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CHAPTER 8
ELEMENT TECHNOLOGY
by Ted Belytschko
Northwestern University
@ Copyright 1997
Introduction
Element technology is concerned with obtaining elements with better performance,
particularly for large-scale calculations and for pressible materials. For large-scale
calculations, element technology has focused primarily on underintegration to achieve faster
elements. For three dimensions, cost reductions on the order of 8 have been achieved
through underintegration. However, underintegration requires the stabilization of the
element. Although stabilization has not been too popular in the academic literature, it is
ubiquitous in large scale calculations in industry. As shown in this chapter, it has a firm
theoretical basis and can bined with multi-field weak forms to obtain elements which
are of high accuracy.
The second major thrust of element technology in continuum elements has been to
eliminate the difficulties associated with the treatment of pressible materials. Low-
order elements, when applied to pressible materials, tend to exhibit volumetric
locking. In volumetric locking, the displacements are underpredicted by large factors, 5 to
10 is not mon for otherwise reasonable meshes. Although pressible materials
are quite rare in linear stress analysis, in the nonlinear regime many materials behave in a
nearly pressible manner. For example, Mises elastic-plastic materials are
pressible in their plastic behavior. Though the elastic behavior may pressible,
the overall behavior is nearly pressible, and an element that locks volumetrically will
not perform well for Mises elastic-plastic materials. Rubbers are also pressible in
large deformations. To be applicable to a large class of nonlinear materials, an element
must be able to treat pressible materials effectively. However, most elements have
ings in their performance when applied to pressible or nearly
pressible materials. An understanding of these ings are crucial in the
s