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An Eshelby inclusion of parabolic shape in a Kirchhoff laminated anisotropic thin plate. (English) Zbl 1473.74087

An analytical solution to the Eshelby problem of a parabolic inclusion with uniform strains and curvatures in a middle plane of an infinite laminated anisotropic thin plate is derived. With aid of the Stroh octet formalism, the elastic field in an infinite Kirchhoff plate was obtained. The plate contains a parabolic Eshelby inclusion. The uniformity of elastic fields of membrane stresses, bending moments, strains, curvatures inside the parabolic inclusion are shown. Non-uniform elastic field in the exterior of the parabolic inclusion was obtained. The internal uniform elastic field and the exterior non-uniform elastic field in the vertex of the parabola are determined explicitly. The obtained solution is employed to study the elastic field inside a through-thickness elliptical elastic inhomogeneous inclusion embedded within a parabolic inclusion. It was established that the elastic field inside the elliptical inhomogeneity remains uniform.

MSC:

74K20 Plates
74E05 Inhomogeneity in solid mechanics
74E30 Composite and mixture properties
74S70 Complex-variable methods applied to problems in solid mechanics
74G05 Explicit solutions of equilibrium problems in solid mechanics
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