1. Non-linear & Buckling analysis with GSA

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3. Who is Oasys? Wholly owned by Arup
Formed in 1976 to develop software for in-house and external use
Most programming and sales staff are engineers
In recent years have added marketing, sales and development staff worldwide

4. Oasys Customers

5. Structural Geotechnical Document Management Crowd simulation CAD
GSA basic concepts
Structural
Geotechnical
Document Management
Crowd simulation
5 structural
10 geotechnical
2 document management
2 CAD
2 sustainability
1 Crowd simulation
CAD
Sustainability

6. Non-linear analysis with GSA

7. Non-linear Basics

8. Linear analysis Based on the assumptions of Results Implication
Displacement - Strain relationship is linear (valid if displacements are small)
Stress - strain relationship is linear (valid if strains are small)
Equilibrium conditions are established at the original (non-deformed) geometry
Results
Equilibrium equations are linear
Load – displacement relationships are linear
Load – internal forces relationships are linear
Implication
Stresses, internal forces etc are obtained based on non-deformed geometry. If deformation or strain are large, results are not accurate

9. Non-linear analysis If either of the following conditions applies
Displacement – strain relationship is not linear (large displacement problem - geometrical non-linearity)
Stress – strain relationship is not linear
Material is elastic-plastic (material non-linear problem)
Material is still elastic, but strain is large (large strain problem, such as rubber)
Results
Equilibrium equations are no longer linear
Load – displacement relationships are not linear
Load – internal forces relationships are not linear
Implication
Equilibrium condition is established on deformed configuration
Structural responses may be path dependent
Analysis results are not combinable

10. Geometric non-linear

11. Geometric non-linear analysis
Ignore deformation when establishing equilibrium P Q h M F V
So:
F = P
V = Q
M = Qh

12. Geometric non-linear analysis
Equilibrium is established at the deformed configuration P Q d h M F V q
So:
F = Pcosq – Qsinq
V = Qcosq + Psinq
M = Qh + Pd

13. Example
Geometric non-linear

14. Non-linear elements

15. Non-linear Elements Strut Tie Cable Fabric Compression-only 1D
Tension-only 1D
Cable
Tension-only chain 1D
Fabric
Tension-only 2D

16. Example
Non-linear elements

17. Material non-linear

18. Material non-linear
Engineering stress (e.g. bar in tension) s = F/A0 where A0 – the original section area e s

19. Material non-linear
Simplified s – e curves in GSA e s

20. Example
Material non-linear

21. Buckling

22. Buckling analysis Linear buckling analysis
Eigen value or Modal buckling
Elastic non-linear buckling analysis
Include effects of nodal displacement
Elasto-plastic non-linear buckling analysis
Add material plasticity

23. Linear buckling analyses (2 step analysis)
Results: The structure is assumed in equilibrium at any deformed positions given by the mode shape
Search for load factor l that factors the loads to make the element stiffness K = 0 (Eigen value extraction) P P lP lP V lV V lV lP lV
K(p) < Ke Ke
Step 1
Step 2
Note: 1. Shear force V has little effect on buckling load capacity
2. Linear buckling analysis does not give actual deflection of the structure for the given loads

24. Elastic non-Linear buckling analysis (multi-step analysis)
d 1
d i
d n
aoP
a1P
aiP
aoV
anP
a1V
Vr1
aiV
Vri
anV
Vrn
Pr1
Pri
Fo = aoP
Ko = f(EI,Fo)
< Ke
Prn
F1 = f(a1P, a1V, d)
K1 = f(EI,F1)
Fi = f(aiP, aiV, d)
Ki = f(EI,Fi)
Prn  anP
Vrn  anV .
Note: 1. d is the actual deflection of the column under the imposed loads
2. If material plasticity is taken into account, this is also the elastic-plastic non-linear buckling analysis

25. Load - deflection curves from the three buckling analyses
Displacement (d)
Linear buckling analysis (no unique relationship between P and d )
Elastic non-linear buckling analysis (may approach the linear buckling load capacity)
Elastic-plastic non-linear buckling analysis

