한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)

  • 제30권5호
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  • Pages.405-413
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  • 2017
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  • 1229-3059(pISSN)
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  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
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비국소 탄성이론을 이용한 자기-전기-탄성 나노 판의 2방향 좌굴 해석

Biaxial Buckling Analysis of Magneto-Electro-Elastic(MEE) Nano Plates using the Nonlocal Elastic Theory

  • 한성천 (대원대학교 철도건설과) ;
  • 박원태 (공주대학교 건설환경공학부)
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College) ;
  • Park, Weon-Tae (Division of Construction and Environmental Engineering, Kongju National University)
  • 투고 : 2017.08.02
  • 심사 : 2017.08.29
  • 발행 : 2017.10.31
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초록

본 연구에서는 1차 전단변형이론을 고려한 비국소 자기-전기-탄성 나노 판의 2방향 좌굴해석에 관하여 연구하였다. 면내 전기-자기-탄성 나노 판에서 전기장과 자기장은 무시할 수 있다. 자기-전기 경계조건과 맥스웰 방정식에 따라 전기-자기-탄성 나노 판의 두께 방향에 따른 자위 및 전위의 변화가 결정된다. 자기-전기-탄성 나노 판의 탄성이론을 재 공식화하기 위하여 에링겐의 비국소 미분 구성 관계식을 사용하였다. 변분이론을 이용하여 비국소 탄성이론의 지배방정식을 연구하였다. 비국소 이론과 국소 이론의 관계를 계산 결과를 통하여 분석하였다. 또한, 비국소 매개변수, 면내 하중 방향 그리고 형상비에 따른 구조적 응답을 연구하였다. 계산 결과들은 전위 및 자위의 효과를 나타내었다. 이러한 계산 결과들은 자기-전기-탄성 재료로 구성된 신소재 구조물의 설계 및 해석에 사용될 수 있고 향후 연구의 비교자료가 될 수 있을 것으로 판단된다.

In this paper, we study the biaxial buckling analysis of nonlocal MEE(magneto-electro-elastic) nano plates based on the first-order shear deformation theory. The in-plane electric and magnetic fields can be ignored for MEE(magneto-electro-elastic) nano plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the MME plate is determined. In order to reformulate the elastic theory of MEE(magneto-electro-elastic) nano-plate, the nonlocal differential constitutive relations of Eringen is used. Using the variational principle, the governing equations of the nonlocal theory are discussed. The relations between nonlocal and local theories are investigated by computational results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on structural responses are studied. Computational results show the effects of the electric and magnetic potentials. These computational results can be useful in the design and analysis of advanced structures constructed from MEE(magneto-electro-elastic) materials and may be the benchmark test for the future study.

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참고문헌

  1. Eringen, A.C. (1983) On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, J. Appl. Phys., 54, pp.4703-4710. https://doi.org/10.1063/1.332803
  2. Eringen, A.C. (2002) Nonlocal Continuum Field Theories, Springer-Verlag, New York.
  3. Kim, W,J., Lee, W.H., Park, W.T., Han, S.C. (2014) Nonlocal Elasticity Effects on Free Vibration Properties of Sigmoid Functionally Graded Material Nano-scale Plates, J. Korea Acad.-Ind. Co. Soc., 15(2), pp.1109-1117. https://doi.org/10.5762/KAIS.2014.15.2.1109
  4. Lee, W.H., Han, S.C., Park, W.T. (2016) Static and Free Vibration Analysis of FGM Plates on Pasternak Elastic Foundation, J. Comput. Struct. Eng. Inst. Korea, 29(6), pp.529-538. https://doi.org/10.7734/COSEIK.2016.29.6.529
  5. Li, Y.S. (2014) Buckling Analysis of Magnetoelectro Elastic Plate Resting on Pastrenak Elastic Foundation, Mech. Res. Commun., 56, pp.104-114. https://doi.org/10.1016/j.mechrescom.2013.12.007
  6. Li, Y.S., Cai, Z.Y., Shi, S.Y. (2014) Buckling and Free Vibration of Magneto-electro-elastic Nanoplate based on Nonlocal Theory, Composite Structures, 111, pp.522-529. https://doi.org/10.1016/j.compstruct.2014.01.033
  7. Pan, E. (2001) Exact Solution for Simply Supported and Multilayered Magneto-electro-elastic Plates, J. Appl. Mech., 68, pp.608-618. https://doi.org/10.1115/1.1380385
  8. Pan, E., Heyliger, P.R. (2002) Free Vibration of Simply Supported and Multilayered Magneto-Electro-elastic Plates, J. Sound Vibrat., 252(3), pp.429-442. https://doi.org/10.1006/jsvi.2001.3693
  9. Park, W.T., Han, S.C. (2017) Buckling Analysis of Nano-scale MEE(Magneto-Electro-Elastic) Plates using the Nonlocal Elasticity Theory, Advances in Mechanical Engineering, Under Review.
  10. Reddy, J.N. (2007) Theory and Analysis of Elastic Plates and Shells, CRC Press, London.
  11. Sladek, J., Sladek, V., Krahulec, S., Pan, E. (2013) The MLPG Analyses of Large Deflections of Magneto-Electro-elastic Plates, Eng. Anal. Bound. Elem, 37, pp.673-682. https://doi.org/10.1016/j.enganabound.2013.02.001
  12. Wang, R., Han, Q., Pan, E. (2010) An Analytical Solution for a Multilayered Magneto-electro-elastic Circular Plate under Simply Supported Lateral Boundary Conditions, Smart. Mater. Struct., 19, 065025. https://doi.org/10.1088/0964-1726/19/6/065025
  13. Xue, C.X., Pan, E., Zhang, S.Y., Chu, H.J. (2011) Large Deflection of a Rectangular Magneto-electro-elastic Thin Plate, Mech. Res. Commun., 38, pp.518-523. https://doi.org/10.1016/j.mechrescom.2011.07.003