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On displacements and stresses in a semi-infinite laminated layer: comparative results

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Abstract

This paper deals with some comparison results for displacements and stresses in a periodically stratified elastic semi-infinite layer determined within the framework of two approaches: (1) based on the homogenized model with microlocal parameters [Woźniak (1987) Int J Eng Sci 25: 483–499; Woźniak (1987) Bull Ac Pol Tech Sci 35: 143–151]; (2) obtained directly from the theory of elasticity. A body is assumed to be composed of n elastic two-component periodically repeated laminae. The perfect mechanical bonding between the layers is assumed. The normal displacements and zero shear stresses on the boundary being a cross-section of the composite component are taken into account. The lateral boundary surfaces are assumed to be rigid fixed. The obtained results from the two approaches are compared and presented in the form of figures.

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References

  1. Achenbach JD (1975) A theory of elasticity with microstructure for directionally reinforced composites. CISM Courses and Lectures. Springer, New York

    Google Scholar 

  2. Bakhalov NS, Panasenko GP (1984) Averaged processes in periodic media. Nauka, Moscow (in Russian)

  3. Bensonssan A, Lions JL, Papanicolaou G (1978) Asymptotic analysis for periodic structures. North Holland, Amsterdam

    Google Scholar 

  4. Broutman LJ, Krock RH (1973–1976) Composite materials. Academic Press, New York, pp 1–8

  5. Christensen RM (1980) Mechanics of composite materials. Wiley, New York

    Google Scholar 

  6. Guz AN et al (1982) Mechanics of composite materials and elements constructions. Naukova Dumka, Kiev (in Moscow)

    Google Scholar 

  7. Jones R (1975) Mechanics of composite materials. McGraw-Hill Book Co., New York

    Google Scholar 

  8. Kaczyński A (1993) On the three-dimensional thermoelastic problems of interface cracks in periodic two-layered composites. Int J Fract 62:283–306

    ADS  Google Scholar 

  9. Kaczyński A, Matysiak SJ (1988) On crack problems in periodic two-layered composites. Int J Fract 37:31–45

    Article  Google Scholar 

  10. Kaczyński A, Matysiak SJ (1989) A system of interface cracks in a periodically layered elastic composites. Eng Fract Mech 32:745–756

    Article  Google Scholar 

  11. Kaczyński A, Matysiak SJ (1988) Plane contact problems of periodic two-layered elastic composite. Ing Arch 58:137–147

    Article  Google Scholar 

  12. Kaczyński A, Matysiak SJ, (1993) Influence of a concentrated body force on an interface crack in periodic two–layered elastic space. Bull Pol Ac: Tech Sci 41: 67–78

    Google Scholar 

  13. Kaczyński A, Matysiak SJ, (1988) On the complex potentials for the linear thermoelasticity with microlocal parameters. Acta Mech 72:245–259

    Article  MathSciNet  Google Scholar 

  14. Kulchytsky-Zhyhailo R, Matysiak SJ (2005) On heat conduction problem in a semi–infinite periodically laminated layer. Int Comm Heat Mass Transfer 32:123–132

    Article  Google Scholar 

  15. Kulchytsky-Zhyhailo R, Matysiak SJ (2005) On some heat conduction problem in a periodically two–layered body. Comparative results. Int Comm Heat Mass Transfer 32:332–340

    Article  Google Scholar 

  16. Matysiak SJ (1995) On the microlocal parameter method in modeling of periodically layered thermoelastic composites. J Theor Appl Mech 33:481–487

    Google Scholar 

  17. Matysiak SJ (1989) Thermal stresses in a periodic two–layered composite weakened by an interface crak. Acta Mech 78:95–108

    Article  MathSciNet  Google Scholar 

  18. Matysiak SJ, Pauk V (1995) Plane contact problem for periodic laminated composite involving frictional heating. Arch Appl Mech 66:82–89

    MATH  Google Scholar 

  19. Matysiak SJ, Woźniak C (1987) Micromorphic effects in a modeling of periodic multilayered elastic composites. Int J Eng Sci 25:549–559

    Article  MATH  Google Scholar 

  20. Pobedria BJ (1984) Mechanics of composite materials. Izd. Moscow University, Moscow (in Russian)

    Google Scholar 

  21. Sanchez-Palencia E (1980) Nonhomogeneus media and vibration theory. Springer, Berlin

    Google Scholar 

  22. Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic. Publ Comp., Westport

    Google Scholar 

  23. Vanin GA (1985) Micromechanics of composite materials. Naukova Dumka, Kiev (in Russian)

    Google Scholar 

  24. Woźniak C (1987) A nonstandard method of modeling of thermoelastic periodic composites. Int J Eng Sci 25:483–499

    Article  Google Scholar 

  25. Woźniak C (1987) On the linearized problems of thermoelasticity with microlocal parameters. Bull Ac. Pol.: Techn. Sci 35:143–151

    Google Scholar 

  26. Woźniak C, Woźniak M (1995) Modeling of composites. Theory and applications. IFTR Reports, Warsaw (in Polish)

  27. Vannucci P (2005) Plane anisotropy by the polar method. Meccanica 40:437–454

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Bialystok University of Technology, 45C, Wiejska St, 15-351, Bialystok, Poland

    Roman Kulchytsky-Zhyhailo, Stanislaw J. Matysiak & Dariusz M. Perkowski

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  1. Roman Kulchytsky-Zhyhailo
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  2. Stanislaw J. Matysiak
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  3. Dariusz M. Perkowski
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Correspondence to Stanislaw J. Matysiak.

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Kulchytsky-Zhyhailo, R., Matysiak, S.J. & Perkowski, D.M. On displacements and stresses in a semi-infinite laminated layer: comparative results. Meccanica 42, 117–126 (2007). https://doi.org/10.1007/s11012-006-9026-6

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  • DOI: https://doi.org/10.1007/s11012-006-9026-6

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