The Nonlinear Theory of Elastic Shells: One Spatial Dimension

A simplified, nonlinear thermodynamic theory of beamshells

“…This paper presents a nonlinear thermodynamical theory for beamshells (infinite cylindrical shells in plane strain each of whose cross sections undergoes identical motion), building on an approach espoused by Simmonds [3], Libai and Simmonds [4][5][6], and others in which approximations are made only in the First Law of Thermodynamics or, equivalently, in the constitutive relations. Physically, this is reasonable because in any continuum theory, all the forms of energy that flow into a body (mechanical, thermal, electromagnetic, ... ) can never be totally accounted for and the constitutive relations, which ultimately rest on experiments, are never exact.…”

Existence, uniqueness, and decay estimates for solutions in the nonlinear theory of elastic, edge-loaded, circular tubes

“…The energy approach is examined with a view to more general shells where a Green's function may not be readily available. 1. Introduction.…”

“…We shall be concerned with a homogeneous, elastically isotropic, semi-infinite circular tube (cylindrical shell) of constant thickness h and midsurface radius R under axisymmetric edge loads. In classical, (first-approximation) theory, the linear field equations can be reduced to the following coupled system of secondorder ordinary differential equations [1]:…”

“…Our aim herein is to characterize, as far as possible, the analogous solution for a nonlinear version of (1.1), namely, the simplified Reissner equations [1,2], f" -e2/+ sin/? = 0, /?"…”

On finite displacements of curved annular elastic membranes without wrinkling

“…Neglecting the iMerm in (2.7), we get the so-called simplified Reissner model (cf. [13,18]), which has been the basis of extensive investigations on flat annular and circular membranes.…”