Lower dimensional approximation of eigenvalue problem for thin elastic shells with nonuniform thickness. (English) Zbl 1468.74034

Job, M.; Sabu, N.

Int. J. Adv. Appl. Math. Mech. 8, No. 1, 27-39 (2020).

Summary: In this paper we consider the eigenvalue problem for thin elastic shells with nonuniform thickness and show that as the thickness goes to zero the eigensolutions of the three dimensional problem converge to the eigensolutions of a two dimensional eigenvalue problem.

MSC:

74K25	Shells
74G10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35Q74	PDEs in connection with mechanics of deformable solids

Keywords:

shallow shell; flexural shell; eigenvalue problem; vanishing thickness; a priori estimate; convergence

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