Civil Engineering Reference
In-Depth Information
the fi rst seed cluster. Then other members are brought in successively. There
are three distinct stages in the cluster formation process: Stage I - initial
clustering, Stage II - secondary clustering, and Stage III - reference cluster-
ing. In Stage I, members are allocated to an existing cluster when doing so
increases the well-formedness of the cluster. If two separate members when
added to an existing cluster separately produce the same well-formedness,
then other criteria are used to decide which of them should be admitted.
They are, in order, the maximum of the minimum damage demands, the
maximum nodal connectivity, and the maximum distance from the refer-
ence cluster. When there are no more members or clusters to be added,
which will increase the well-formedness of the cluster, then another cluster
is initialized. In Stage II, the value of the well-formedness of the growing
cluster will decrease as loosely connected existing clusters are combined.
Those clusters are merged together fi rst which result in least reduction of
the well-formedness. The criteria to terminate the process is that no further
valid structural clusters can be formed except by including the reference
cluster. The inclusion of the reference cluster is the fi nal Stage III of cluster
formation. The clustering fi nishes when the whole structure is one complete
cluster.
The exact growth of a cluster much depends on the nature of joints in
the cluster. In a 3D truss, a tetrahedron can grow in many different ways
by adding one or more members at a time. In a completely rigid-jointed
structure, a seed cluster grows by adding one neighbouring member or a
cluster at a time. Some typical clustering sequences for 2D/3D trusses and
frames are shown in Fig. 8.3. All members fi nally evolve, through different
clusters at a fi nite number of levels of description, into a single cluster which
represents the whole structure. Such a hierarchical representation (for an
example, see Fig. 8.7) results in continuing selective loss of details up the
hierarchy. It is a map showing how the clusters are inter-related.
8.3.3 Deteriorating events and failure scenarios
Deteriorating events affect structural form; they cause failure at the lowest
level in the hierarchy but may affect a large part of the hierarchy. The detail
and nature of the actions causing the deterioration are not considered at
this stage. These may arise, for example, due to excessive loading, natural
disaster, accidental force, or human errors. A deteriorating event has an
associated concept of damage demand which measures the effort required
to trigger that event. A failure scenario may have one or more deteriorating
events resulting in a failure mechanism. The consequences of failure events
of the same nature vary and largely depend upon how the corresponding
member or cluster is confi gured in the system hierarchy. The references (i.e.
supports) play an important role in determining the failure consequence.
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