It is commonly understood that if a structure with certain symmetry is
subjected to loading with identical symmetry, considerable time and
computational effort can be saved by making use of this symmetry as
part of an analysis. It is less well known these savings are also available
if the structure is subjected to any general loading.
An example of a general analysis that is well understood (and is even
part of the engineering department's second year structural mechanics
course!) is the use of symmetry and antisymmetry to
simplify the analysis of a structure with bilateral symmetry. This
talk will outline how the same basic ideas can be extended to
structures with more complicated symmetries using group
representation theory.
A recent development has been the application of group representation
theory to equilibrium and compatibility relationships for symmetric
structures. The talk will outline this development, and describe
some of its implications to understanding the mechanics of symmetric
structures. These include the ability to detect finite
mechanisms based only on a linear analysis and symmetry arguments, and
the development of a symmetry extension of Maxwell's rule for the
rigidity of frames.
