Asymptotic analysis of boundary value problems for strongly inhomogeneous multi-layered elastic plates

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Civil, aerospace and automotive engineering are nowadays facing exciting industrial developments, inspiring new multifunctional and sustainable materials to be implemented within structural components. A key area, experiencing major technological changes, is concerned with design of multi-layered structures which are often characterised by a high contrast in mechanical and geometric properties of the layers. A diverse variety of such composites arises in numerous applications, including lightweight structural components widely exploited in automotive engineering which is currently strongly focused on green car production. In addition, the modern aerospace industry benefits from making use of multi-layered structures incorporating new lightweight multifunctional materials, such as aerogels, providing both thermal and acoustical insulation in aircrafts. In spite of rapidly growing industrial demands, a consistent mathematical approach for modelling of thin elastic laminates with a strong vertical inhomogeneity has not yet been developed. The main reason for this is presence of the contrast in mechanical and geometrical characteristics, resulting in numerous extra problem parameters. Another fundamental problem is that the most practically important low-frequency vibrations of high-contrast laminates manifest novel features which has not been previously observed for homogeneous or weakly inhomogeneous structures. A sophisticated low-frequency response significantly complicates interpretation of numerical and experimental data aimed at structural optimisation and non-destructive evaluation.This project will provide a fairly universal approximate model for high-contrast multi-layered thin plates covering a broad range of problem parameters and involving the mathematically consistent equations of the low-frequency motion and the boundary conditions along the edges. The derivation of the boundary conditions is traditionally the main challenge in the rigorous theories for thin elastic structures and have been attempted only within the homogeneous framework.