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**Complex potentials in two-dimensional problems of periodically layered elastic composites.**
*(English)*
Zbl 0669.73050

In this paper the complex variable method for two-dimensional problems of elasto-statics for periodically layered composites of plane structures is adopted. The consideration is based on the linear theory of elasticity with microlocal parameters proposed by C. Woźniak [e.g. Bull. Pol. Acad. Sci., Tech. Sci. 35, 365-370 (1987; Zbl 0623.73020); ibid. 35, 133-142 and 143-151 (1987; Zbl 0615.73003; Zbl 0615.73004)]. The complex potentials are introduced for the reduction of the two-dimensional elasto-static problems of the layered periodic composites to the boundary values problems of analytical functions.

Basing on Woźniak’s approach the authors present the following items: Formulation of the problem and the fundamental equations of the homogenized model of the periodic layered linear elastic composites for the two-dimensional elasto-static problems. Next, the complex representation of the solution for the equations of the homogenized model are introduced. Finally, a particular example describing the stress distribution in the periodic two-layered half-space is considered as an illustration of the presented method.

The method of complex potentials for the homogenized model of microperiodic two-layered composites which seems to be very useful and effective in two-dimensional problems may be probably applied to solve contact problems, crack problems, as well as two-dimensional problems of multilayered microperiodic composites.

Basing on Woźniak’s approach the authors present the following items: Formulation of the problem and the fundamental equations of the homogenized model of the periodic layered linear elastic composites for the two-dimensional elasto-static problems. Next, the complex representation of the solution for the equations of the homogenized model are introduced. Finally, a particular example describing the stress distribution in the periodic two-layered half-space is considered as an illustration of the presented method.

The method of complex potentials for the homogenized model of microperiodic two-layered composites which seems to be very useful and effective in two-dimensional problems may be probably applied to solve contact problems, crack problems, as well as two-dimensional problems of multilayered microperiodic composites.

Reviewer: Z.F.Baczyński

### MSC:

74E30 | Composite and mixture properties |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74E05 | Inhomogeneity in solid mechanics |