Vol.300, pp.265-293, 2016. DOI:https://doi.org/10.1016/j.cma.2015.11.026
  4. S. Wu, Y. Zhang, S. Liu, Transient thermal dissipation efficiency based method for topology optimization of transient heat conduction structures. International Journal of Heat and Mass Transfer, Vol.170, pp.121004, 2021. DOI:https://doi.org/10.1016/j.ijheatmasstransfer.2021.121004
  5. V. Shobeiri, The topology optimization design for cracked structures. Engineering Analysis with Boundary Elements, Vol.58, pp.26-38, 2015. DOI:https://doi.org/10.1016/j.enganabound.2015.03.002
  6. T.T. Banh, D. Lee, Multi-material topology optimization design for continuum, structures with crack patterns. Composite Structures, Vol.186, pp.193-209, 2018. DOI:https://doi.org/10.1016/j.compstruct.2017.11.088
  7. P.A. Nguyen, T.T. Banh, D. Lee, J. Lee, J. Kang, S. Shin, Design of multiphase carbon fiber reinforcement of crack existing concrete structures using topology optimization. Steel and Composite Structures, Vol.29, pp.635-645, 2018. DOI:https://doi.org/10.12989/scs.2018.29.5.635
  8. J. Thomsen, Topology optimization of structures composed of one or two materials. Journal of Structural Optimization, Vol5(1-2), pp.108-115, 1992. DOI:https://doi.org/10.1007/BF01744703
  9. 정상훈, 박찬수, 서상교, 분포질량과 집중질량방식의 비교에 의한 평면뼈대구조물의 고유치에 대한 자동해석, 대한건축학회 학술발표대회논문집, pp.103-106, 1983.
  10. O. Sigmund, A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, Vol.21, pp.120-127, 2001. DOI:https://doi.org/10.1007/s001580050176