This work considers the design of large and complex receivers used in the field of radio astronomy, e.g. for the Square Kilometer Array (SKA) project. The purpose of this work is to consider a coupled simulation where the electromagnetic analysis, performed with the computational electromagnetic software package FEKO, is enhanced by the structural analysis offered by HyperWorks products such as HyperMesh and Optistruct. External influences such as gravity, wind-loading and thermal properties will be taken into account. This will enhance the electromagnetic simulation results, thereby aiding designers to mitigate these environmental effects. Speakers Dr. Danie Ludick, Postdoctoral researcher, Stellenbosch University

1. Fakulteit Ingenieurwese

Faculty of Engineering
A coupled Electromagnetic-Mechanical analysis of
next generation Radio Telescopes for the SKA
D.J. Ludick, D.B. Davidson, D. de Villiers, M. P. Venter, G. Venter
2015 European Altair Technical Conference
Stellenbosch University, Stellenbosch, South Africa, dludick@sun.ac.za
This work considers the design of large and complex receivers used in the field of radio astronomy, e.g. for the
Square Kilometer Array (SKA) project. The purpose of this work is to consider a coupled simulation where the
electromagnetic analysis, performed with the computational electromagnetic software package FEKO, is enhanced
by the structural analysis offered by HyperWorks products such as HyperMesh and Optistruct. External influences
such as gravity, wind-loading and thermal properties will be taken into account. This will enhance the
electromagnetic simulation results, thereby aiding designers to mitigate these environmental effects.

2. Overview of Presentation
• Introduction to the SKA
• Overview (SKA, XDM, KAT-7, MeerKAT)
• EM analysis and parameter (mechanical) variation studies
• Analysing an Offset Gregorian telescope using FEKO and OptiStruct
• Mechanical model (using OptiStruct)
• Electromagnetic analysis (using FEKO)
• Conclusions
2

3. INTRODUCTION TO
THE SKA
3

4. The SKA
• SKA will be next major international radio telescope, originally planned to have a receiving
aperture of more than 1 000 000m2 (1 square km) operating over various frequency bands
• 11 member countries (including India, which is an associate member)
• Australia, Canada, Germany, China, India, Italy, New Zealand, South Africa, Sweden,
The Netherlands and the United Kingdom
• 100 organisations across about 20 countries have participated in the design and development of
the SKA
• Co-hosted in South Africa and Australia
• Need EM quiet space = sparsely populated
• Several precursor instruments built –
• SA’s KAT-7 (Karoo Array Telescope)
• MeerKAT (“more of KAT”);
• Australian ASKAP;
• Dutch LOFAR (“pathfinder”)
4

5. The SKA – Key Science Cases
• Key science projects:
• probing the “dark ages” and the Epoch of Reionization.
• strong field tests of gravity (testing general relativity);
• galaxy evolution, cosmology and dark energy;
• origin and evolution of cosmic magnetism;
• search for exoplanets (“cradle of life”);
• Search for life on other planets (SETI)
5
Artist’s concept of black hole via SKA
Organization/Swinburne Astronomy
Productions.
Photo credits: http://earthsky.org

6. Instrument Location Element
Type
Number of
elements
Freq Configuration
SKA1-mid Karoo, South
Africa
WBSPF -
dishes
64x13.5m
MeerKAT &
±140x15m SKA1
350 MHz -14
GHz in 3 bands
(Dish spec to
20GHz)
Compact central core (1km),
random to 3km radius, 3 spiral
arms, max baseline 150 km.
SKA1-low Western
Australia
Log-P
dual-pol.
±125 000 30-350 MHz
(low. freq.
aperture arrays)
Compact central core (1km);
rest in stations in three spiral
arms
SKA2 Western
Australia +
South Africa
Dishes +
Appert.
arrays
+ 3000 dishes
S.A: Mid freq. AA
Aus: Low freq. AA
30 MHz – 14
GHz (mid +
low)
To be specified
6
Left / Center: Artist’s impression of SKA mid-frequency and low frequency arrays dishes (credits: ibid).
Right: Artist’s impression of SKA dishes - note feed up (Credits: SKA organization/Swinburne Astronomy Productions)
2013-20232024+

7. Instrument Location Element
Type
Number of
elements
Freq Configuration
SKA1-mid Karoo, South
Africa
WBSPF -
dishes
64x13.5m
MeerKAT &
±140x15m SKA1
350 MHz -14
GHz in 3 bands
(Dish spec to
20GHz)
Compact central core (1km),
random to 3km radius, 3 spiral
arms, max baseline 150 km.
SKA1-low Western
Australia
Log-P
dual-pol.
±125 000 30-350 MHz
(low. freq.
aperture arrays)
Compact central core (1km);
rest in stations in three spiral
arms
SKA2 Western
Australia +
South Africa
Dishes +
Appert.
arrays
+ 3000 dishes
S.A: Mid freq. AA
Aus: Low freq. AA
30 MHz – 14
GHz (mid +
low)
To be specified
7
Left / Center: Artist’s impression of SKA mid-frequency and low frequency arrays dishes (credits: ibid).
Right: Artist’s impression of SKA dishes - note feed up (Credits: SKA organization/Swinburne Astronomy Productions)
2013-20232024+

