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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i2.40
pages 193-200

STATIC DEFLECTION ANALYSIS OF FLEXURAL SIMPLY SUPPORTED SECTORIAL MICRO-PLATE USING P-VERSION FINITE-ELEMENT METHOD

A. R. Ahmadi
International Center for Science and High Technology and Environmental Sciences, Kerman, Iran
H. Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
S. Arabnejad
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran

ABSTRACT

In this paper, flexural Kirchhoff plate theory is utilized for static analysis of isotropic sectorial micro-plates based on a modified couple stress theory containing one material length scale parameter. The Levy method is implemented and the resulting sixth-order differential equation is solved for the unknown deflection using the p-version finite-element method. The Galerkin form of this differential equation is first reduced to its weak form and then solved using hierarchical p-version finite elements with second-order global smoothness. The computed deflection distribution of the micro-plate is compared with that of the classical theory, in which micro-effects are not present. A series of studies have revealed that when the length scale parameters are considered, deflection of a sectorial plate decreases as the length scale effect is increased; in other words, the micro-plate exhibits more rigidity.

REFERENCES

  1. Aifantis, E. C., Strain gradient interpretation of size effects. DOI: 10.1023/A:1018625006804

  2. Cosserat, E. and Cosserat, F., Theorie des Corps Deformables.

  3. Eringen, C. A., Linear theory of micropolar elasticity.

  4. Exadaktylos, G. E. and Vardoulakis, I., Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics. DOI: 10.1016/S0040-1951(01)00047-6

  5. Farahmand, H. and Arabnejad, S., Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures. DOI: 10.1615/IntJMultCompEng.v8.i4.70

  6. Koiter, W. T., Couple stresses in the theory of elasticity.

  7. Lakes, R., Experimental methods for study of Cosserat elastic solids and other generalized elastic continua.

  8. Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J., and Tong, P., Experiments and theory in strain gradient elasticity. DOI: 10.1016/S0022-5096(03)00053-X

  9. Mindlin, R. D., Micro-structure in linear elasticity. DOI: 10.1007/BF00248490

  10. Mindlin, R. D. and Eshel, N. N., On first strain-gradient theories in linear elasticity. DOI: 10.1016/0020-7683(68)90036-X

  11. Papargyri-Beskou, S. and Beskos, D. E., Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates. DOI: 10.1007/s00419-007-0166-5

  12. Park, S. K. and Gao, X.-L., Variational formulation of a modified couple stress theory and its application to a simple shear problem. DOI: 10.1007/s00033-006-6073-8

  13. Reddy, J. N., Theory and Analysis of Elastic Plates and Shells.

  14. Surana, K. S., Petti, S. R., Ahmadi, A. R., and Reddy, J. N., On p-version hierarchical interpolation functions for higher order continuity finite element models.

  15. Tiersten, H. F. and Bleustein, J. L., Generalized elastic continua.

  16. Toupin, R. A., Elastic materials with couple-stresses. DOI: 10.1007/BF00253945

  17. Vardoulakis, I. and Sulem, J., Bifurcation Analysis in Geomechanics.


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