# Abstract

The stress concentration must often be examined at two levels while analyzing the stress condition of composite materials. The macroconcentration depends on the presence of holes, notches and other local areas of a construction. Typical dimensions of macroconcentration distribution areas are of the order of 0,01-0,1 m. Macroconcentration analysis is performed using the models of homogeneous material. Microstress concentration occurs in structurally inhomogeneous composites due to the structural heterogeneity of the composite. The sizes of concentration areas in regular structures are defined by the sizes of periodically recurring areas. In fibrous composites, such areas have the size of approximately 0,0001 m or less. This makes it necessary to use a two-level approach for the analysis of the stress concentration in the construction of composite materials. The aim of the present study was to compute the stress concentration in unidirectional reinforced composite plate with circular hole with respect to the volume ratio of the component materials in composite. The contour of the circular hole and its dependency on the structure of plates was calculated in order to study the behaviors of macro- and microstresses. The boundary conditions at a large distance from the hole are pressure, uniformly distributed on the plate. Also this problem is analyzed with the finite element method by package ANSYS. Macroconcentration is defined based on the solution of the plane problem of elasticity theory of the orthotropic material by the virtue of functions of a complex variable. The finite element method was used to investigate the stress distribution at microlevel. Boundary conditions that model the state of the specified two-dimensional representative cell in the composite structure were established. The results demonstrated the macro- and microstresses and behavior of the orthotropic plate with a circular hole calculated for two different structures.

#### Keywords

National Technical University «Kharkiv Polytechnic Institute»

### G I Lvov

National Technical University «Kharkiv Polytechnic Institute»

# References

1. Muskhelishvilii N. Some Basic Problems of the Mathematical Theory of Elasticity. Leiden: Noordhoff, 1963.
2. Lekhnitskii S. Anisotropic Plates. London: Gordon Breach, 1968.
3. Savin G. Stress Concentration around Holes. New York: Pergamon Press, 1961.
4. Greszczuk L.B. Stress Concentration and Failure Criteria for Orthotropic and Anisotropic Plates with Circular Openings, Second Conference “Composite Materials: Testing and Design”, 20-22 April 1971, Anaheim, California, Amercan Society for Testing and Materials, 1972, pp. 363-381.
5. Berbinau P., Soutis C. A new approach for solving mixed boundary value problems along holes in orthotropic plates. International Journal of Solid and Arrangements, 2001, vol. 38, pp. 143-159.
6. Gruber B., Hufenbach W., Kroll L., Lepper M., Zhou B. Stress concentration of analysis of fiber-reinforced multilayered composites with pin-loded holes. Composites Science and Technology, 2007, vol. 67, pp. 1439-1450.
7. Puhui Chen, zhen Shen Stress Resultants and moments around holes in unsymmetrical composite laminates subjected to remote uniform loading. Mechanics Research Communications, vol. 30, 2003, pp. 79-86.
8. Toubal L., Karama M., Lorrain B. Stress concentration in a circular hole in composite plate. Compos. Struct., 2005, vol. 68, pp. 31-6.
9. Yang Z., Kim C.B., Cho C., Beom H.G. The concentration of stress and strain in finite thickness elastic plate containing a circular hole. Int J Solids Struct 2008; 45:713-31.
10. Yang Z., Kim C.B., Beom H.G., Cho C. The stress and strain concentrations of out-of-plane bending plate containing a circular hole. Int. J. Mech. Sci., 2010, vol. 52, pp. 836-46.
11. Yang Z. The stress and strain concentrations of an elliptical hole in an elastic plate of finite thickness subjected to tensile stress. Int. J. Fract., 2009, vol. 155(1), pp. 43-54.
12. Rhee J., Cho H.K., Marr D.J., Rowlands R.E. Local compliance, stress concentrations and strength in orthotropic materials. J. Strain Anal. Eng. Des., 2012, vol. 47(2), pp. 113-28.
13. Rhee J., Cho H.K., Marr D.J., Rowlands R.E. On reducing stressconcentrations in composites by controlling local structural stiffness. Proceedings of conference experimental and applied mechanics, 2005.
14. Jahed H., Noban M.R., Eshraghi M.A. ANSYS Finite Element. Iran: University Tehran, 2010.
15. Ever. J. Barbero, Finite element analysis of composite materials. CRC Press Tailor & Group, USA, 2008.
16. Matthews F.L, Davies G.A.O., Hitchings D., Soutis C. Finite element modeling of composite materials and structure. CRC Press Tailor & Group, USA, 2008.
17. Pal B., Haseebuddin M.R. Analytical Estimation of Elastic Properties of Polypropylene Fiber Matrix Composite by Finite Element. Advances in Materials Physics and Chemistry, 2012, vol. 2, no. 1, pp. 23-30.
18. Tawakol A., Enab A. Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Engineering Journal, 2014, vol. 5, iss. 3, pp. 839-850.
19. Vanin G. Micro Mechanical of composite materials. Kiev: Naukova Dumka, 1985.
20. Jones M. Robert Mechanics of Composite Materials. Taylor & Francis, USA, 1999.
21. Schmauderand S.Jr., Mishnaevsky L. Micromechanics and Nanosimulation of Metals and Composites, Springer, Germany (420), 2009.
22. Altenbach H., Fedorov V.A. Structural elastic and creep models of a UD composite in longitudinal shear. Mechanics of composite materials, 2007, vol. 43, №. 4, pp. 437-448.
23. Altenbach H., Fedorov V.A. Structural elastic and creep models of a ud composite in longitudinal shear. Mechanics of composite materials, 2007, vol. 43, no. 4, pp. 289-298.
24. Odegarda G.M., Pipesb R.B., Hubertc P. Comparison of Two Models of SWCN Polymer Composites. Composites Science and Technology, 2004, vol. 64, no. 7-8, pp. 1011-1020.
25. Whitney J.M., McCullough R.L. Micromechanical Materials Modeling.Delaware Composites Design Encyclopedia. Technomic, Lancaster, Basel, 1990. 232 c.
26. Fedorov V.A. Symmetry in a problem of transverse shear of unidirectional composites. Composites, Part B, 2014, no. 56, pp. 263-269.
27. Nguyen Dinh. Duc., Minh Khac. Bending analysis of three-phase polymer composite plates reinforced by glass fibers and titanium oxide particles. Computational Materials, 2010, vol. 49, no. 4, pp. 194-198.
28. Andrianov I.V., Danishevskii V.V., Guillet A., Pareige P. Effective properties and micro-mechanical response of filamentary composite wires under longitudinal shear. European Journal of Mechanics - A/Solids, 2005, vol. 24, no. 2, pp. 195-206.
29. Hutapea P., Yuan F.G., Pagano N.J. Micro-stress prediction in composite laminates with high stress gradients. International Journal of Solids and Structures, 2003, vol. 40, iss. 9, pp. 2215-2248.
30. Leepatov Yu.C., Omancki E.S. Composite materials Spravochnik. Kiev: Naukova Dumka, 1985.
31. Basov K.A. ANSYS Spravochnik pol’zovatelia. Moscow, 2005.

# Statistics

#### Views

Abstract - 96

PDF (Russian) - 68