#### 539.3 Multiscale modeling of thin multilayer composite plates with solitary defects

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University)

###### MULTISCALE MODELING, MULTILAYER THIN PLATES, COMPOSITE, SOLITARY DEFECTS, FINITE ELEMENT METHOD, ASYMPTOTIC DECOMPOSITION.

doi: 10.18698/2309-3684-2016-4-4766

We developed a multiscale model of deformation of thin multilayer composite plates with solitary defects. The model is based on the asymptotic analysis of general threedimensional equations of deformable solid mechanics. The general solution of threedimensional equations is reduced to the solution of two classes of problems: problems for thin plates without defects and local three-dimensional problems in the vicinity of the defect with the condition of damping solution at the distance from the defect. A solution of local problems is used for averaged problems of the multilayer plates theory, which enables us to find an explicit solution for all six components of the stress tensor in the field without the defect, based on the solution of the averaged two-dimensional problem of the plate theory. In the defect area the general solution is a superposition of the two solutions: the one obtained on the basis of the plates theory and local three-dimensional mechanics problems. The paper gives an example of a numerical finite element solution of the local mechanics problem for the three-layer composite plate with a solitary defect in the middle layer. Moreover, findings of the research show that the defect impact is localized in its immediate vicinity and the maximum transverse stress concentration is achieved in the vicinity of the defect peak.

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Dimitrienko Y., Yurin Y. Multiscale modeling of thin multilayer composite plates with solitary defects. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 47-66