1. Using non-linear analysis solver in GSA 1 Non-Linear & Form-Finding Analysis In GSA (Using GsRelax Solver)

2. Using non-linear analysis solver in GSA 2 Programme  Introduction  Non-linear analysis  Form-finding analysis

3. Using non-linear analysis solver in GSA 3 Introduction

4. Using non-linear analysis solver in GSA 4 What are we here for?  Have you used GSA before?  Have you used GsRelax before?  What design work are you involved in relating to nonlinear analysis?  What do you think you might use GsRelax for?  What do you want to learn from this course?

5. Using non-linear analysis solver in GSA 5 Sources of advice  Thomas Li : Software Technology Group  Sarah Kaethner: Structural development and support, AT&R  Course notes and GSA manual on Intranet  On-line help includes description of features and chapters on GsRelax analysis and theory  GSA intranet site  ‘Tension & Lightweight Structures’ on intranet

6. Using non-linear analysis solver in GSA 6 What is GsRelax  A non-linear structure analysis program embedded in Windows GSA as a Solver (previously called – Fablon)  It uses a non-linear solution method called Dynamic Relaxation  It specialises in doing: uGeometrically non-linear analysis uNon-linear buckling analysis uMaterial non-linear analysis uForm-finding analysis

7. Using non-linear analysis solver in GSA 7 The model vibrates under the action of out of balance forces until it is in equilibrium Equilibrium position: No out of balance force (‘residual’ ) - system ‘converged’ Unbalanced position: There is an out of balance force (‘residual’) which will generate an acceleration F = ma oscillation The solution method: ‘Dynamic Relaxation’

8. Using non-linear analysis solver in GSA 8 Dynamic relaxation is not a matrix method 1F = m  To apply the equations of motion, each node needs a mass. This is calculated by GsRelax 2Damping To prevent continuous oscillation, GsRelax applies damping to the system. Equilibrium position: maximum speed, zero acceleration, Most unbalanced position: zero speed, acceleration in peak,

9. Using non-linear analysis solver in GSA 9 Original position Balanced position Original position Balanced position Extremely Geometric nonlinearity

10. Using non-linear analysis solver in GSA 10 Using non-linear analysis solver in GSA Advantages of using GsRelax  Geometric non-linear effects are considered automatically, so it gives more accurate results  Versatile in terms of structure types. No limitation on structure types to be analysed. For example, it can analyse: urigid structures uflexible structures ufabric structures ucable structures umechanisms

11. Using non-linear analysis solver in GSA 11 Using non-linear analysis solver in GSA Non-linear behaviour  Material nonlinearity  Geometric nonlinearity  Buckling

12. Using non-linear analysis solver in GSA 12 Using non-linear analysis solver in GSA Material nonlinearity: Tension only and compression only (Tensegrity)

13. Using non-linear analysis solver in GSA 13 Using non-linear analysis solver in GSA  Material non-linearity: fabric panel, tension only:  Stiffness from axial force, geometry & pre-stress  Pre-stress in tension only elements to give initial stiffness (important for lightweight structures)  The flat fabric panels resist load through deflections

14. Using non-linear analysis solver in GSA 14 Using non-linear analysis solver in GSA Material nonlinearity: cable net, tension only: make use of the form to sustain loads, the cable net gets its stiffness from its FORM. Load is resisted through form, pre-stress, and deflections.

15. Using non-linear analysis solver in GSA 15 Using non-linear analysis solver in GSA  Material nonlinearity: fabric structure, tension only:  Use anticlastic curvature to stabilise the shape of the model  Pre-stress and deflection are needed to adjust the surface shape to take loads

16. Using non-linear analysis solver in GSA 16 Using non-linear analysis solver in GSA Material nonlinearity: Un- grouted stone arch, compression only: Stone is modelled as Compression only elements. The joints only sustain compression force, when applied moment/force changes direction, the joints will ‘flip-flap’ to form new load paths.

17. Using non-linear analysis solver in GSA 17 Using non-linear analysis solver in GSA Material nonlinearity: tension only cables with pre-stress to stabilise/stiff compression only stone arches

18. Using non-linear analysis solver in GSA 18 Using non-linear analysis solver in GSA Material nonlinearity – compression only: load path changes with loads

19. Using non-linear analysis solver in GSA 19 Using non-linear analysis solver in GSA Nonlinear analysis of flip flap joints Using compression only bar to simulate (use Tie element in GSA) It involve geometric nonlinearity - ‘large’ deformations

20. Using non-linear analysis solver in GSA 20 Using non-linear analysis solver in GSA Geometric nonlinearity: Vertical loads on the cable trusses are resisted through the geometric stiffness of the cables due to their pre-stress.

21. Using non-linear analysis solver in GSA 21 Using non-linear analysis solver in GSA Geometric nonlinearity: In order for the struts to rotate about their pin at the glass frame, The cables need to rotate about a separate pin point. This gives out of plane stiffness to the loading point.

22. Using non-linear analysis solver in GSA 22 Using non-linear analysis solver in GSA Buckling: Bicycle wheel spokes reduce the effective length of the arch – very slender arches

23. Using non-linear analysis solver in GSA 23 Using non-linear analysis solver in GSA Buckling: The cable net restrains the arch from buckling. The key is the relative stiffness

24. Using non-linear analysis solver in GSA 24 Using non-linear analysis solver in GSA Summary: when to use GsRelax  Large nonlinearity features  Features specific to fabric and cable structures  Material plastic behaviour and yielding  Form-finding analysis features  Search processes to investigate ‘ultimate’ capacity of models  Search processes to isolate individual elements and their buckling behaviour and the degree of restraint offered by the rest of the model

25. Using non-linear analysis solver in GSA 25 Using non-linear analysis solver in GSA www.oasys-software.com