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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.

•
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 
 