Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Evaluation of Effective In-Plane Elastic Properties by Imposing Periodic Displacement Boundary Conditions

주기적 변형 경계조건을 적용한 면내 유효 탄성 물성치의 계산

  • 정일섭 (영남대학교 기계공학부)
  • Published : 2004.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Analysis for structures composed of materials containing regularly spaced in-homogeneities is usually executed by using averaged material properties. In order to evaluate the effective properties, a unit cell is defined and loaded somehow, and its response is investigated. The imposed loading, however, should accord to the status of unit cells immersed in the macroscopic structure to secure the accuracy of the properties. In this study, mathematical description for the periodicity of the displacement field is derived and its direct implementation into FE models of unit cell is attempted. Conventional finite element code needs no modification, and only the boundary of unit cell should be constrained in a way that the periodicity is preserved. The proposed method is applicable to skew arrayed in-homogeneity problems. Homogenized in-plane elastic properties are evaluated for a few representative cases and the accuracy is examined.

Keywords

References

  1. Slot, T. and O'Donnell, W. J., 1971, 'Effective Elastic Constants for Thick Perforated Plates with Square and Triangular Penetration Patterns,' J. of Engineering for Industry, Tran. ASME, Vol. 93, No.4, pp. 935-942 https://doi.org/10.1115/1.3428087
  2. O'Donnell, W. J. and Porowski, J., 1973, 'Yield Surfaces for Perforated Materials,' J. of Applied Mechanics, Tran. ASME, Vol. 40, No.3, pp. 263-270 https://doi.org/10.1115/1.3422938
  3. Baik, S. C., Oh, K. H. and Lee, D. N., 1996, 'Analysis of the Deformation of a Perforated Sheet under Uniaxial Tension,' J. of Materials Processing Technology, Vol. 58, No.2, pp. 139-144 https://doi.org/10.1016/0924-0136(95)02096-9
  4. Baik, S. C., Han, H. N., Lee, S. H., Oh, K. H. and Lee, D. N., 1997, 'Plastic Behavior of Perforated Sheets under Biaxial Stress State,' Int. J. of Mechanical Sciences, Vol. 39, No.7, pp. 781-793 https://doi.org/10.1016/S0020-7403(96)00091-4
  5. Theocaris, P. S., Stavroulakis, G. E. and Panagiotopoulos, P. D., 1997, 'Calculation of Effective Transverse Elastic Moduli of Fiber-Reinforced Composites by Numerical Homogenization,' Composites Sciences and Technology, Vol. 57, No.5, pp. 573-586 https://doi.org/10.1016/S0266-3538(97)00018-3
  6. Park, S. K., Kim, J., Chang, Y. C. and Kang, B. S., 2001, '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 https://doi.org/10.1016/S0924-0136(01)00696-3
  7. Meguid, S. A., Kalamkarov, A. L., Yao, J. and Zougas, A., 1996, '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 https://doi.org/10.1115/1.2805932
  8. Kalamkarov, A. L., 1997, 'Analysis, Design, and Optimization of composite structures,' J. Wiley & Sons, New York
  9. Lee, J. H., 1995, '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
  10. Ghosh, S., Lee, K. and Moorthy S., 1996, '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 https://doi.org/10.1016/0045-7825(95)00974-4
  11. Jang, J., Yoon, M. and Lee, J., 1998, 'Computation of Equivalent Material Properties of Woven Fabric Composites Using Homogenization Technique,' Tran. of KSME A, Vol. 22, No.3, pp. 588-594
  12. Ohno, N., Wu, X. and Matsuda, T., 2000, 'Homogenized properties of Elastic-Viscoplastic Composites with Periodic Internal Structures,' Int. J. of Mechanical Sciences, Vol. 42, No.8, pp. 1519-1536 https://doi.org/10.1016/S0020-7403(99)00088-0
  13. Yun, S. H., 2000, '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
  14. Hassani, B. and Hinton, E., 1998, 'A Review of Homogenization and Topology Optimization II - Analytical and Numerical Solution of Homogenization Equations,' Computers and Sturctures, Vol. 69, pp.719-738 https://doi.org/10.1016/S0045-7949(98)00132-1
  15. Anthoine, A., 1995, 'Derivation of the In-Plane Elastic Characteristics of Masonry through Homogenization Theory,' Int. J. Solids Structures, Vol. 32, No. 2, pp. 137-163 https://doi.org/10.1016/0020-7683(94)00140-R