Journal of the Society of Disaster Information (한국재난정보학회 논문집)

The Korean Society of Disaster Information (한국재난정보학회)
권호 표지
DOI QR코드

DOI QR Code

Isogeometric Analysis of FGM Plates in Combination with Higher-order Shear Deformation Theory

등기하해석에 의한 기능경사복합재 판의 역학적 거동 예측

  • Jeon, Juntai (Department of Civil&Environmental Engineering, Inha Technical College)
  • Received : 2020.11.25
  • Accepted : 2020.12.17
  • Published : 2020.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Purpose: This study attempts at analyzing mechanical response of functionally graded material (FGM) plates in bending. An accurate and effective numerical approach based on isogeometric analysis (IGA) combined with higher-order shear deformation plate theory to predict the nonlinear flexural behavior is developed. Method: A higher-order shear deformation theory(HSDT) which accounts for the geometric nonlinearity in the von Karman sense is presented and used to derive the equilibrium and governing equations for FGM plate in bending. The nonlinear equations are solved by the modified Newton-Raphson iterative technique. Result: The volume fraction, plate length-to-thickness ratio and boundary condition have signifiant effects on the nonlinear flexural behavior of FGM plates. Conclusion: The proposed IGA method can be used as an accurate and effective numerical tool for analyzing the mechanical responses of FGM plates in flexure.

연구목적: 본 연구에서는 고차전단변형이론을 적용한 등기하해석 방법을 이용하여 기능경사복합재 판의 휨에 의한 역학적 거동을 해석하고자 하였다. 연구방법: 기능경사복합재 판의 역학적 거동을 보다 더 정확하게 해석하기 위해서 전단보정계수를 도입할 필요가 없는 기하학적 비선형을 고려한 고차전단변형이론을 이용하여 휨을 받는 기능경사복합재 판의 평형방정식과 지배방정식을 도출하였으며, 등기하 해석방법에 의한 수정된 Newton-Raphson 반복법을 이용하여 방정식들을 풀었다. 연구결과: 판의 용적비, 길이-두께 비 및 경계조건은 기능경사복합재 판의 휨 거동에 상당한 영향을 미치는 것을 알 수 있었다. 결론: 제안된 등기하해석 방법은 휨을 받는 기능경사복합재 판의 역학적 거동을 해석하는데 있어 정확하고 효과적인 수치해석 방법임을 확인하였다.

Keywords

References

  1. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y. (2005) "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement." Computer Methods in Applied Mechanics and Engineering, Vol. 194, pp. 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
  2. Kashtalyan, M. (2004) "Three-dimensional elasticity solution for bending of functionally graded plates." European Journal of Mechanics A/Solid, Vol. 23, pp. 853-864. https://doi.org/10.1016/j.euromechsol.2004.04.002
  3. Koizumu, K. (1993). "The concept of FGM, ceramic transactions." Functionally Graded Materials, Vol. 34, pp. 3-10.
  4. Levy, S. (1942). Square Plate with Clamped Edges Under Normal Pressure Producing Large Deflections. Technical Report, National Advisory Committee for Aeronautics.
  5. Pica, A., Wood, R.D., Hinton, E. (1980). "Finite element analysis of geometrically nonlinear plate behaviour using a mindlin formulation." Computers and Structures, Vol. 11, pp. 203-215. https://doi.org/10.1016/0045-7949(80)90160-1
  6. Reddy, J.N. (2000). "Analysis of functionally graded plates." International Journal for Numerical Methods in Engineering, Vol. 47, pp. 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  7. Urthaler, Y., Reddy, J.N. (2008) "A mixed finite element for the nonlinear bending analysis of laminated composite plates based on FSDT." Mechanics of Advanced Material Structures, Vol. 15, pp. 335-354. https://doi.org/10.1080/15376490802045671
  8. Zenkour, A.M., Alghamdi, N.A. (2008) "Thermoelastic bending analysis of functionally graded sandwich plates." Journal of Materials Sciences, Vol. 43, pp. 2574-2589. https://doi.org/10.1007/s10853-008-2476-6
  9. Zhao, X., Liew, K.M. (2009) "Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method." Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 2796-2811. https://doi.org/10.1016/j.cma.2009.04.005
  10. Zhu, P., Zhang, L.W., Liew, K.M. (2014) "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation." Composite Structures, Vol. 107, pp. 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001