In the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the shell and solids.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
I. I. Vorovich, “On the existence of solutions in the nonlinear theory of shells,” Izv. Akad.Nauk SSSR Ser. Mat. 19 (4), 173–186 (1955).
I. I. Vorovich, “On the existence of solutions in the nonlinear theory of shells,” Dokl. Akad. Nauk SSSR (N.S.) 117 (2), 203–206 (1957).
I. I. Vorovich, Mathematical Problems of the Nonlinear Theory of Shallow Shells (Nauka, Moscow, 1989) [in Russian].
L. P. Lebedev and V. A. Eremeyev, “Academician Iosif I. Vorovich,” ZAMM 91 (6), 429–432 (2011).
P. G. Ciarlet, Mathematical Elasticity, Vol. III: Theory of Shells (Elsevier, Amsterdam, 2000).
L. P. Lebedev, “On the solution of a dynamic problem for viscoelastic shells,” Dokl. AN SSSR, 267 (1), 62–64 (1982).
V. A. Eremeyev and L. M. Zubov, Mechanics of Elastic Shells (Nauka, Moscow, 2008) [in Russian].
V. A. Eremeyev, L. P. Lebedev, and H. Altenbach, Foundations of Micropolar Mechanics (Springer, Heidelberg, 2013).
V. A. Eremeyev, M. J. Cloud, and L. P. Lebedev, Applications of Tensor Analysis in Continuum Mechanics (World Scientific, New Jersey, 2018).
A. Libai and J. G. Simmonds, The Nonlinear Theory of Elastic Shells (Cambridge Univ. Press, Cambridge, 1998).
V. Konopińska and W. Pietraszkiewicz, “Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells,” Int. J. Solids Struct. 44 (1), 352–369 (2007).
J. Chróścielewski, A. Sabik, B. Sobczyk, and W. Witkowski, “2-D constitutive equations for orthotropic Cosserat type laminated shells in finite element analysis,” Compos. Part B: Eng. 165, 335–353 (2019).
V. A. Eremeyev and L. P. Lebedev, “Existence theorems in the linear theory of micropolar shells,” ZAMM 91 (6), 468–476 (2011).
V. A. Eremeyev and L. P. Lebedev, “Existence of weak solutions in elasticity,” Math. Mech. Solids 18 (2), 204–217 (2013).
V. A. Eremeyev, F. dell’ Isola, C. Boutin, and D. Steigmann, “Linear pantographic sheets: existence and uniqueness of weak solutions,” J. Elast. 132 (2), 175–196 (2018).
This work was supported by the Russian Foundation for Basic Research (grant no. 20-08-00450А).
Translated by I. K. Katuev
About this article
Cite this article
Eremeev, V.A., Lebedev, L.P. On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions. Mech. Solids 55, 852–856 (2020). https://doi.org/10.3103/S0025654420050052
- micropolar shells
- weak solutions
- existence and uniqueness
- rigid inclusions