26. Examples
Buckling

27. Non-linear analysis cases and combinations

28. Cases and Combinations
Load Cases
Loads are assigned to a Load Case
Referenced as L1, etc
Analysis Cases
Analyse single or multiple load cases for results
Load factors can be applied: 1.35L1+1.5L2
Referenced as A1, etc
Combination cases
Combine multiple linear analysis cases
Load factors can be applied: 1.35A1+1.5A2
Envelope Analysis and Combination cases

29. Cases and Combinations
Linear Analysis
Load cases
Analysis Cases
Combination Cases
L1 (e.g. Dead Load)
A1 = L1
C1 = 1.35A A2
L2 (e.g. Live Load)
A2 = L2
C2 = 1.35A A3
L3 (e.g. Wind Load)
A3 = L3
C3 = 1.35A A A3
C4 = C1 or C2 or C3
Non-Linear Analysis
Load cases
Analysis Cases
Combination Cases
L1 (e.g. Dead Load)
A1 = 1.35L L2
C1 = A1 or A2 or A3
L2 (e.g. Live Load)
A2 = 1.35L L3
L3 (e.g. Wind Load)
A3 = 1.35L L L3

30. Dynamic Relaxation

31. Dynamic relaxation solution method
Basic idea of dynamic relaxation
Most unbalanced position:
zero speed,
acceleration at peak,
zero kinetic energy
Equilibrium position:
maximum speed,
zero acceleration,
Kinetic energy at peak
vibration

32. Damping used in GsRelax analysis
1 Viscous Damping
Apply resistance against the vibration, the resistance is proportional to the velocity of the node
2 Kinetic Damping
Reposition nodes once the system kinetic energy exceeds peak value (pass equilibrium position)
Equilibrium position:
maximum speed
peak kinetic energy
zero acceleration
Most unbalanced position:
zero speed
zero kinetic energy
peak acceleration

33. Effect of viscous damping
24/04/2017
Effect of viscous damping
no damping
Deflection
Time
equilibrium deflection
damping just smaller than critical
damping larger than critical

34. Example projects

35. 'Water Cube' bubbles
A recent job: the Beijing Olympics Water Cube

36. MOMA – Liquid Skies
This is a GSA job from the New York Museum of Modern Art’s summer exhibition.
it might not be a standard fabric structure, but you can see all the elements
Struts
Edge cables
Double curved surfaces

37. Khalifa Stadium
Note the tension mesh and the slender compression arch, which also needs to be part of the form finding
The arch is also prevented from buckling by the cable net
It looks so simple, but this is a very complex example of form finding

38. Melbourne Cricket Ground

39. Singapore Flyer

40. United States Air Force Memorial

41. National Assembly for Wales
Awards
RIBA Awards - Wales Royal Institute of British Architects RIBA
Winner Structural Steel Design Award
Sustainable Regeneration Award - Winner Building Exchange BEX Awards
Innovative Regeneration Award - Runner-up Building Exchange BEX Awards

42. Royal Ontario Museum

43. Kurilpa Bridge

44. Infinity Footbridge
In 2009, Expedition won the Institution of Structural Engineer’s Supreme award for the Infinity Footbridge in Stockton-on-Tees
With its primary span of 120m and secondary of 60m, it is the biggest footbridge in the country
Awards
IStructE Supreme Award for Structural Engineering Excellence 2009
IStructE Award for Pedestrian Bridges 2009
The judges praised it as "a bold and daring design which demonstrates what can be done with artistic flair, technical excellence, complex analysis and excellent engineering teamwork. The bridge will be one of those iconic designs to be talked about for years."
ICE Robert Stephenson Award 2009
The judges described it as "imaginatively engineered" acting as "a catalyst for regeneration and a landmark much appreciated by the community."
North East Constructing Excellence Awards 'Project of the Year' 2009
Concrete Society Civil Engineering Award 2009
International Green Apple Gold Award for Civic Pride: New Build 2009

45. Any Questions? GSA basic concepts
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Let me know if there’s some part of the software that you’d like me to go over.
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Sorry we don’t have time to answer all your questions right now but we will be answer all your questions by very soon. And if you didn’t get a chance to put your questions in I’ll send out a survey which you can put any additional questions in.

46. Future Webinars Soil Movement and Slope Stability
14th March
What’s New in GSA 8.6
21st March