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On displacements and stresses in a semi-infinite laminated layer: Comparative results. (English) Zbl 1162.74342

Summary: 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 [Cz. Woźniak [Int. J. Eng. Sci. 25, 483–498 (1987; Zbl 0607.73010); Bull. Pol. Acad. Sci., Tech. Sci. 35, 133–142 and 143–151 (1987; Zbl 0615.73003; Zbl 0615.73004)]; (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.

MSC:

74E30 Composite and mixture properties
74Q05 Homogenization in equilibrium problems of solid mechanics
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[1] Achenbach JD (1975) A theory of elasticity with microstructure for directionally reinforced composites. CISM Courses and Lectures. Springer, New York · Zbl 0381.73022
[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
[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
[6] Guz AN et al (1982) Mechanics of composite materials and elements constructions. Naukova Dumka, Kiev (in Moscow)
[7] Jones R (1975) Mechanics of composite materials. McGraw-Hill Book Co., New York
[8] Kaczyński A (1993) On the three-dimensional thermoelastic problems of interface cracks in periodic two-layered composites. Int J Fract 62:283–306
[9] Kaczyński A, Matysiak SJ (1988) On crack problems in periodic two-layered composites. Int J Fract 37:31–45 · doi:10.1007/BF00017821
[10] Kaczyński A, Matysiak SJ (1989) A system of interface cracks in a periodically layered elastic composites. Eng Fract Mech 32:745–756 · doi:10.1016/0013-7944(89)90171-9
[11] Kaczyński A, Matysiak SJ (1988) Plane contact problems of periodic two-layered elastic composite. Ing Arch 58:137–147 · Zbl 0631.73096 · doi:10.1007/BF00536233
[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 · Zbl 0777.73053
[13] Kaczyński A, Matysiak SJ, (1988) On the complex potentials for the linear thermoelasticity with microlocal parameters. Acta Mech 72:245–259 · Zbl 0652.73006 · doi:10.1007/BF01178311
[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 · doi:10.1016/j.icheatmasstransfer.2004.08.023
[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 · doi:10.1016/j.icheatmasstransfer.2004.05.014
[16] Matysiak SJ (1995) On the microlocal parameter method in modeling of periodically layered thermoelastic composites. J Theor Appl Mech 33:481–487
[17] Matysiak SJ (1989) Thermal stresses in a periodic two–layered composite weakened by an interface crak. Acta Mech 78:95–108 · Zbl 0687.73011 · doi:10.1007/BF01174003
[18] Matysiak SJ, Pauk V (1995) Plane contact problem for periodic laminated composite involving frictional heating. Arch Appl Mech 66:82–89 · Zbl 0837.73065
[19] Matysiak SJ, Woźniak C (1987) Micromorphic effects in a modeling of periodic multilayered elastic composites. Int J Eng Sci 25:549–559 · Zbl 0607.73011 · doi:10.1016/0020-7225(87)90106-6
[20] Pobedria BJ (1984) Mechanics of composite materials. Izd. Moscow University, Moscow (in Russian)
[21] Sanchez-Palencia E (1980) Nonhomogeneus media and vibration theory. Springer, Berlin · Zbl 0432.70002
[22] Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic. Publ Comp., Westport
[23] Vanin GA (1985) Micromechanics of composite materials. Naukova Dumka, Kiev (in Russian) · Zbl 0602.73055
[24] Woźniak C (1987) A nonstandard method of modeling of thermoelastic periodic composites. Int J Eng Sci 25:483–499 · Zbl 0607.73010 · doi:10.1016/0020-7225(87)90102-9
[25] Woźniak C (1987) On the linearized problems of thermoelasticity with microlocal parameters. Bull Ac. Pol.: Techn. Sci 35:143–151 · Zbl 0615.73004
[26] Woźniak C, Woźniak M (1995) Modeling of composites. Theory and applications. IFTR Reports, Warsaw (in Polish) · Zbl 0831.05054
[27] Vannucci P (2005) Plane anisotropy by the polar method. Meccanica 40:437–454 · Zbl 1106.74016 · doi:10.1007/s11012-005-2132-z
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