Analysis of engineering systems through graph representations

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Presentation transcript:

Analysis of engineering systems through graph representations

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)

Analysis of a frame through its graph representation Pb 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

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

Graph representation of an integrated system The highly coupled integrated system The corresponding generalized Graph model

Equivalency between Node and Displacement Methods

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)

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