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Formulation of a Non‐linear Higher‐Order Shell Theory Using the Convective Description
Author(s) -
Sparr H.,
Ulbricht V.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310239
Subject(s) - boundary value problem , shell (structure) , tensor (intrinsic definition) , position (finance) , mathematical analysis , mathematics , series (stratigraphy) , space (punctuation) , surface (topology) , vector space , convection , classical mechanics , physics , computer science , geometry , mechanics , engineering , paleontology , civil engineering , finance , economics , biology , operating system
By formulating a higher‐order non‐linear shell theory, we start with the basic equations of continuum mechanics of a three‐dimensional body. By assuming a director set on a reference surface of a shell, the description shifts into the shell space. The position vector for the body is introduced as a power series with respect to the out‐of‐surface variable. By considering more than the usual linear part of the series, the complete three‐dimensional strain tensor is available. The motion of the continuum can be represented through the usage of the convective description which combines properties from both the spatial and the material description. Furthermore, the rate‐type formulation gives the opportunity to deal with geometrical nonlinearities in a three‐dimensional field problem efficiently. Following these two concepts results as well in a position‐dependent as in a time‐dependent base vector set; applying them leads to an initial boundary value problem (IBVP).