Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures

Abstract

The authors make no attempt to summarize the results available in this area through approximate solutions of various kinds to the 3-D field equations. Nor do they present, for readers prepared to utilize modern computer techniques, finite element, boundary integral, and other numerical techniques for obtaining such solutions. Finally, it seems to the reviewer that there is little added to this book by an "Introductory Chapter" of approximately 40 pages, authored by Sih, on the "strain-energy-density factor" theory of crack growth and its extension to 3-D problems. First, the chapter seems extraneous in the sense that nothing else in the book touches on theories of crack growth. But this theory, while presented with evident enthusiasm, seems to derive from no self-consistent or physically plausible description of the crack growth process. Instead, failure is assumed to occur when a local minimum value of the energy density, at some given radius from the crack tip, reaches a critical value. Why the energy density, and especially, a local minimum of it, should be chosen is unclear enough. But the function does indeed have a local minimum, in general, and it seems disconcerting to take as critical a value of the energy density for which both greater and lesser values occur at other points at the same given radius from the crack tip. Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures.

Strain measures and compatibility equations in the linear high-order shell theories

“…By identifying the coefficients of the same powers in (13) and (20), the following relationship between and results:…”

“…(i) in the monograph [19], the general theory of shells as substantiated in the framework of the Cosserat continuum concept furnishes valuable results for the high-order shell (and plate) theories, as well, and (ii) a large part of the monograph [20] deals with the substantiation of the high-order shell (and plate) theories, treated both in linear and nonlinear formulations. compatibility equations (C.E.)…”

The resultant linear six‐field theory of elastic shells: What it brings to the classical linear shell models?

“…The refined linear theory of elastic shells with an additional account of transverse shear deformations, here called of the TimoshenkoReissner type, was extensively treated for example by Naghdi [8], Librescu [9], Pelekh [10], or Reddy [11]. Almost all linear versions of shell theory are based on various approximations in kinematical description of linear elasticity following from a through-the-thickness polynomial expansion with truncation at some level, asymptotic analyses, applying kinematic constraints etc., see Fig.…”

A parametric study on supersonic/hypersonic flutter behavior of aero-thermo-elastic geometrically imperfect curved skin panel

“…It was recognized that geometrical non-linearities due to moderate plate deflection (mainly mid-plane stretching forces) represented following the Von Kármán large deflection plate theory combined with the linear piston theory, one of the popular unsteady aerodynamic theories used, can play an important role in panel flutter [8]. This led to a number of studies [9][10][11][12][13][14][15][16] which showed that, when geometrically nonlinearities are included in the model, the linear stability boundary can be exceeded, thereby inducing stable LCO with finite amplitudes, having an order of magnitude equal to the thickness of the panel. Librescu et al [66][67][68] presented the analytical results of simply supported single-layer and three-layer flat and curved panels made from transversely isotropic materials.…”

“…These panels are subjected to in-plane loads and normal aerodynamic loads, and it is well known that unstable oscillatory motions of the panels can be caused by the coupling of elastic, inertia, and acting aerodynamic forces. This phenomenon is known as "panel flutter" [4,[9][10][11]. Dynamic aeroelastic instabilities, such as the panel flutter, are of great concern for aerospace designers, since these instabilities can lead to immediate failure or long-term fatigue failure.…”