文档介绍：T. Belytschko, Chapter 9, Shells and Structures, December 16, 1998
CHAPTER 9
SHELLS AND STRUCTURES
DRAFT
by Ted Belytschko
Northwestern University
Copyright 1997
INTRODUCTION
Shell elements and other structural elements are invaluable in the modeling of
many ponents and natural structures. Thin shells appear in many
products, such as the sheet metal in an automobile, the fuselage, wings and rudder of an
airplane, the housings of products such as cell phones, washing machines, computers.
Modeling these items with continuum elements would require a huge number of elements
and lead to extremely putations. As we have seen in Chapter 8, modeling a
beam with hexahedral continuum elements requires a minimum of about 5 elements
through the thickness. Thus even a low order shell element can replace 5 or more
continuum elements, which putational efficiency immensely. Furthermore,
modeling thin structures with continuum elements often leads to elements with high
aspect ratios, which degrades the conditioning of the equations and the accuracy of the
solution. In explicit methods, continuum element models of shells are restricited to very
small stable time steps. Thus it can be seen that structural elements are very useful in
engineering analysis.
Structural elements are classified as:
1. beams, in which the motion is described as the function of a single independent
variable;
2. shells, where the motion is described as a function of two independent
variables;
3. plates, which are flat shells.
Plates are usually modeled by shell elements puter software. Since they are just
flat shells, we will not consider plate elements separately. Beams on the other hand,
require some additional theoretical considerations and provide simple models for learning
the fundamentals of structural elements, so we will devote a substantial part of this
chapter to beams.
There are two approaches to developing shell finite elements:
1. develop the formulatio