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Non-Linear & Form-Finding Analysis In GSA

(Using GsRelax Solver)

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Programme

Introduction

Non-linear analysis

Form-finding analysis

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Introduction

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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?

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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

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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:

Geometrically non-linear analysis

Non-linear buckling analysis

Material non-linear analysis

Form-finding analysis

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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’

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Dynamic relaxation is not a matrix method

1 F = m

To apply the equations of motion, each node needs a mass. This is calculated by GsRelax

2 Damping

To prevent continuous oscillation, GsRelax applies damping to the system.

Equilibrium position:maximum speed,zero acceleration,

Most unbalanced position:zero speed,acceleration in peak,

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Original position

Balanced position

Original position

Balanced position

Extremely Geometric nonlinearity

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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:

rigid structures

flexible structures

fabric structures

cable structures

mechanisms

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Non-linear behaviour

Material nonlinearity

Geometric nonlinearity

Buckling

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Material nonlinearity: Tension only and compression only (Tensegrity)

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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

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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.

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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

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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.

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Material nonlinearity: tension only cables with pre-stress to stabilise/stiff compression only stone arches

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Material nonlinearity – compression only: load path changes with loads

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Nonlinear analysis of flip flap joints

Using compression only bar to simulate (use Tie element in GSA)

It involve geometric nonlinearity - ‘large’ deformations

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Geometric nonlinearity:

Vertical loads on the cable trusses are resisted through the geometric stiffness of the cables due to their pre-stress.

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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.

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Buckling: Bicycle wheel spokes reduce the effective length of the arch – very slender arches

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Buckling: The cable net restrains the arch from buckling. The key is the relative stiffness

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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

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