DOI QR코드

DOI QR Code

비국소 탄성이론을 이용한 S형상 점진기능재료 나노-스케일 판의 이축 좌굴해석

Biaxial buckling analysis of sigmoid functionally graded material nano-scale plates using the nonlocal elaticity theory

  • 이원홍 (경남과학기술대학교 토목공학과) ;
  • 한성천 (대원대학교 철도건설과)
  • Lee, Won-Hong (Department of Civil Engineering, Gyeongnam National University of Science and Technology) ;
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College)
  • 투고 : 2013.08.08
  • 심사 : 2013.11.07
  • 발행 : 2013.11.30

초록

Erigen의 비국소 탄성이론을 이용한 S형상 점진기능재료 나노-스케일 판의 전단변형이론을 정식화하여 평형방성식을 유도하였다. 비국소 탄성이론은 미소 규모 효과를 고려할 수 있고 S형상함수는 점진기능재료의 정확한 특성 변화를 고려할 수 있다. 4변이 단순지지된 나노-스케일 판의 지배방정식을 풀기 위해 Navier 방법을 사용하였다. 거듭 제곱 지수와 비국소 변수의 효과를 나타내기 위한 나노-스케일 판의 해석적 좌굴하중을 제시하였고, 국소 탄성이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 나노-스케일 판의 크기, (iii) 비국소 계수, (iv) 형상비 그리고 (v) 모드 수 등이 나노-스케일 판의 이축 무차원 좌굴하중에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였다.

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.

키워드

참고문헌

  1. T. Hirano and T. Yamada, "Multi-paradigm expert system architecture based upon the inverse design concept", International Workshop on Artificial Intelligence for Industrial Applications, Hitachi, Japan, 1988. DOI: http://dx.doi.org/10.1109/AIIA.1988.13301
  2. F. Delale, F. Erdogan, "The crack problem for a nonhomogeneous plane", J. Appl. Mech.(ASME), Vol. 50, pp. 609-614, 1983. DOI: http://dx.doi.org/10.1115/1.3167098
  3. G. Bao, L. Wang, "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Solids Struct., Vol. 32, pp. 2853-2871, 1995. DOI: http://dx.doi.org/10.1016/0020-7683(94)00267-Z
  4. Y. L. Chung, S. H. Chi, "The residual stress of functionally graded materials", Journal of Chinese Institute of Civil and Hydraulic Engineering, Vol. 13, pp. 1-9, 2001.
  5. S. H. Chi, Y. L. Chung, Y.L. "Cracking in sigmoid functionally graded coating". Journal of Mechanics, Vol. 18, pp. 41-53, 2002.
  6. A. M. Zenkour, "On vibration of functionally graded plates according to a refined trigonometric plate theory", Int. J. Struct. Stab. Dyna., Vol. 5, pp. 279-297, 2005. DOI: http://dx.doi.org/10.1142/S0219455405001581
  7. W. H. Lee, S. C. Han, W. T. Park, "Bending, Vibration and Buckling Analysis of Functionally Graded Material Plates, J. Korea Academia-Industrial cooperation Society, Vol. 9(4), pp. 1043-1049, 2008. DOI: http://dx.doi.org/10.5762/KAIS.2008.9.4.1043
  8. A. C. Eringen, "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., Vol. 54, pp. 4703-4710, 1983. DOI: http://dx.doi.org/10.1063/1.332803
  9. A. C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002.
  10. S. Narendar, D. R. Mahapatra, S. Gopalakrishnan, "Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation ", Int. J. Eng. Sci., Vol. 49, pp. 509-522, 2011. DOI: http://dx.doi.org/10.1016/j.ijengsci.2011.01.002
  11. S. Narendar, "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., Vol. 93, pp. 3093-3103, 2011. DOI: http://dx.doi.org/10.1016/j.compstruct.2011.06.028
  12. J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC Press, London, 2007.
  13. W. H. Lee, S. C. Han, W. T. Park, "Nonlocal elasticity theory for bending and free vibration analysis of nano plates, J. Korea Academia-Industrial cooperation Society, Vol. 13(7), pp. 3027-3215, 2012. DOI: http://dx.doi.org/10.5762/KAIS.2012.13.7.3207
  14. B. Babaei, A. R. Shahidi, "Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method", Arch. Appl. Mech., Vol. 81, pp. 1051-1062, 2011. DOI: http://dx.doi.org/10.1007/s00419-010-0469-9
  15. H. T. Thai, D. H. Choi, "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Comps. Struct., Vol. 95, pp. 142-153, 2013. DOI: http://dx.doi.org/10.1016/j.compstruct.2012.08.023
  16. Q. Wang, C. M. Wang. "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes". Nanotechnology, Vol. 18, pp. 075702-075709, 2007. DOI: http://dx.doi.org/10.1088/0957-4484/18/7/075702