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Simulation
Tool
Structural
Analysis Tool
Structural
Design Tool
• Response of a structure or system to the loads imposed
• Measuring critical loads or failure criteria • Modifying the structure to improve performance
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Calculated circumference 2Πr
Number of Edges
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Node
Element
Mesh
Load
Boundary Condition
Material Property
TrueGrid®
• Compatibility
• Equilibrium
• Constitutive Law
• Things fit together with no gaps
• Each node and element boundary matches the one beside it.
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F2
Fk
F1
Fn
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E
P
A
P
P
A
A
P
Pn
A
Pn lim A 0 A
Ps
A
Ps lim A 0 A
Megson
Normal components
Shear components
τxy
Megson
Perpendicular to this axis
x,
y,
z
xy ,
yx ,
yz ,
zy ,
zx , xz
xy
yx
yz
zy
zx
xz
Parallel to this axis •
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–
–
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x
xy
xz
yx
y
yz
zx
zy
z
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Sigma
x
Epsilon
y
Tau
Careful with the shear terms, different sources use different order
z
x y σ
Gamma
z
yz
yz
zx
zx
xy
xy
ε
E
σ E ε
1
x
1
y
z
E (1 ) 1
(1
)(1
2
)
0
yz
zx
xy
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
(1 2 )
2(1 )
0
1
0
0
0
(1 2 )
2(1 )
0
0
0
0
0
x
0 y
z
0 yz
zx
0 xy
(1 2 )
2(1 )
0
Continuum
(Displacement only)
• Bar
(u)
1D
2D
• Truss
(u,v,w)
• Plane stress (u,v)
• Plane
Strain
(u,v)
• Bricks
(u,v,w)
3D
Structural
(Displacement and Slope)
• Beam
(u,v,w,
θx,θy,θz)
• Plate
(u,v,w,
θx,θy)
• Shell
(u,v,w,
θx,θy,θz)
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Model of Structure
Different Model of Structure
Discretised Model
Discretised Model
Magnitude of Errors
Real Structure
Remember:
Refinement does not make your closer to REALITY.
Refinement makes your results closer to your MODEL!
(a) Von mises stress
(b) Fore-aft load paths showing detail around mast step
E, A, L
P1
P2
u1
u2
k11
k
21
k12 u1 P1
k22 u2 P2
Node 1
Node 2
P1
P2
N u1=0 N u2=1 • What if we have multiple elements or loads? I
II
III
• We can assemble multiple elements using equilibrium at the nodes (+ compatibility)
P1
P2
P1 I
I
P2I
P3
P2II
II
P3II
P4
P3III
III
P4III
– At Node 1:
P1 I P1 0
AI EI
AI EI u1 u2 P1
LI
LI
– At Node 2:
P2I P2II P2 0
AI EI
AI EI AII EII u1
LII
LI
LI
AII EII u3 P2
u2
LII
Garth Pearce 2012
– In matrix form
AI EI
L
I
AI EI
L
I
0
0
AI EI
LI
AI EI
A E
II II
LI
LII
AII EII
LII
0
AII EII
LII
AII EII
A E
III III
LII
LIII
0
I
u1
u1 P1
0
u P
2
2
u
P
A E
III III 3 3
LIII
u4