Numerical analysis of heterogeneous mathematical model of elastic body with thin inclusion by combined BEM and FEM

This article dwells upon the multiscale elastic structures consisting of matrix medium and thin coatings or inclusions.  The matrix medium is described by the equations of classical elasticity theory, while Timoshenko shell theory is used for the description of the thin parts of the structure.   On the interface between media, perfect contact conditions are assumed to hold.  The coupled algorithm is developed, based on the boundary element method in the matrix part and on the high order finite element method in the thin parts of the structure.  The two methods are coupled using a domain decomposition approach.  Two numerical examples are considered to illustrate the proposed approach: a Girkmann-type problem and an elastic structure with a thin inclusion.  The dependence of the displacement and the stress-strain state on the different shell shapes in the first example and on the inclusion thicknesses in the second example are analyzed.

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Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 239–250 (2019)