DOI QR코드

DOI QR Code

Universal Theory for Planar Deformations of an Isotropic Sandwich Beam

등방성 샌드위치 빔의 평면 변형을 위한 통합 이론

  • Lee, Chang-Yong (School of Mechanical Engineering, Pukyong National University)
  • 이창용 (부경대학교 기계공학과)
  • Received : 2020.03.27
  • Accepted : 2020.04.14
  • Published : 2020.07.31

Abstract

This work is concerned with various planar deformations of an isotropic sandwich beam, which generally consists of three layers: two stiff skin layers and one soft core layer. When one layer of the sandwich beam is modeled as a beam, the variational-asymptotic method is rigorously used to construct a zeroth-order beam model, which is similar to a generalized Timoshenko beam model capable of capturing the transverse shear deformations but still carries out the zeroth-order approximation. To analyze the planar sandwich beam, the sum of the energies of the two skin layers and one core layer is then formulated with different material and geometric properties and represented by a universal beam model in terms of the core-layer kinematics through interface displacement and stress continuity conditions. As a preliminary validation, two extreme examples are presented to demonstrate the capability and accuracy of this present approach.

Keywords

References

  1. Birman, V. and Kardomateas, G. A., "Review of Current Trends in Research and Applications of Sandwich Structures," Composites Part B, Vol. 142, pp. 221-240, 2018. https://doi.org/10.1016/j.compositesb.2018.01.027
  2. Sayyad, A. S. and Ghugal, Y. M., "Bending, Buckling and Free Vibration of Laminated Composite and Sandwich Beams: A Critical Review of Literature," Composite Structures, Vol. 171, pp. 486-504, 2017. https://doi.org/10.1016/j.compstruct.2017.03.053
  3. Kardomateas, G. A. and Phan, C. N., "Three Dimensional Elasticity Solution for Sandwich Beams/Wide Plates with Orthotropic Phases: The Negative Discriminant Case," Journal of Sandwich Structures and Materials, Vol. 13, No. 6, pp. 641-661, 2011. https://doi.org/10.1177/1099636211419127
  4. Phan, C. N., Frostig, Y. and Kardomateas, G. A., "Analysis of Sandwich Beams with a Compliant Core and with In-Plane Rigidity-Extended High-Order Sandwich Panel Theory Versus Elasticity," Journal of Applied Mechanics, Vol. 79, pp. 041001-1-11, 2012. https://doi.org/10.1115/1.4005550
  5. Berdichevsky, V. L., "Variational-Asymptotic Method of Shell Theory Construction," PMM, Vol. 43, pp. 664-687, 1979.
  6. Berdichevsky, V. L., "An Asymptotic Theory of Sandwich Plates," International Journal of Engineering Science, Vol. 43, pp. 383-404, 2010. https://doi.org/10.1016/j.ijengsci.2009.09.001
  7. Berdichevsky, V. L., "Nonlinear Theory of Hard-Skin Plates and Shells," International Journal of Engineering Science, Vol. 48, pp. 357-369, 2010. https://doi.org/10.1016/j.ijengsci.2009.09.003
  8. Hodges, D. H., Nonlinear Composite Beam Theory for Engineers, AIAA, pp. 63-70, 2006.
  9. Yu, W., "Variational Asymptotic Modeling of Composite Dimensionally Reducible Structures," A Thesis for a Doctorate, Georgia Institute of Technology, USA, 2002.