Summary
This paper deals with the two-dimensional static punch problems in the presence of friction for a periodically layered half-space. Within the framework of the homogenized model of linear elasticity with microlocal parameters [8–11] the exact solutions of the considered problems are obtained. The case of the indentation of the composite body by a rigid rectangular punch has been discussed in detail.
Übersicht
In dieser Arbeit wird das zweidimensionale statische Stempelproblem mit Reibung für einen periodisch geschichteten Halbraum betrachtet. Im Rahmen eines Homogenisierungsmodells der linearen Elastizitätstheorie mit mikropolaren Parametern werden die exakten Lösungen der betrachteten Probleme gewonnen. Im Detail wird das Eindringen eines rechteckigen starren Stempels behandelt.
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References
Bahvalov, N. S.; Panasenko, G. P.: Averaging methods for processes in periodic bodies (in Russian). Moscow: Science 1984
Bensoussan, A.; Lions, J. L.; Papanicolaou, G.: Asymptotic analysis for periodic structure. Amsterdam: North Holland 1978
Sanchez-Palencia, E.: Non-homogeneous media and vibration theory (Lecture notes in physics, no. 127). Berlin, Heidelberg, New York: Springer 1980
Achenbach, J. D.: A theory of elasticity with microstructure for directionally reinforced composites (CISM courses and lectures, no. 167). Wien, New York: Springer 1975
Christensen, R. M.: Mechanics of composite materials. New York: Wiley-Interscience 1979
Jones, R.: Mechanics of composite materials. New York: McGraw-Hill 1975
Bufler, H.: Theory of elasticity of a multilayered medium. J. Elasticity 2 (1971) 125–143
Woźniak, Cz.: A nonstandard method of modelling of thermoelastic periodic composites. Int. J. Eng. Sci. 5 (1987) 483–499
Woźniak, Cz.: Nonstandard analysis in mechanics. Adv. Mech. 1 (1986) 3–35
Woźniak, Cz.: Nonstandard analysis and microlocal effects in the multilayered bodies. Bull. Pol. Acad. Sci. Tech. Sci. 34 (1986) 385–392
Matysiak, S. J.; Woźniak, Cz.: Micromorphic effects in a modelling of periodic multilayered elastic composites. Int. J. Eng. Sci. 5 (1987) 549–559
Kaczyński, A.; Matysiak, S. J.: Complex potentials in two-dimensional problems of periodically layered elastic composites. Mech. Teor. Stosow. 25 (1987)
Kaczyński, A.; Matysiak, S. J.: On crack problems in periodic two-layered elastic composites. Int. J. Fract. (submitted for publication)
Matysiak, S. J.; Woźniak, Cz.: On the modelling of thermoelastic periodic composites. J. Tech. Phys. (submitted for publication)
Muskhelishvili, N. I.: Some basic problems of mathematical theory of elasticity. Groningen: Noordhoff 1953
Muskhelishvili, N. I.: Singular integral equations. Groningen: Noordhoff 1953
Gakhov, F. D.: Boundary-value problems (in Russian). Moscow: Science 1977
Galin, L. A.: Contact problems of the theory of elasticity and viscoelasticity (in Russian). Moscow: Science 1980
Gladwell, G. M. L.: Contact problems in the classical theory of elasticity. Amsterdam: Sijthoff and Noordhoff 1980
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Kaczyński, A., Matysiak, S.J. Plane contact problems for a periodic two-layered elastic composite. Ing. arch 58, 137–147 (1988). https://doi.org/10.1007/BF00536233
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DOI: https://doi.org/10.1007/BF00536233