8. Instrument Location Element
Type
Number of
elements
Freq Configuration
SKA1-mid Karoo, South
Africa
WBSPF -
dishes
64x13.5m
MeerKAT &
±140x15m SKA1
350 MHz -14
GHz in 3 bands
(Dish spec to
20GHz)
Compact central core (1km),
random to 3km radius, 3 spiral
arms, max baseline 150 km.
SKA1-low Western
Australia
Log-P
dual-pol.
±125 000 30-350 MHz
(low. freq.
aperture arrays)
Compact central core (1km);
rest in stations in three spiral
arms
SKA2 Western
Australia +
South Africa
Dishes +
Apperture
arrays
+ 3000 dishes +
S.A: Mid freq. AA
Aus: Low freq. AA
30 MHz – 14
GHz (mid +
low)
To be specified
8
Left / Center: Artist’s impression of SKA mid-frequency and low frequency arrays dishes (credits: ibid).
Right: Artist’s impression of SKA dishes - note feed up (Credits: SKA organization/Swinburne Astronomy Productions)
2013-20232024+

9. Geographical location and radio astronomy reserve
• For sensitivity planned for SKA,
very radio-quiet location
required.
• South African site: central
Karoo, elevated semi-desert
plateau of central SA.
• Astronomy Geographic
Advantage Act (2007) protects
12.5 million hectares as a
“radio astronomy reserve”.
9

10. KAT-7: dishes and receivers (1)
10
Photo credits: SKA-SA
2008
XDM
(KAT Prototype)
Composite “honeycomb”
dish with steel backing
2011
KAT-7
Composite “sandwich”
with steel backing
2012
MeerKAT
40 Aluminium panels with
steel (pipe) backing

11. MeerKAT: overall system
MeerKAT system specifications – phase 1
Number of dishes 64 Gregorian offset
reflectors
Main dish diameter
(minor axis)
13.5m projected
diameter
F/D (Prime fed
equivalent)
0.55
Number of dishes 64
Polarization Linear (H/V)
Baselines (min/max) 29m-8km
Freq band (MHz) 900-1670
Max processed BW
(MHz)
770
Ae/Tsys > 220m2/K (L-band)
11
Above: Artists impression
of the final MeerKAT
design. Below: The
MeerKAT Back Up
Structure. Photo credits:
DBD.

12. MeerKAT: extreme antenna engineering
12
The first MeerKAT antenna
goes up. Photo credits:
SKA-SA.
• Az-el mount: El:15 to 880; Az: -185 to +2750 (north is 00)

13. EM Analysis and mechanical variation studies
13
• Need to analyse effect of environmental factors (e.g. wind, gravity, thermal
effects on telescope performance) – esp. in design phase
• Typical approaches:
• Parameter study (on EM side) to capture
effect of varying a mechanical tolerance
• Map this to system performance
(e.g. Gain pattern, efficiency, polarization purity, etc.)
• Various “smart” parameter study methods, (Young, et. al., de Villiers, et. al) –
for efficient sampling of parameter space
• Our goal: Use mechanical analysis (OptiStruct) to produce structural
deviations due to gravity, wind (later thermal) on realistic telescope structures
Vary

14. ANALYSING AN OFFSET
GREGORIAN DISH USING
OPTISTRUCT AND FEKO
14

15. Offset Gregorian – Mechanical model
• Mechanical model
• Use a combination of 1D and 2D
elements
• FEM analysis using OptiStruct (use
symmetry to speedup calculation)
• Constraints as shown in image
• NOTE: Beam structure is not
representative of the actual
MeerKAT design – this model is
used to get the process flow
between OptiStruct and FEKO
started
• Panels approximated by shell
elements (mid-surface extraction)
• … needs more detail … and
therefore more computational
resources (HPC)
15
Total DoF 140,568
Memory (RAM) 231 MByte
Memory (Disk) ~ 2 GByte
Runtime ~ 5 minutes
Intel Core i7-4700MQ CPU @ 2.4 GHz, 16 GByte RAM, Sequential run

16. Offset Gregorian – Mechanical model
16
• Assume a Gravitational loading with the dish in vertical position
• For this load-case, we get a maximum deflection of ~ 29 cm on the main
reflector at the top and ~ 10 cm on the sub-reflector
• Deflections quite a lot (too much) due to backing-structure (needs work)
G
~ 29 cm deviation
~ 10 cm deviation

17. Offset Gregorian – Mechanical model
17
• Comparing results to MeerKAT analysis (more accurate backing
structure)
• Deformations less severe (max ~ 1.68 cm)
~ 1.68 cm
~ 0. 8 cm ~ 1.01 cm
~ 0.6 cm
Photo credits: SKA-SA
Displacements at 15 deg. elevation Displacements at 90 deg. elevation

