Analysis of engineering systems through graph representations Solving

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 solution(problem(si) i)) solution(problem(gk) k))

Analysis of a frame through its graph representation R 4 RR 11 a PS 1 a' b PS 2 c' R 2 PS 3 c d' R 3 d Pb FS 3 FS 1+2 Da o R 0 0 H -I 0 0 R 0 -H -I I 0 0 R 0 H -I -H -I 0 0 I H -I 0 K D 1 R 1 D 2 R 3 F 1 D 3 F 2 F 3 Dd C 4 F F F D D PS 1 PS 2 PS 3 FS 1+2 FS 3 I 0 0 0 -I K 0 0 C 4 a D D F b D a D d P b 1 Pb=-352 Mb=4800 4 d 3 2 c

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 Dc Dd Gl T-1 Db

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

Equivalency between Node and Displacement Methods

Transferring theis system, both mechanical Now, Applying the Now, graph interpreted as asystem representation offor a single the containing methodology the integrated is solved electronic circuit, which enables the electrical engineer to deal and electronic elements into a unified graph solely by the electrical engineer Integrated Systems with the wholerepresentation integrated system, by himself. G 1 ΔCP 1 A G B JCF 1 C Δi Δo Fi ΔA O The forces in Two portsthe. V beam affects 1 Dt Fo The electrostatic force affects the distance between the capacitor plates R ut Ft the. I 1 electrostatic force O L A The distance between Vthe 2 Gcapacitor 1 plates I affects the 2 force in the beam R vt qt B Ft=f(ut, vt) qt=f(ut, vt) Vt Electrical Engineer Vt

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