DOI QR코드

DOI QR Code

유한요소해석을 통한 다공성 보의 거동 분석

Analysis of Porous Beams Through FEM Simulation

  • 김현영 (금오공과대학교 기계시스템공학과 대학원) ;
  • 김준식 (금오공과대학교 기계시스템공학과)
  • Kim, Hyun-Young (Department of Mechanical System Engineering, Kumoh National Institute of Technology) ;
  • Kim, Jun-Sik (Department of Mechanical System Engineering, Kumoh National Institute of Technology)
  • 투고 : 2020.04.08
  • 심사 : 2020.04.22
  • 발행 : 2020.06.30

초록

본 연구에서는 다공성 보와 논로컬 매개변수 사이의 관계에 대한 유한요소해석을 수행한다. 논로컬 매개변수는 다공성 보의 결함을 표현하는 변수들로 정의하여, 하중조건 및 경계조건에 대한 수치모사를 통해 계산한다. 다공성 보와는 반대 개념의 결함을 가지는 보에 대한 해석도 수행하였다. 이러한 보들의 거동은 논로컬 매개변수의 항으로 표현하였으며, 이 매개변수는 구멍의 지름의 제곱 그리고 원기둥 지름의 세제곱에 비례하는 것을 확인하였다. 특히 작은 원기둥을 가지는 보에 축 하중을 가하는 경우, 예상과는 다르게 3차원 유한요소 해석 결과와 2차원 평면응력 해석 결과는 다름을 알 수 있었다.

In this study, various types of porous beams were designed and analyzed to examine the relationship between the behavior of a porous beam and certain nonlocal parameters. The nonlocal parameters were defined as functions of the conditions of defects in the porous material. Finite element analysis was conducted on the beams under typical boundary and loading conditions. Beams with stiffeners having the same dimensions as the defects in the porous beams were also analyzed. The deformation tendency of these beams was determined and described in terms of the nonlocal parameters. The deformation of a porous beam was linearly proportional to the square of the diameters of the defects, whereas that of a beam with a stiffener was linearly proportional to the cube of the diameter of the stiffener. Furthermore, for a stiffened beam with axial loading, the results derived from a 3D solid element and those under 2D plane stress conditions were different.

키워드

참고문헌

  1. Eringen, A.C. (1983) On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves, J. Appl. Phys., 54(9), pp.4703-4710. https://doi.org/10.1063/1.332803
  2. Eringen, A.C. (2002) Nonlocal Continuum Field Theories, Springer-Verlag New York, Inc.
  3. Gurtin, M.E., Murdoch, A.I. (1975) A Continuum Theory of Elastic Material Surfaces, Arch. Rat. Mech. Anal., 57(4), pp.291-323. https://doi.org/10.1007/BF00261375
  4. Gurtin, M.E., Murdoch, A.I. (1978) Surface Stress in Solids, Int. J. Solid Struct., 14(6), pp.431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  5. Kim, J.-S. (2014) Application of Nonlocal Models to Nano Beams, Part I: Axial Length Scale Effect, J. Nanosci. Nanotechnol., 14(10), pp.7592-7596. https://doi.org/10.1166/jnn.2014.9749
  6. Lam, D.C.C., Yang, F., Chong, A.C.M., W ang, J., Tong, P. (2003) Experiments and Theory in Strain Gradient Elasticity, J. Mech. Phys. Solid., 51(8), pp.1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  7. Ma, H.M., Gao, X.-L., Reddy, J.N. (2008) A Microstructure-Dependent Timoshenko Beam Model based on a Modified Couple Stress Theory, J. Mech. Phys. Solid., 56(12), pp.3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  8. Mindlin, R.D. (1964) Micro-Structure in Linear Elasticity, Arch. Rat. Mech. Anal., 16(1), pp.51-78. https://doi.org/10.1007/BF00248490
  9. Mindlin, R.D. (1965) Second Gradient of Strain and Surface-Tension in Linear Elasticity, Int. J. Solids Struct., 1(4), pp.417-438. https://doi.org/10.1016/0020-7683(65)90006-5
  10. Peddieson, J., Buchanan, G.G., McNitt, R.P. (2003) Application of Nonlocal Continuum Models to Nanotechnology, Int. J. Eng. Sci., 41(3), pp.305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  11. Reddy, J.N. (2007) Nonlocal Theories for Bending, Buckling and Vibration of Beams, Int. J. Eng. Sci., 45(2), pp.288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  12. Wang, C.M., Zhang, Y.Y., Ramesh, S.S., Kitipornchai, S. (2006) Buckling Analysis of Micro- and Nano-Rods/Tubes based on Nonlocal Timoshenko Beam Theory, J. Phys. D: Appl. Phys., 39(17), pp.3904-3909. https://doi.org/10.1088/0022-3727/39/17/029
  13. Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P. (2002) Couple Stress based Strain Gradient Theory for Elasticity, Int. J. Solids Struct., 39(10), pp.2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X