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 representationPb
FS3
FS1+2 Da
PS1 R1 R2 R3
PS2
PS3 R4 a a' d' d b c c' o Dd Pb
FS3
FS1+2 Da
PS1 R1 R2 R3
PS2
PS3 R4 a a' d' d b c c' o Dd 1 3 2 a b c d
Pb=-352 4
Mb=4800 F PS 1 2 3 D FS
1+2 a P b d R 1 H D 1 -I I R 2 3 -H D -I I H -H F 2 -I H 1 I H F 3 -I K C 4 K C 4

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
T-1 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
Applying the methodology for Integrated Systems
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 O G1
ΔCP1
JCF1 A ΔA B Dt G Δi Fi Δo Fo O C R G1 Vt
Two ports
Two ports V1 I1 V2 I2 R Vt G1
Electrical
Engineer
Electrical Engineer L B A Vt R vt qt ut Ft
Ft=f(ut,vt)
qt=f(ut,vt)

8. Checking system stability through transformations
Stable ???? 8 5 9 2 4 7 10 11 1 12 6 3 11 7 3 4 12 2 1 5 8 9 10 6
Due to links 1 and 9 being located on the same line
Definitely locked !!!!! 8 12 ’ 2 1 10 6 7 3 5 9 R’ 4 12 ’ 9 10 R’ 11 6 7 8 2 3 5 1 4