Temat: asymptotic shell - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Characterization of the space of solutions of the membrane shell equation for arbitrary C[sup 11] midsurfaces
Autorzy:: Delfour, M.
Powiązania:: https://bibliotekanauki.pl/articles/206735.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: asymptotic shell models
membrane shell equation
shells
Opis:: A comprehensive convergence theory of dynamical thin shell models for the purposes of control theory relies heavily on a thorough analysis of the static model and the complete specification of the spaces of solutions of the asymptotic solution for general midsurfaces ranging from the plate to arbitrary C[sup 1,1] midsurfaces. In this paper the existence of solution to the membrane shell equation is studied in a bounded open connected domain [omega] (Lipschitzian when [omega] has a boundary [gamma]) in a C[sup 1,1] midsurface for homogeneous Neumann boundary conditions or homogeneous Dirichlet boundary conditions on a part [gamma,omikron] of [gamma]. It is proved that its tangential part is solution of the reduced membrane shell equation in H[sup 1](omega)[sup N] (resp. H[sup 1][sub gamma,omikron](omega)[sup N]) unique up to an element of a finite dimensional subspace, while its normal component belongs to a weighted L[sup 2](omega) space by the pointwise norm of the second fundamental form. It is also shown that the reduced equation is equivalent to the equation for the projection onto the linear subspace of vector functions whose linear change of metric tensor is orthogonal to the second fundamental form of the midsurface.
Źródło:: Control and Cybernetics; 1999, 28, 3; 481-501
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
Autorzy:: Delfour, M. C.
Powiązania:: https://bibliotekanauki.pl/articles/970297.pdf
Data publikacji:: 2008
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: thin shell
asymptotic shell
midsurface
smoothness
representation of a surface
oriented distance function
bi-Lipschitz mapping
tubular neighborhood
Opis:: Many hypersurfaces ω in R^N can be viewed as a subset of the boundary Γ of an open subset Ω of R^N. In such cases, the gradient and Hessian matrix of the associated oriented distance function ba to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C1'1-hypersurfaces is available in Delfour (2000). In the theory of thin shells, the asymptotic model only depends on the choice of the constitutive law, the midsurface, and the space of solutions that properly handles the loading applied to the shell and the boundary conditions. A central issue is the minimal smoothness of the midsurface to still make sense of asymptotic membrane shell and bending equations without ad hoc mechanical or mathematical assumptions. This is possible for a C1'1-midsurface with or without boundary and without local maps, local bases, and Christoffel symbols via the purely intrinsic methods developed by Delfour and Zolesio (1995a) in 1992. Anicic, LeDret and Raoult (2004) introduced in 2004 a family of surfaces ω that are the image of a connected bounded open Lipschitzian domain in R² by a bi-Lipschitzian mapping with the assumption that the normal field is globally Lipschizian. >From this, they construct a tubular neighborhood of thickness 2h around the surface and show that for sufficiently small h the associated tubular neighborhood mapping is bi-Lipschitzian. We prove that such surfaces are C1'1-surfaces with a bounded measurable second fundamental form. We show that the tubular neighborhood can be completely described by the algebraic distance function to ω and that it is generally not a Lipschitzian domain in R³ by providing the example of a plate around a flat surface ω verifying all their assumptions. Therefore, the G1-join of K-regular patches in the sense of Le Dret (2004) generates a new K-regular patch that is a C1'1-surface and the join is C1'1. Finally, we generalize everything to hypersurfaces generated by a bi-Lipschitzian mapping defined on a domain with facets (e.g. for sphere, torus). We also give conditions for the decomposition of a C1'1-hypersurface into C1'1-patches.
Źródło:: Control and Cybernetics; 2008, 37, 4; 879-911
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Hybrid asymtotic method for the effect of local thickness defects and initial imperfections on the buckling of cylindrical shells
Hybrydowa asymptotyczna metoda szacowania wpływu lokalnych zmian grubości i początkowych zaburzeń strukturalnych na wyboczenie powłok walcowych
Autorzy:: Gristchak, V. Z.
Golovan, O. A.
Powiązania:: https://bibliotekanauki.pl/articles/280445.pdf
Data publikacji:: 2003
Wydawca:: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:: cylindrical shell
asymptotic method
local thickness defects
initial imperfections
asymptotic formulas
Opis:: A double asymptotic method for the effect of local thickness defects and initial imperfections on the buckling problems of some mechanical systems is proposed. asymptotic formulas for the critical buckling load parameter are obtained with the perturbation technique.
W pracy zaprezentowano podwójnie asymptotyczną metodę szacowania wpływu początkowych zaburzeń strukturalnych i lokalnych uszkodzeń zmieniających grubość na wyboczenie wybranych układów mechanicznych. Zastosowane wyrażenia asymptotyczne pozwalające na określenie krytycznych parametrów wyboczenia otrzymano techniką perturbacyjną.
Źródło:: Journal of Theoretical and Applied Mechanics; 2003, 41, 3; 509-520
1429-2955
Pojawia się w:: Journal of Theoretical and Applied Mechanics
Dostawca treści:: Biblioteka Nauki

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