18. Offset Gregorian – Mechanical model  EM model
18
Import then this STEP
geometry file into CADFEKO
to obtain a PEC model of the
dish
We import the FEM model in
HyperMesh and extract the surface
geometry (for the panels these are the
mid-surfaces) and export the *.STEP
geometry file

19. Offset Gregorian – Electromagnetic model
• EM model
• Planar triangles
• Main reflector requires
additional mesh fixing due
to mid-surface
approximation for panels
• Use a generic horn feed
at 1.4 GHz
19

20. Offset Gregorian – Electromagnetic model
• Effect of secondary reflector deformation
• As reference, use EM model of “undeformed” system
(ref: D. B. Davidson, “Modelling MeerKAT using FEKO”)
• OptiStruct model contains an extension to reduce spillover – see
I.P. Theron, et. al, “The design of the MeerKAT dish Optics”
20
~ 10 cm
4 m

21. Offset Gregorian – Electromagnetic model
• Effect of secondary + main reflector deformation
• Due to mid-surfacing of CAD model, we are left with too much (unrealistic)
surface errors (general shape deviation however useful)
• “Fit” ideal reflector over the OptiStruct model
• Far field gain pattern measured along ZX-plane
(theta = -180 deg. to + 180 deg.)
21

22. Offset Gregorian – Simulation methods (f =1.4 GHz)
22
MLFMM
MLFMM – PO
(λ/5 meshing for PO)
MLFMM-LEPO
(λ meshing for LEPO)
Total unknowns 448, 539 47, 240 (MoM) 402, 499 (PO) 47,240 (MoM) 16156 (LEPO)
Memory (all processes) 21.7 Gbyte 7.5 GByte 4.5 GByte
Total Runtime 9.27 min 27.1 min 15.4 min
Intel Xeon CPU at 2.3 GHz, 512 GByte RAM, 24 processes
MLFMM
PO
• Calc. of coupling for PO/Fock : 14.4 min
• Calc. of RHS vector : 8.1 min
• 2 Iterations (res. of 3.3E-4)

23. Offset Gregorian – Simulation methods (f =1.4 GHz)
23
MLFMM
Generating Spherical mode
source (of subreflector+feed)
Spherical mode source + PO
(λ/5 meshing for PO on dish)
Total unknowns 448, 539 47, 240 (MoM) 402, 499 (PO)
Memory (all processes) 21.7 Gbyte 4.5 GByte 3.4 GByte
Total Runtime 9.27 min 1.5 min 15.3 min
Intel Xeon CPU at 2.3 GHz, 512 GByte RAM, 24 processes
Spherical mode source
PO
• Calc. of coupling for PO/Fock : 12.5 min
• 10950 spherical modes

24. Offset Gregorian – Simulation methods (f =1.4 GHz)
24
MLFMM
MLFMM – PO
(λ/5 meshing for PO)
MLFMM-LEPO
(λ meshing for LEPO)
Total unknowns 448, 539 47, 240 (MoM) 402, 499 (PO) 47,240 (MoM) 16156 (LEPO)
Memory (all processes) 21.7 Gbyte 7.5 GByte 4.5 GByte
Total Runtime 9.27 min 27.1 min 15.4 min
Intel Xeon CPU at 2.3 GHz, 512 GByte RAM, 24 processes
MLFMM
• Calc. of coupling for PO/Fock : 14.4 min
• Calc. of RHS vector : 8.1 min
• 2 Iterations (res. of 3.3E-4)
Solver used

25. Offset Gregorian – Electromagnetic model (f=1.4 GHz)
• Far field gain pattern assuming 29 cm deviation for main reflector
25
• 3 dBi Gain reduction
• 1.7 deg. Shift in main beam
• Defocussing of feed
29 cm
(1.35λ)
10 cm
(0.47 λ)

26. Offset Gregorian – Electromagnetic model (f=1.4 GHz)
• Far field gain pattern assuming 1.6 cm deviation for subreflector
26
~ 1.68 cm
~ 1.68 cm
(0.078λ)
• No Gain reduction
• No Beam shift
Minor influence in lower
sidelobes (not a problem)

27. CONCLUSIONS
27

28. Conclusions
• SKA is one of the most exiting international science projects –
and in our core field.
• KAT-7 was conceptualized, specified, planned & built within around 5
years.
• MeerKAT has similar tight time-frames: construction in progress,
completion planned for 2019.
• Parallel MLFMM in FEKO provides fast and efficient solution
method for this type of analysis
• Mechanical analysis of dish + backing structure – should aid
electromagnetics analysis … more work is needed to get an
accurate enough FEM model for OptiStruct analysis (Step 1)
• Step 2 and beyond: Wind / Thermal loading
28

29. SKA analysis with FEKO at Stellenbosch University
• RFI studies (H. Reader, G. Wiid)
• Lighting induces studies – current injected
into port
• Measurements compare very
well with simulation results
• Modelling of dual-polarized dense dipole array for mid-frequency aperture
arrays (J. Gilmore, et. al)
29
Left: a 10x10x2 dipole array above ground plane (elements λ/2 apart). Right: Manufactured model
Photo credits: J. Gilmore