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3. Geometry Stase constraints to form the sys.
• solve for joint displacements
• if all disp. Zero, stable; otherwise unstable；...
3 -5§2 Elem. Analysis element = member
§ Element model and division Coord.
• rigid members y v2
θ θ2
• two nodes with local x u2
numbers 1, 2 l 2
• each node has 3 disp. v1
components (DOF) θ1
• an elem. has 6 DOF u1
e T 1
Δ = {u1 v1 θ1 u2 v2 θ2}
• small displacement θ positive frm x to y
• 6 disp. not independent
3 -6Modeling actual components
Internal redundant
constraints
3 -7§ Element geometry constraint equations
2”
u1
Disp.：12 → 1′2′
Rot.：1′2′ → 1′2′′ 2’
θ1 = θ2 v2
Small： 2′2′′ ⊥1′2′
1’ 2
2′2′′ = lθ1 = lθ2 v1 l
1
α u2
Elem. Geo. Constraint eq.
u = u − lθ sinα u2 = u1 −θ1( y2 − y1)
2 1 1
v2 = v1 + lθ2 cosα v2 = v1 +θ2 (x2 − x1)
θ = θ
2 1 θ2 = θ1
3 -8Matrix form e
u1
e v1
1 0 y1 − y2 −1 0 0 0
θ1
0 1 0 0 −1 x2 − x1 = 0 (1)
u2
0 0 1 0 0 −1 0
v2
θ2