Analysis of engineering systems through graph representations

1
Analysis of engineering systems through graph
representations
2
Solving Engineering Analysis Problems

• The transformations are used to substitute the
  physical problems related with engineering system
  si with mathematical problem related with gk
• T(problem(si)) problem(gk)
• solution(problem(si))T(solution(problem(gk
  ))

Gl
Dj
T-1
T
solution(problem(gk))
problem(gk)
solution(problem(si))
problem(si)
3
Analysis of a frame through its graph
representation
I
I
4
Treating integrated systems

• When a number of engineering domains can be
  represented by the same graph representation,
  this representation can be used as unified
  representation of integrated systems comprising
  element corresponding to these domains.

Integrated systems
Da
Gl
Dc
T-1
T
Dd
Db
5
Graph representation of an integrated system
The highly coupled integrated system
The corresponding generalized Graph model
6
Equivalency between Node and Displacement Methods
7
Applying the methodology for Integrated Systems
Transferring the system, containing both
mechanical and electronic elements into a
unified graph representation
Now, the graph is interpreted as a representation
of a single electronic circuit, which enables the
electrical engineer to deal with the whole
integrated system, by himself.
Now, the integrated system is solved solely by
the electrical engineer
8
Checking system stability through transformations
Due to links 1 and 9 being located on the same
line