Evaluation of In-Plane Effective Properties of Circular-Hole Perforated Sheet

원형 다공 평판의 면내 유효 물성치 계산

  • 정일섭 (영남대학교 기계공학부)
  • Published : 2004.01.01

Abstract

Structural analysis for materials containing regularly spaced in-homogeneities is usually executed by using averaged material properties. For the homogenization process, a unit cell is defined and loaded somehow, and its response is investigated to evaluate the properties. The imposed loading conditions should accord to the behavior of unit cell immersed in the macroscopic structure in order to guarantee the accuracy of the effective properties. Each unit cell shows periodic variation of strain if the material is loaded uniformly, and in this study, direct implementation of this characteristic behavior is attempted on FE models of unit cell. Conventional finite element analysis tool can be used without any modification, and the boundary of unit cell is constrained in a way that the periodicity is satisfied. The proposed method is applicable to skew arrayed in-homogeneity problems. The flexibility matrix relating tonsorial stress and strain components in skewed rectilinear coordinate system is transformed so that the required engineering constants can be evaluated. Effective properties are computed for the materials with square and skew arrayed circular holes, and its accuracy is examined.

Keywords

References

  1. Slot, T. and O'Donnell, W. J., 'Effective Elastic Constants of Thick Perforated Plates with Square and Triangular Penetration Patterns,' J. of Engineering for Industry, Tran. ASME, Vol. 93, No. 4, pp.935-942, 1971 https://doi.org/10.1115/1.3428087
  2. O'Donnell, W.J. and Porowski, J., 'Yiled Surfaces for Perforated Materials,' J. of Applied Mechanics, Tran. ASME, Vol.40, No.3, pp.263-270, 1973 https://doi.org/10.1115/1.3422938
  3. Meguid, S. A., Kalamkarov, A. L.,Yao, J., and Zougas, A., 'Analytical, Numerical and Experimental Studies of Effective Elastic Properties of Periodically Perforated Materials,' J. of Engineering Materials and Technology, Tran. ASME, Vol. 118, No. 1, pp.43-48, 1996 https://doi.org/10.1115/1.2805932
  4. Baik, S. C.,Oh ,K. H., and Lee, D. N., 'Analysis of the Deformation of a Perforated Sheet under Uniaxial Tension,' J. of Materials Processing Technology, Vol. 58, No. 2, pp. 139-144, 1996 https://doi.org/10.1016/0924-0136(95)02096-9
  5. Baik, S. C., Han, H. N., Lee, S. H., Oh, K. H., and Lee, D. N., 'Plastic Behavior of Perforated Sheets under Biaxial Stress State,' Int. J. of Mechanical Science, Vol. 39, No. 7, pp.781-793, 1997 https://doi.org/10.1016/S0020-7403(96)00091-4
  6. Theocaris, P. S., Stavroulakis, G. E., Panagio-topoulos, P. D., 'Calculation of Effective Transverse Elastic Moduli of Fiber-Reinforced Composites by Numerical Homogenization,' Composites Sciences and Technology, Vol. 57, No. 5, pp. 573-586, 1997 https://doi.org/10.1016/S0266-3538(97)00018-3
  7. Park, S. K., Kim, J., Chang, Y. C. and Kang, B. S., 'Analysis of the Deformation of a Perforated Sheet under Thermal and Tension Load Using Finite Element Method,' J. of Materials Processing Technology, Vol. 113, No. 1, pp. 761-765, 2001 https://doi.org/10.1016/S0924-0136(01)00696-3
  8. Kalamkarov, A. L., 'Analysis, Design, and Optimization of composite structures,' J. Wiley & Sons, New York, 1997
  9. Lee, J. H., 'Simplified Stress Analysis of Perforated Plates Using Homogenization Technique,' J. of the Computational Structural Engineering Institute of Korea, Vol. 8, No. 3, pp. 51-58, 1995
  10. Ghosh, S., Lee, K., Moorthy S., 'Two Scale Analysis of Heterogeneous Elastic-Plastic Materials with Asymptotic Homogenization and Voronoi Cell Finite Element Model,' Comput. Methods Appl. Mech. Engrg., Vol. 132, No. 1, pp. 63-116, 1996 https://doi.org/10.1016/0045-7825(95)00974-4
  11. Jang, J., Yoon, M., and Lee, J., 'Computation of Equivalent Material Properties of Woven Fabric Composites Using Homogenization Technique,' Tran. of KSME A, Vol. 22, No. 3, pp. 588-594, 1998
  12. Ohno, N., Wu, X., and Matsuda, T., 'Homogenized properties of Elastic-Viscoplastic Composites with Periodic Internal Structures,' Int. J. of Mechanical Sciences, Vol. 42, No. 8, pp. 1519-1536, 2000 https://doi.org/10.1016/S0020-7403(99)00088-0
  13. Yun, S. H., 'The Finite Element Analysis for Calculation of Equivalent Elastic Constants Using the Homogenization Method,' J. of the Computational Structural Engineering Institute of Korea, Vol. 13, No. 1, pp.51-61, 2000
  14. Anthoine, A., 'Derivation of the In-Plane Elastic Characteristics of Masonry through Homogenization Theory,' Int. J. Solids Structures, Vol. 32, No. 2, pp. 137-163, 1995 https://doi.org/10.1016/0020-7683(94)00140-R