# Analysis of Symmetric Structures using Group Theory and the Force Method

## R D Kangwai

*Abstract*:

A symmetric structure is a structure that can be brought into a new position
which is mechanically and geometrically identical to its original position.
Symmetric structures commonly occur in nature and in engineering design due
to their optimal load carrying abilities and their aesthetic appeal.

The symmetry properties of a structure allows any structural problem to
be simplified into smaller subproblems using group theory. Group theory
is the mathematical language best suited to the description of the symmetry
properties of a structure. Using group theory the symmetry properties
of even the most complex structure can be fully exploited.

Previous work applied group theory to the stiffness method of structural
analysis in order to exploit symmetry properties of the structure and hence
simplify the analysis of the induced displacements of the structure.
This thesis provides a new application of group theory to the force method
of structural analysis in order to simplify the full analysis of a symmetric
structure. The equilibrium equations can be decomposed into a number
of independent subsystems of equations, each with differing symmetry properties
of the structure. The induced bar-forces, bar elongations and displacements
of the structure can be found by solving these subsystems of equilibrium equations.
In particular, states of self-stress and inextensional mechanisms in each
of these subsystems of equilibrium equations can be found which have the
particular symmetry properties of the subsystem.

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This page is maintained by rcb@eng.cam.ac.uk (last update 10 November 2003)