Folding Plate Roof StructuresProgramme : MSc in Civil Engineering with Integrated Design

Name of Student : Sokratis Baltas

Supervisor : Alessandro Margnelli, Daniel BosiaIndustrial Supervisor: Daniel Bergsagel

UCL Department of Civil, Environmental and Geomatic Engineering, Gower St, London ,WC1E 6BT

Industrial Partnership with AKT II Ltd

1. Introduction

2. Aims & Objectives

Establish a design and analysis methodology for folding structures

Investigate the possibility of accommodating thickness on a folding pattern so that it is able to be foully folded

Investigate the performance of novel materials on folding structures

Access the structural behavior of the structure when deployed on different positions

Investigate the dynamic response of the system and the change inflicted due to the change of deployment

Understand kinematics of deployment and suggest a design solution of the moving mechanism

Investigate the correlation of geometry to the structural properties of the system

3. Methodology

4. Analysis Results & Discussion

5. Conclusion 6. Future Work

The transformation of flat structural surfaces into folded geometries

through a series of folds, has been of interest to engineers, architects

and mathematicians. A folding pattern whether simple or complex,

is proven to provide aesthetically interesting architecture, as well as

structurally efficient systems. Origami tessellations, has been a field of

those research endeavors, whether it is on smaller scale applications

such as in aerospace engineering, or on a building scale. The

attribute of such folding patterns to evolve into spatial geometries

form flat surfaces, offers the opportunity for researching the feasibility

and design procedures of folding structures inspired by such

patterns.

In this thesis a roof structure that is designed to possess the attribute to fold and unfold and thus changing its

geometry in respect to its deployment position, is investigated. The concept of deployability, imposes design

challenges that need to be examined and resolved. However, the aspiration for designing a structure that

alternates its geometry to accommodate different function needs, or to acquire an optimum shape depending

on load or environment conditions, is interesting from an architectural and engineering perspective. Additionally,

folding patterns as the one studied hereby, offer the opportunity to design structures capable to be fully folded on

a flat pack stowed state and transported to be deployed on several locations or sites needed.

Fig.1 Paper model of the structure

Fig.2 Methodology process

Fig.5 Roof Tip (Uz) Deflection of the SLS combination on all deployment angles (100|200mm thickness set)

The structural analysis concluded into comparative

results among the different deployment angles in terms

of deflection and stresses. It has been shown that both

deflections and stresses increase as the angle ξ

increases up to 90o. There is also a significant

concertation of stresses along the basic fold line of the

cantilever support. At those concertation areas, there

are stressed parts by both principal tensile and

compressive forces. The constant increase of deflection

and stresses is due to the decrease of system inertia

because of the unfolding.Fig.6 Principal Forces on roof basic fold point (dashed lines are on vertical posts, continuous are on rood)

Fig.3 Physical Foamboard model that displays the folding motion and the material thickness trimming on the fold

The geometry of the system was inspired by

a simple Origami folding pattern

The foldability of the roof was investigated

when thickness is added

For the roof to be fully foldable, the plate

thickness had to be halved at the section of

the reverse fold

The final geometry was parametrically

designed

The plates were designed as carbon fibre

ribbed stressed skin panels

Finite Element analysis was executed (elastic

and modal) for 5 deployment angles and

two different panel thickness sets

(100|200mm & 200|400mm)

The folding motion was assessed and a base

moving mechanism was proposed

A business case for folding structures has

been established

The structural behavior is primarily depending to

the geometry rather that material. The inertia of

the structure is the one of the dominant

parameters

A multi variable optimization process should be

engaged to refine thickness and geometry

The ability of folding can be used to address

different structural needs depending on loading

conditions

Dynamics of the system are changing as it unfolds

Formulate a multi variable optimization design

process

Investigate the effect of wind on folding

lightweight structures (dynamically)

Investigate kinematics of deployment and

dynamics of folding movement

Design the linear hinges for the structure

Optimize material usage by following principal

stress paths and utilizing state of the art

fabrication methods

A modal analysis has been executed to evaluate

the change in dynamic response in relation to the

deployment process. It was concluded that as

the structure unfolds the global stiffness is

alternating, which results into different modal

periods [eigen values] and different modal

shapes [eigen vectors]. The translational mode in

axis Z starts as the 3rd mode in 22.5o, ending up to

be the 1st mode at 60o and 90o. A key

observation is that mostly at 60o and 45o , the 1st

and 2nd periods are almost identical, which

maybe raising aeroelastic concerns.

Fig.4 Folding pattern of the structure (a), geometric parameters of folds (b)

(a)

(b)

Fig.7 Fundamental mode shapes for each deployment

Fig.8 Fundamental periods

ξ=22.5ο ξ=30ο ξ=45ο ξ=60ο ξ=90ο

Fig.9 Structural and performance indicators

Fig.10 Correlation of calculated deflection to ρ

Fig.11 Optimal ξ in respect to deflection and

covered area

Evaluation indicators derived from the uniformly loaded

cantilever equations and correlated mathematically

only to angle ξ, were introduced.

y3: inertia indicator, ρ: tip deflection indicator, ρ’: fold

stress indicator, A: projected covered area by the roof.

This thesis was conducted with industrial partnership and under the supervision and guidance of AKT II Ltd

Software used:

September 2017 |London | United Kingdom