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Homogenization of fissured Reissner-like plates. III: Some particular cases and illustrative example. (English) Zbl 0738.73037

In the first part of the paper [ibid. 40, No. 1, 97-117 (1988; Zbl 0702.73004)] the method of two-scale asymptotic expansions was used to derive the general formulae describing various homogenized models of Reissner-like plates. From a rigorously mathematical viewpoint such an approach is formal. A rigorous study of the convergence as \(\varepsilon\to 0\) has been presented in part II [ibid. 40, No. 1, 119- 134 (1988; Zbl 0702.73005)].
The last part of the paper is concerned with two problems. First, in Sect. 2, we discuss three particular cases of homogenization of fissured plates. These cases are determined by the bending cracking mode, shear cracking mode and tension cracking mode. For the first case we show that the curvature tensor influences the membrane forces and vice-versa, the moment tensor is influenced by the in-plane strain tensor. Section 3 presents an example of homogenization of the Reissner-like plate weakened by fissures distributed parallely to one of the in-plane coordinate axes. Flexural fissures are studied. Though the fissures considered are not microfissures and the basic cell not connected, yet the derived homogenization formulae can effectively be applied.

MSC:

74K20 Plates
74E05 Inhomogeneity in solid mechanics
74R99 Fracture and damage
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure