Ci a ion: Man e ola-Ubillos, M.;
Gonzalez-Quin ial, F.; Rico-Ma inez,
J.M.; Beni o Ayuca , J.; Begi is ain-
Mi xelena, J.A. Analysis o Plana
Double-Laye Timbe Spa ial F ames
by Using Pa ame ic Tools. Appl. Sci.
2024,14, 6400. h ps://doi.o g/
10.3390/app14156400
Academic Edi o : Lau en Daude ille
Recei ed: 29 May 2024
Re ised: 6 July 2024
Accep ed: 9 July 2024
Published: 23 July 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
applied
sciences
A icle
Analysis o Plana Double-Laye Timbe Spa ial F ames by
Using Pa ame ic Tools
Maddi Man e ola-Ubillos 1, F ancisco Gonzalez-Quin ial 2, Jose Miguel Rico-Ma inez 2,* ,
Josu Beni o Ayuca 3and Jon Andoni Begi is ain-Mi xelena 2
1Independen Resea che , 20018 Donos ia-San Sebas ián, Spain; maddiman e [email p o ec ed]
2A chi ec u e Depa men , School o A chi ec u e, Uni e si y o he Basque Coun y (UPV/EHU),
Oña i Plaza 2, 20018 Donos ia-San Sebas ián, Spain; [email p o ec ed] (F.G.-Q.);
[email p o ec ed] (J.A.B.-M.)
3TECNALIA, Basque Resea ch and Technology Alliance (BRTA), Cons uc ion Ma e ials—Lab Se ices,
Polígono Lasao—Á ea Ana di, 5, 20730 Azpei ia, Spain; [email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +34-657712374 o +34-943015896
Abs ac : I is in he p elimina y design phase o a p ojec ha he designe makes decisions con-
ce ning he global geome y o he s uc u e. When wo king wi h space ames, he choice o he
ame opology is key o he s uc u al beha io . I is di icul o ind manuals ha p o ide guidance
on which o he mos common opologies is he igh one o he p ojec , le alone in wood con-
s uc ion. In esponse o his sho coming, he use o pa ame ic so wa e is p oposed (G asshoppe
build1.0.0007 and Ka amba 3D 2.2.0.16-220828). The aim is o c ea e a dynamic ca alog ha esponds
ins an aneously o changes in he pa ame e s o p o ide in o ma ion on s uc u al beha io , p e-
dimensioning and me ics. Wi h he display o all his in o ma ion, he a chi ec will ha e enough
echnical a gumen a ion o choose o ejec op ions. The p oposal is de eloped h ough a case s udy:
he ea ly design and analysis s ages o la double-laye imbe spa ial ames as o ec angula
medium-span oo s.
Keywo ds: compu a ional design; pa ame ic ools; G asshoppe ; Ka amba 3D; imbe cons uc ion;
la double-laye space ames
1. In oduc ion
1.1. Space F ames
A space ame is o en de ined as a s uc u al sys em designed om linea elemen s
a anged in such a way ha he ansmission o o ces is h ee-dimensional. This leads o
an idea o opposi ion be ween spa ial s uc u es and so-called “ la ” ones. Howe e , he
di ision be ween “ la ” and “spa ial” s uc u es e e s no o he s uc u e i sel , which is
always spa ial, bu o he me hods o analysis [1].
In plana sys ems, s esses a e ansmi ed om he less igid elemen s o he mo e
igid ones up o he ounda ions. On he way o he ounda ion, he o ces become, as
well as he sec ion, la ge and la ge . On he con a y, in a space ame s uc u e, all he
elemen s con ibu e acco ding o he h ee-dimensional geome y gi en o hem, wi h
no ob ious o ce ans e sequence. In o he wo ds, he ansmission o o ces o he
suppo is bi u ca ed in se e al elemen s so as no o ha e a concen a ion o o ces in jus a
ew elemen s.
The objec i e o his ype o cons uc ion is o use he minimum amoun o ma e ial
o ob ain ligh weigh s uc u es wi hou losing s i ness, s abili y and esis ance. These
a e appealing s uc u es no only om he enginee ing poin o iew, bu also om he
a chi ec u al one. These sys ems ha e led o he unde s anding o he building as a li ing
being, as an o ganic s uc u e, capable o adap ing o he unce ain y o he u u e. The e
a e app oaches such as hose o Louis Kahn, who plays wi h he na u al g ow h o he
Appl. Sci. 2024,14, 6400. h ps://doi.o g/10.3390/app14156400 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2024,14, 6400 2 o 19
spa ial ames om he mul iplica ion o he base spa ial module. Ano he well-known
p ojec is he Fun Palace by Ced ic P ice and Joan Li lewood (Figu e 1), a dismoun able
and econ igu able a e ac capable o housing any p og am ha could espond o social
needs. This logic is e en ex apola ed o he ci y and e i o y, gi ing ise o p ojec s such
as, among o he s, he megas uc u es o A chig am (Figu e 1) o he h ee-dimensional
u banism o Yona F iedman.
Appl.Sci.2024,14,xFORPEERREVIEW2o 21
app oachessuchas hoseo LouisKahn,whoplayswi h hena u alg ow ho hespa ial
ames om hemul iplica iono hebasespa ialmodule.Ano he well-knownp ojec is
heFunPalacebyCed icP iceandJoanLi lewood(Figu e1),adismoun ableand econ-
igu ablea e ac capableo housinganyp og am ha could espond osocialneeds.This
logicise enex apola ed o heci yand e i o y,gi ing ise op ojec ssuchas,among
o he s, hemegas uc u eso A chig am(Figu e1)o he h ee-dimensionalu banismo
YonaF iedman.
(a)(b)
Figu e1.(a)Ced icP ice,FunPalace.(Sou ce: o an,i .h ps://www. lick .com/pho-
os/136374633@N04/23341131945/,accessedon6Ap il2023);(b)A chig am,PluginCi y.(Sou ce:
Wyliepoonh ps://www. lick .com/pho os/wyliepoon/49224543288/,accessedon7Ap il2023).
In ecen yea s, esea chhasbeenca iedou inse e al ela eda eas.On heone
hand,calcula ionme hodsha ebeenp oposed omeasu e heca bonemissions o he
li e imeo he ames[2].On heo he hand, obo iza ionp ocessesa ebeingde eloped
o assemblyanddisassembly[3,4].In his ega d,a e yp omisinglineo esea chhas
beenopenedwi h espec o hepossibili ieso disassemblyand euseo he ames[5–8].
Gi en hecu en eme gingcon ex , hisisapa h ha undoub edlydese es obein es-
iga ed.
Back o hes ic lys uc u al-enginee ingaspec ,spa ials uc u escanbeg ouped
in o h eemainca ego ies[9,10](Figu e2):
1. la icedisc e es uc u es: heya ebasedondisc e iza ion oc ea eamo eo less
egula ame(g id,ba el aul s,domes, owe sand ee o ms).
2. con inuouss uc u es:asinglesu aceac ingasamemb ane(slabs,shell, ab ic).
3. bi o ms uc u es:combina iono bo hdisc e eandcon inuouspa s.
Figu e2.Spaces uc u eca ego ies.(1)la icedisc e es uc u e;(2)con inuouss uc u e.
Thispape willbecen e edon he i s g oup o womain easons:
- Bo hplana andcu edsu acescanbeused.This esea chis ocusedon la ames
wi h heawa eness ha p ocessesdesigned o asimpleshapecanbeex apola ed
omo ecomplexones.Pa ame ically,i ispossible oapplyanyalgo i hmicallyde-
signedp ocess oany ypeo geome y.
Tha said,inshells uc u es,s iffnessisachie ed h oughshape.Thei geome ydi-
ec lyde i es om hei lowo o cesandde ines hei load-bea ingbeha io andligh -
ness[11].On heo he hand,la icespa ials uc u esachie e esis ance h oughc oss-
12
Figu e 1. (a) Ced ic P ice, Fun Palace. (Sou ce: o an, i . h ps://www. lick .com/pho os/13637463
3@N04/23341131945/, accessed on 6 Ap il 2023); (b) A chig am, Plug in Ci y. (Sou ce: Wyliepoon
h ps://www. lick .com/pho os/wyliepoon/49224543288/, accessed on 7 Ap il 2023).
In ecen yea s, esea ch has been ca ied ou in se e al ela ed a eas. On he one hand,
calcula ion me hods ha e been p oposed o measu e he ca bon emissions o he li e ime o
he ames [
2
]. On he o he hand, obo iza ion p ocesses a e being de eloped o assembly
and disassembly [
3
,
4
]. In his ega d, a e y p omising line o esea ch has been opened
wi h espec o he possibili ies o disassembly and euse o he ames [
5
–
8
]. Gi en he
cu en eme ging con ex , his is a pa h ha undoub edly dese es o be in es iga ed.
Back o he s ic ly s uc u al-enginee ing aspec , spa ial s uc u es can be g ouped
in o h ee main ca ego ies [9,10] (Figu e 2):
1.
la ice disc e e s uc u es: hey a e based on disc e iza ion o c ea e a mo e o less
egula ame (g id, ba el aul s, domes, owe s and ee o ms).
2. con inuous s uc u es: a single su ace ac ing as a memb ane (slabs, shell, ab ic).
3. bi o m s uc u es: combina ion o bo h disc e e and con inuous pa s.
Appl.Sci.2024,14,xFORPEERREVIEW2o 21
app oachessuchas hoseo LouisKahn,whoplayswi h hena u alg ow ho hespa ial
ames om hemul iplica iono hebasespa ialmodule.Ano he well-knownp ojec is
heFunPalacebyCed icP iceandJoanLi lewood(Figu e1),adismoun ableand econ-
igu ablea e ac capableo housinganyp og am ha could espond osocialneeds.This
logicise enex apola ed o heci yand e i o y,gi ing ise op ojec ssuchas,among
o he s, hemegas uc u eso A chig am(Figu e1)o he h ee-dimensionalu banismo
YonaF iedman.
(a)(b)
Figu e1.(a)Ced icP ice,FunPalace.(Sou ce: o an,i .h ps://www. lick .com/pho-
os/136374633@N04/23341131945/,accessedon6Ap il2023);(b)A chig am,PluginCi y.(Sou ce:
Wyliepoonh ps://www. lick .com/pho os/wyliepoon/49224543288/,accessedon7Ap il2023).
In ecen yea s, esea chhasbeenca iedou inse e al ela eda eas.On heone
hand,calcula ionme hodsha ebeenp oposed omeasu e heca bonemissions o he
li e imeo he ames[2].On heo he hand, obo iza ionp ocessesa ebeingde eloped
o assemblyanddisassembly[3,4].In his ega d,a e yp omisinglineo esea chhas
beenopenedwi h espec o hepossibili ieso disassemblyand euseo he ames[5–8].
Gi en hecu en eme gingcon ex , hisisapa h ha undoub edlydese es obein es-
iga ed.
Back o hes ic lys uc u al-enginee ingaspec ,spa ials uc u escanbeg ouped
in o h eemainca ego ies[9,10](Figu e2):
1. la icedisc e es uc u es: heya ebasedondisc e iza ion oc ea eamo eo less
egula ame(g id,ba el aul s,domes, owe sand ee o ms).
2. con inuouss uc u es:asinglesu aceac ingasamemb ane(slabs,shell, ab ic).
3. bi o ms uc u es:combina iono bo hdisc e eandcon inuouspa s.
Figu e2.Spaces uc u eca ego ies.(1)la icedisc e es uc u e;(2)con inuouss uc u e.
Thispape willbecen e edon he i s g oup o womain easons:
- Bo hplana andcu edsu acescanbeused.This esea chis ocusedon la ames
wi h heawa eness ha p ocessesdesigned o asimpleshapecanbeex apola ed
omo ecomplexones.Pa ame ically,i ispossible oapplyanyalgo i hmicallyde-
signedp ocess oany ypeo geome y.
Tha said,inshells uc u es,s iffnessisachie ed h oughshape.Thei geome ydi-
ec lyde i es om hei lowo o cesandde ines hei load-bea ingbeha io andligh -
ness[11].On heo he hand,la icespa ials uc u esachie e esis ance h oughc oss-
12
Figu e 2. Space s uc u e ca ego ies. (1) la ice disc e e s uc u e; (2) con inuous s uc u e.
This pape will be cen e ed on he i s g oup o wo main easons:
-
Bo h plana and cu ed su aces can be used. This esea ch is ocused on la ames
wi h he awa eness ha p ocesses designed o a simple shape can be ex apola ed
o mo e complex ones. Pa ame ically, i is possible o apply any algo i hmically
designed p ocess o any ype o geome y.
Tha said, in shell s uc u es, s i ness is achie ed h ough shape. Thei geome y
di ec ly de i es om hei low o o ces and de ines hei load-bea ing beha io and
ligh ness [
11
]. On he o he hand, la ice spa ial s uc u es achie e esis ance h ough
c oss-sec ion. Being mul iple-laye s uc u es, he e y composi ion o he shee has a le e
a m ha s i ens hem. By no being so o m-dependen , he ange o applica ion o la ices
is conside ably wide , and ha makes hem appealing as he scope o his wo k.
Appl. Sci. 2024,14, 6400 3 o 19
-
A wide ange o pa en ed sys ems is a ailable on he ma ke . E en hough mos o
hem a e aimed a me al cons uc ion, de elopmen in imbe cons uc ion is also
being accomplished. The main ocus o he esea ch is he node solu ion. I is a
he join whe e he s ess ansmission is concen a ed and whe e he cons uc i e
equi emen s end o educe he c oss-sec ion o he imbe ba . This con adic ion
poses a challenge in he de elopmen o he connec ion. I is, howe e , a di icul y ha
can be o e come, since imbe cons uc ion is an op ion ha looks e y p omising in
he cu en clima e c isis [3,6,7].
1.2. Cons uc ion Sys ems
His o ically, space ames ha e belonged o he ield o s eel cons uc ion. S eel allows
o hin sec ions wi hou losing s uc u al e iciency. Timbe , while equi ing ca e in he
design o he join s, is also a sui able ma e ial o his ype o sys em.
The p esen pape will ocus on imbe cons uc ion, and a b ie s a e o he a is
p esen ed abou he applica ion o imbe in space ames. The elemen s ha o m he
spa ial sys em will be de eloped indi idually as ollows:
1.2.1. Ba Elemen s
This is an elemen in which he longi udinal dimension is o highe o de han he
o he wo. In he buil examples, h ee ypes o wood ba s ha e gene ally been used
(Figu e 3): bamboo ba s (a), solid wood logs (b) and lamina ed imbe sec ions (c1, c2).
Appl.Sci.2024,14,xFORPEERREVIEW3o 21
sec ion.Beingmul iple-laye s uc u es, he e ycomposi iono heshee hasale e a m
ha s iffens hem.Byno beingso o m-dependen , he angeo applica iono la icesis
conside ablywide ,and ha makes hemappealingas hescopeo hiswo k.
- Awide angeo pa en edsys emsisa ailableon hema ke .E en houghmos o
hema eaimeda me alcons uc ion,de elopmen in imbe cons uc ionisalso
beingaccomplished.Themain ocuso he esea chis henodesolu ion.I isa he
join whe e hes ess ansmissionisconcen a edandwhe e hecons uc i e e-
qui emen s end o educe hec oss-sec iono he imbe ba .Thiscon adic ion
posesachallengein hede elopmen o heconnec ion.I is,howe e ,adifficul y
ha canbeo e come,since imbe cons uc ionisanop ion ha looks e yp omis-
ingin hecu en clima ec isis[3,6,7].
1.2.Cons uc ionSys ems
His o ically,space amesha ebelonged o he ieldo s eelcons uc ion.S eelal-
lows o hinsec ionswi hou losings uc u alefficiency.Timbe ,while equi ingca ein
hedesigno hejoin s,isalsoasui ablema e ial o his ypeo sys em.
Thep esen pape will ocuson imbe cons uc ion,andab ie s a eo hea is
p esen edabou heapplica iono imbe inspace ames.Theelemen s ha o m he
spa ialsys emwillbede elopedindi iduallyas ollows:
1.2.1.Ba Elemen s
Thisisanelemen inwhich helongi udinaldimensioniso highe o de han he
o he wo.In hebuil examples, h ee ypeso woodba sha egene allybeenused(Fig-
u e3):bambooba s(a),solidwoodlogs(b)andlamina ed imbe sec ions(c1,c2).
Figu e3.Ba elemen ypes.(a)bambooba s;(b)solidwoodlongs;(c1)lamina ed imbe sec ion;
(c2)lamina ed imbe hollowsec ion.
The i s wog oupsbelong oma e ialsob aineddi ec ly omna u e,and he e o e,
asinsawn imbe cons uc ion, heshapeanddimensionswillno necessa ilybeop i-
mized o he equi emen so hep ojec .
Rega ding he hi dg oup,i iswo hmen ioning hecon ibu iono hedoc o al
hesiso JoséAn onioVázquezRod íguez[12].Thiswo ka gues o head an ageso
heshapingo ba sbymeanso hollowsec ionso lamina ed imbe (c2).Thea gumen
canbesumma izedin ou poin s:
- Thehollowsec ionequals hema e ial’s alueandoffe slesssensi i i y odimen-
sional a ia ionsdue ochangesinen i onmen al ac o s.Also, he eisa educ ion
in iskagains possiblea ackso abio icandbio ico igindue o he ac ha i is
easie oca you hein eg al ea men gi eni shollowcha ac e .
- The eisexploi a iono head an agesoffe edbywoodp oduc singene alandlam-
ina edonesinpa icula .I isama e ial ha ,due oi sp oduc ionp ocess,has ewe
impe ec ionsand, he e o e,ahighe esis ancepe o mance.Thesamecouldbe
saido mic olam(VLV).
- Thep ocesso simpleindus ialexecu ionconsis so lamina ing ec angula pieces
h eeo ou imeswide han hewall hicknesso hehollowsec ionso ha ,once
he acesha ebeenob ainedbysimplecu ing, heycanbegluedagains amas e o
guidepieceand hus o m he inalpiece.Consequen ly, hehandling equi edis
educed,making hemanu ac u ingcos compe i i e.
abc1 c2
Figu e 3. Ba elemen ypes. (a) bamboo ba s; (b) solid wood longs; (c1) lamina ed imbe sec ion;
(c2) lamina ed imbe hollow sec ion.
The i s wo g oups belong o ma e ials ob ained di ec ly om na u e, and he e o e,
as in sawn imbe cons uc ion, he shape and dimensions will no necessa ily be op imized
o he equi emen s o he p ojec .
Rega ding he hi d g oup, i is wo h men ioning he con ibu ion o he doc o al
hesis o JoséAn onio Vázquez Rod íguez [
12
]. This wo k a gues o he ad an ages o he
shaping o ba s by means o hollow sec ions o lamina ed imbe (c2). The a gumen can be
summa ized in ou poin s:
-
The hollow sec ion equals he ma e ial’s alue and o e s less sensi i i y o dimensional
a ia ions due o changes in en i onmen al ac o s. Also, he e is a educ ion in isk
agains possible a acks o abio ic and bio ic o igin due o he ac ha i is easie o
ca y ou he in eg al ea men gi en i s hollow cha ac e .
-
The e is exploi a ion o he ad an ages o e ed by wood p oduc s in gene al and
lamina ed ones in pa icula . I is a ma e ial ha , due o i s p oduc ion p ocess, has
ewe impe ec ions and, he e o e, a highe esis ance pe o mance. The same could
be said o mic olam (VLV).
-
The p ocess o simple indus ial execu ion consis s o lamina ing ec angula pieces
h ee o ou imes wide han he wall hickness o he hollow sec ion so ha , once
he aces ha e been ob ained by simple cu ing, hey can be glued agains a mas e
o guide piece and hus o m he inal piece. Consequen ly, he handling equi ed is
educed, making he manu ac u ing cos compe i i e.
-
The squa e o ec angula hollow sec ion is conside ed sui able o any ype o ame,
al hough i seems o be pa icula ly sui able o he semi-oc ahed on ame.
Appl. Sci. 2024,14, 6400 4 o 19
1.2.2. Join s
Depending on he ype o ba used, he join solu ion also a ies. In imbe cons uc-
ion, he c i ical pa seems o be he connec ion be ween he imbe ba and he (usually
me allic) node. I is whe e he joining elemen s weaken he imbe sec ion and, a he same
ime, whe e he highes s ess concen a ion occu s. In his ega d, some o he esea ch
ha has been de eloped (o is s ill in p og ess) is shown below:
-
Bamboo connec o s (Figu e 4a): Gha ami and Mo ei a [
13
] de eloped a join o he
cons uc ion o double-laye ed bamboo space ames om oc agonal pla es welded o
an oc agonal base pla e. Du ing he esea ch, he join was es ed on a double-laye
bamboo space ame p o o ype wi h single suppo s e e y 4 m. The esul s we e
sa is ac o y. Cu en ly, esea ch is being con inued wi h p o o ypes o la ge spans.
-
Solid wood log connec o s (Figu e 4b): One o he mos well-known esea che s in
his ield is D . Huybe s [
14
]. In e es ed in he use o small-diame e logs, which,
un il hen, had no use and we e abundan in o es y was e, he de eloped a simple
wi e- ying me hod o a aching gal anized s eel connec o pla es o he p e iously
hollowed ends o oundwood poles.
Wi hou going in o much dep h, some o he join s ha ha e been p oposed a e he
KT-W join by Ka suhiko Imai (Uni e si y o Osaka) and he 14FTC-U join by Alphose
Zingoni (Uni e si y o Cape Town).
-
Connec o s in glulam sec ions (Figu e 4c): In he same hesis [
12
] in which hollow
sec ions o glulam a e de eloped as ba s, he app op ia e join solu ion o hem is also
unco e ed. A hollow sphe e is p oposed wi h a sc ewed co e ha allows access o he
in e io and inco po a es un h eaded holes o inse ing he h eaded ods and ixing
hem inside he sphe e by means o nu s. A he opposi e end, he ba is h eaded in o
an oc agonal nu . To a ach he node o he wood, cas ing pla es a e ixed o he inside
o he wooden elemen .
-
Connec o s by CNC ab ica ion (Figu e 4d): So a , me al- o-wood join s ha e been
p esen ed. The node is usually made o a high s eng h s eel, since he s ess concen a-
ion is e y high a ha poin . S eel is a ma e ial easily shaped o he desi ed geome y
(sphe ical, cylind ical, e c.) and s ong enough o esis his punc ual concen a ion
o o ces.
A g oup o esea che s om Vic o ia Uni e si y o Welling on [
15
] p oposed o wo k
wi h plywood cu wi h he CNC ou e o c ea e a wood–wood join .
The esul s o he es s pe o med on he p o o ypes showed ha his solu ion wo ks
wi h de o ma ions o abou 1/400 when o e loads o use ype A1 ( esiden ial zone housing)
and B (adminis a i e zones) a e applied o i . Al hough he s uc u e was no a i s ul ima e
limi (collapse), i was concluded ha he join should be u he s i ened.
Be o e mo ing on, we gi e one las no e on he join s. Among he s uc u es o med
by ba s, wo sub ypes can be dis inguished: hose in which he connec ion be ween ba s is
made h ough igid nodes ( ha is, i he node unde goes a ce ain o a ion, all he concu en
ba s in i unde go he same o a ion) o h ough a icula ed nodes (each concu en ba can
o a e independen ly o he o he s). This dis inc ion, howe e , can o en be o e idden by
he shape appea ing when ea ing he nodes as igid o as a icula ed, since he bending
momen s ha necessa ily appea in he i s case a e e y small in compa ison wi h he
axial o ces, which a e o e y simila magni ude in bo h cases. This conside a ion allows
ha i is no necessa y o cons uc pe ec a icula ed nodes and o use ypes o nodes ha ,
in eali y, a e nei he igid no a icula ed bu a e loca ed, in gene al, in an in e media e
zone [1,16].
Appl. Sci. 2024,14, 6400 5 o 19
Appl.Sci.2024,14,xFORPEERREVIEW5o 21
mo a
d1
d1
(a)(b)
(c)(d)
Figu e 4. (a) Gha ami and Mo ei a’s bamboo ame connec o ; (b) Hybe s’ solid wood log connec-
o ; (c) J.A. Vázquez’s glulam hollow sec ion join ; (d) Finch, Ma iage, Gje de and Pelosi’s CNC
ab ica ion ame wi h wood–wood join s.
Appl. Sci. 2024,14, 6400 6 o 19
1.2.3. Topology
The opology e e s o he geome ical o de o he ba s and nodes. Fo g ea e
s i ness o he la spa ial ames (indispensable in la ge spans), wo laye s a e a anged
connec ed o each o he h ough he se o diagonal ba s. Al hough he a ie y o ypology
is p ac ically in ini e, he p esen wo k ocuses on hose pa en ed and comme cialized o
use in cons uc ion. The use o a cus om-designed opology would also in ol e he design
o he cons uc ion sys em o join s and ba s, an a ea ha is no he ocus o his wo k.
Based on he bibliog aphy [
12
,
17
–
21
], he se en mos men ioned and used ypologies ha e
been chosen. A classi ica ion has been p oposed (Figu e 5). To o de hem, each one has
been named wi h a le e and a numbe o be able o iden i y hem easily h oughou he
pape (Figu e 6).
Appl.Sci.2024,14,xFORPEERREVIEW6o 21
Figu e4.(a)Gha amiandMo ei a’sbamboo ameconnec o ;(b)Hybe s’solidwoodlogcon-
nec o ;(c)J.A.Vázquez’sglulamhollowsec ionjoin ;(d)Finch,Ma iage,Gje deandPelosi’sCNC
ab ica ion amewi hwood–woodjoin s.
1.2.3.Topology
The opology e e s o hegeome icalo de o heba sandnodes.Fo g ea e s iff-
nesso he la spa ial ames(indispensableinla gespans), wolaye sa ea angedcon-
nec ed oeacho he h ough hese o diagonalba s.Al hough he a ie yo ypologyis
p ac icallyin ini e, hep esen wo k ocuseson hosepa en edandcomme cialized o
useincons uc ion.Theuseo acus om-designed opologywouldalsoin ol e hedesign
o hecons uc ionsys emo join sandba s,ana ea ha isno he ocuso hiswo k.
Basedon hebibliog aphy[12,17–21], hese enmos men ionedandused ypologiesha e
beenchosen.Aclassi ica ionhasbeenp oposed(Figu e5).Too de hem,eachonehas
beennamedwi hale e andanumbe obeable oiden i y hemeasily h oughou he
pape (Figu e6).
Figu e5.F ame opologyclassi ica ion.(A)g oupA;(B)g oupB;(C)g oupC;(D)g oupD.
G oupA: ameswhoseuppe andlowe laye sa einpa alleldi ec ion o heedges.
A1—Squa eonsqua e:cubicmodulewi h e icalanddiagonalba s.Absenceo
obliquediagonals.
A2—Squa eono hogonallyoffse squa e:basedon hepy amidalmodulewi ha
squa ebase.I is hemos commonlyused opology.
A3—Squa eono hogonallyoffse iplesqua e:basedon hep e ious ame(A2),
ba sa esupp essedin helowe laye ino de oligh eni .
G oupB: ameswhoseuppe andlowe laye sa ediagonal(45°)wi h espec o he
edges.
B1—Squa eondiagonallyoffse squa e:py amidalmodule amewi hasqua ebase
a angeddiagonally,a 45° o heedge.
G oupC: amesinwhichonelaye ispa allel o heedgesand heo he diagonal
(45°).
C1—Diagonalonsqua e:c ea ed om heA1 ame, he oplaye isgi ena45° wis .
I alsohasnoobliquediagonals.
G oupD: amesbasedon he iangula module.
D1—T iangleonoffse iangle:c ea ed om heg oupingo e ahed almodules.I
is hemos igido he ames,asall he aceso hepolyhed ona e iangula , heunde-
o mablegeome ypa excellence(Figu e7).
D2—T iangleonhexagon:basedon heD1 ame, helowe laye isligh enedby
emo ingba s oc ea eequila e alhexagons.
Thediffe en opologiesbeha ediffe en lydependingon heappliedloads, hepo-
si iono hesuppo sand hesizeo hemodule.Fu he a ia ionscanbein oducedby
changing hesizeo he opcho dg id ela i e o hebo omcho dg id.Wide geome ies
a eusuallypossiblein hebo omlaye o adouble-laye amebecause hemembe sa e
no mallyin ension.Tha is, helowe ensioncho dsmaybelonge han heuppe com-
p essionmembe s(nobucklingeffec ).
ABDC
Figu e 5. F ame opology classi ica ion. (A) g oup A; (B) g oup B; (C) g oup C; (D) g oup D.
Appl.Sci.2024,14,xFORPEERREVIEW7o 21
Figu e6.Analyzed opologies.
Figu e7.Rigidi yo he e ahed almodule.
1.3.Compu a ionalDesign
Visualp og ammingso wa eallow hec ea iono pa ame icsc ip swi hou e-
qui inganycompu e p og ammingknowledge.Thishelpsa chi ec sin hedesignp o-
cessbyligh eningda amanagemen ,au oma ing epe i i e asksandp oducingsimula-
ions[22].I isallabou da amanagemen ; hep incipleso hemodela epa ame e s ha
canbechangedany ime.Themos illus a i eexampleisp obably heupside-down
modelo chu chesbyAn onioGaudi.Thedesigne c ea edin ica eca ena ya chesby
suspendedweigh eds ings.Byadjus ing heposi iono heweigh s( hepa ame e in
hiscase), heshapeo heca ena ya cheschanged.Thispa ame icmodelenabledGaudi
oanalyzein eal ime hes uc u als abili yo hisp ojec .Nowadays, hep ocesshas
beendigi alized,bu heconcep emains hesame[23].
A1_Squa e on squa e A2_Squa e on o hogonally o se
squa e
A3_Squa e on o hogonally o se
iple squa e
B1_Squa e on diagonally o se
squa e
C1_diagonal on squa e
D1_T iangle on o se iangle D2_T iangle on hexagon
uppe laye
diagonals
down laye
Figu e 6. Analyzed opologies.
G oup A: ames whose uppe and lowe laye s a e in pa allel di ec ion o he edges.
A1—Squa e on squa e: cubic module wi h e ical and diagonal ba s. Absence o
oblique diagonals.
A2—Squa e on o hogonally o se squa e: based on he py amidal module wi h a
squa e base. I is he mos commonly used opology.
A3—Squa e on o hogonally o se iple squa e: based on he p e ious ame (A2),
ba s a e supp essed in he lowe laye in o de o ligh en i .
Appl. Sci. 2024,14, 6400 7 o 19
G oup B: ames whose uppe and lowe laye s a e diagonal (45
◦
) wi h espec o
he edges.
B1—Squa e on diagonally o se squa e: py amidal module ame wi h a squa e base
a anged diagonally, a 45◦ o he edge.
G oup C: ames in which one laye is pa allel o he edges and he o he diagonal (45◦).
C1—Diagonal on squa e: c ea ed om he A1 ame, he op laye is gi en a 45
◦
wis .
I also has no oblique diagonals.
G oup D: ames based on he iangula module.
D1—T iangle on o se iangle: c ea ed om he g ouping o e ahed al modules.
I is he mos igid o he ames, as all he aces o he polyhed on a e iangula , he
unde o mable geome y pa excellence (Figu e 7).
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 o 21
Figu e 6. Analyzed opologies.
Figu e 7. Rigidi y o he e ahed al module.
1.3. Compu a ional Design
Visual p og amming so wa e allow he c ea ion o pa ame ic sc ip s wi hou e-
qui ing any compu e p og amming knowledge. This helps a chi ec s in he design p o-
cess by ligh ening da a managemen , au oma ing epe i i e asks and p oducing simula-
ions [22]. I is all abou da a managemen ; he p inciples o he model a e pa ame e s ha
can be changed any ime. The mos illus a i e example is p obably he upside-down
model o chu ches by An onio Gaudi. The designe c ea ed in ica e ca ena y a ches by
suspended weigh ed s ings. By adjus ing he posi ion o he weigh s ( he pa ame e in
his case), he shape o he ca ena y a ches changed. This pa ame ic model enabled Gaudi
o analyze in eal ime he s uc u al s abili y o his p ojec . Nowadays, he p ocess has
been digi alized, bu he concep emains he same [23].
Figu e 7. Rigidi y o he e ahed al module.
D2—T iangle on hexagon: based on he D1 ame, he lowe laye is ligh ened by
emo ing ba s o c ea e equila e al hexagons.
The di e en opologies beha e di e en ly depending on he applied loads, he posi-
ion o he suppo s and he size o he module. Fu he a ia ions can be in oduced by
changing he size o he op cho d g id ela i e o he bo om cho d g id. Wide geome ies
a e usually possible in he bo om laye o a double-laye ame because he membe s
a e no mally in ension. Tha is, he lowe ension cho ds may be longe han he uppe
comp ession membe s (no buckling e ec ).
1.3. Compu a ional Design
Visual p og amming so wa e allow he c ea ion o pa ame ic sc ip s wi hou equi -
ing any compu e p og amming knowledge. This helps a chi ec s in he design p ocess by
ligh ening da a managemen , au oma ing epe i i e asks and p oducing simula ions [
22
].
I is all abou da a managemen ; he p inciples o he model a e pa ame e s ha can be
changed any ime. The mos illus a i e example is p obably he upside-down model o
chu ches by An onio Gaudi. The designe c ea ed in ica e ca ena y a ches by suspended
weigh ed s ings. By adjus ing he posi ion o he weigh s ( he pa ame e in his case), he
shape o he ca ena y a ches changed. This pa ame ic model enabled Gaudi o analyze in
eal ime he s uc u al s abili y o his p ojec . Nowadays, he p ocess has been digi alized,
bu he concep emains he same [23].
In his ega d, compu a ional design is highly sui able o he design and analysis o
bo h simple and complex modula imbe s uc u es, such as he ones discussed in his
pape . Some au ho s [
24
] a gue ha , despi e he e iden ad an ages o hese p og ams o
p oduce ee o m and aes he ically pleasing designs, he challenge in hei applica ion lies
in he compu a ional cos associa ed wi h he op imiza ion o hei layou and limi a ions in
hei ab ica ion. In ha aspec , his pape wan s o con ibu e by p o ing ha geome ically
simple la space ames a e as wo hy o pa ame ic analysis as he mo e complex ones.
The e is alue in using p e-es ablished la opologies because hey ha e an indus y
backing hem up and a e no as dominan —speaking abou a chi ec u al composi ion—as a
o m- inding me hod o geome y can be. A chi ec s need assis ance in ea ly design s ages
o de elop hose simple p ojec s as well.
Appl. Sci. 2024,14, 6400 8 o 19
1.4. Objec i e
To sum up he ideas ha ha e been p esen ed in he in oduc ion, he aim o his pape
is o es he u ili y o pa ame ic ools in he ea ly design and analysis s ages o la wooden
spa ial ames.
To do so, a case s udy will be de eloped. All he opologies o be used a e hose men-
ioned in he li e a u e on space ames [
20
,
21
,
25
]. They ha e pa en ed cons uc ion sys ems
and a e a ailable on he ma ke . E en so, i is no easy o ind he echnical/comme cial
documen a ion necessa y o design spa ial ames in he p elimina y design phase (much
less in wood), and his wo k in ends o ul ill his need.
This is why, in his case, he pa ame ic ools a e no used o ob ain a geome y bu o
analyze which o he geome ies o e ed by he ma ke is he mos sui able o he speci ic
p ojec . The idea is o c ea e a ile ha ga he s he men ioned opologies in a pa ame ic way
o gene a e and p e-dimension hem a he eques o he designe . The compu e p ocess
o e s he esul s in eal ime, and i is up o he designe o choose he bes i [
26
–
36
]. The
case s udy will be a simula ion o his p ocess.
2. Ma e ials and Me hods
The chosen so wa e o his wo k is G asshoppe (build 1.0.0007) [
37
], an ex ension
o Rhinoce os 3D ( e sion 7.24.22297.11002) [
38
] (NURBS-based 3D modeling so wa e)
o algo i hmic modeling ha allows he c ea ion and pa ame ic edi ion o geome ies.
G asshoppe also has ano he plugin called Ka amba 3D ( e sion 2.2.0.16-220828) [
39
],
which enables ini e elemen analysis and p e-dimensioning o he pa ame ized geome y.
By combining he wo so wa e, i has been possible o c ea e a “g aphical calcula ion
able” (Figu e 8), which, by adjus ing pa ame e s such as dimensions and numbe o modules
and choosing he opology (ou o he 7 men ioned in Sec ion 1.2.3 “Topology”), is able o com-
pa e esul s in eal ime and choose he combina ion ha bes sui s he p ojec . The geome y
can also be impo ed in o Rhino o Au oCAD o p oduce he g aphical documen a ion.
Appl.Sci.2024,14,xFORPEERREVIEW9o 21
Figu e8.Wo k lowdiag am.
2.1.C ea iono hePa ame icModel
All he amesa epa ame e izedbasedon hepa ame e ssumma izedinFigu e9.
In hecaseo iangula andhexagonalmodules,beingequila e al, hesides(L)o he
modulesa ede ined.Fu he de ailson heG asshoppe pa ame iza ionp ocesswillno
bede eloped,asi isno hesubjec o hiswo k.
Figu e9.Pa ame e sin he ile.
Figu e10shows,on he igh ,asc eensho o hecomple edG asshoppe ileandon
hele , heRhino iewe .Themodeliso ganizedin he ollowingg oups(numbe edin
Figu e10):
1. pa ame icde ini iono hegeome yo he ame: he7chosen ame opologiesand
hei espec i epa ame e izedsuppo s.
2. g oupingo hepa ame e s:boxg oupingall hepa ame e s obechosen o he
calcula ion,suchas he ame opology,dimensionsandnumbe o modulesand he
dep h.
3. ans o ma ion omgeome icalmodel os uc u almodel:byen e ingda a(loads,
suppo s,ma e ial,c oss-sec ionsandjoin s), hechosengeome y(in hepa ame e s
g ouping,2)is ansla edin oa ini eelemen model.
4. calcula ionandop imiza ion:bymeanso Ka amba3D, he ameiscalcula ed.Ce -
aincomponen s(sec ionop imiza ionandgene icalgo i hms)a eadded oop imize
he esul s.
Figu e 8. Wo k low diag am.
Al hough i is no wi hin he scope o his wo k, i is wo h men ioning ha add-ons
can be ins alled o G asshoppe in o de o enable he bidi ec ional da a exchange be ween
he p e-dimensioned pa ame ic model and he FEM so wa e ( h ee-dimensional ini e
elemen analysis so wa e) o a deepe calcula ion. I is an added alue o be able o
pe o m all design and calcula ion phases wi h he same pa ame ic model.
Appl. Sci. 2024,14, 6400 9 o 19
2.1. C ea ion o he Pa ame ic Model
All he ames a e pa ame e ized based on he pa ame e s summa ized in Figu e 9.
In he case o iangula and hexagonal modules, being equila e al, he sides (L) o he
modules a e de ined. Fu he de ails on he G asshoppe pa ame iza ion p ocess will no
be de eloped, as i is no he subjec o his wo k.
Appl.Sci.2024,14,xFORPEERREVIEW9o 21
Figu e8.Wo k lowdiag am.
2.1.C ea iono hePa ame icModel
All he amesa epa ame e izedbasedon hepa ame e ssumma izedinFigu e9.
In hecaseo iangula andhexagonalmodules,beingequila e al, hesides(L)o he
modulesa ede ined.Fu he de ailson heG asshoppe pa ame iza ionp ocesswillno
bede eloped,asi isno hesubjec o hiswo k.
Figu e9.Pa ame e sin he ile.
Figu e10shows,on he igh ,asc eensho o hecomple edG asshoppe ileandon
hele , heRhino iewe .Themodeliso ganizedin he ollowingg oups(numbe edin
Figu e10):
1. pa ame icde ini iono hegeome yo he ame: he7chosen ame opologiesand
hei espec i epa ame e izedsuppo s.
2. g oupingo hepa ame e s:boxg oupingall hepa ame e s obechosen o he
calcula ion,suchas he ame opology,dimensionsandnumbe o modulesand he
dep h.
3. ans o ma ion omgeome icalmodel os uc u almodel:byen e ingda a(loads,
suppo s,ma e ial,c oss-sec ionsandjoin s), hechosengeome y(in hepa ame e s
g ouping,2)is ansla edin oa ini eelemen model.
4. calcula ionandop imiza ion:bymeanso Ka amba3D, he ameiscalcula ed.Ce -
aincomponen s(sec ionop imiza ionandgene icalgo i hms)a eadded oop imize
he esul s.
Figu e 9. Pa ame e s in he ile.
Figu e 10 shows, on he igh , a sc eensho o he comple ed G asshoppe ile and on
he le , he Rhino iewe . The model is o ganized in he ollowing g oups (numbe ed in
Figu e 10):
1.
pa ame ic de ini ion o he geome y o he ame: he 7 chosen ame opologies and
hei espec i e pa ame e ized suppo s.
2.
g ouping o he pa ame e s: box g ouping all he pa ame e s o be chosen o he calcula-
ion, such as he ame opology, dimensions and numbe o modules and he dep h.
3. ans o ma ion om geome ical model o s uc u al model: by en e ing da a (loads,
suppo s, ma e ial, c oss-sec ions and join s), he chosen geome y (in he pa ame e s
g ouping, 2) is ansla ed in o a ini e elemen model.
4.
calcula ion and op imiza ion: by means o Ka amba 3D, he ame is calcula ed. Ce -
ain componen s (sec ion op imiza ion and gene ic algo i hms) a e added o op imize
he esul s.
5.
isualiza ion o esul s: a command is gi en o isualize he esul s in he Rhino
iewe (6).
Appl.Sci.2024,14,xFORPEERREVIEW10o 21
5. isualiza iono esul s:acommandisgi en o isualize he esul sin heRhino
iewe (6).
Figu e10.Sc eensho o heG asshoppe ile.(1)pa ame icde ini ion;(2)pa ame e s;(3) ans o -
ma ion omgeome y os uc u e;(4)calcula ion;(5) isualiza ion;(6) hino iewe .
Be o ep oceeding,ab ie asideon hein e ope abili ybe weenFEMso wa eand
G asshoppe .A es hasbeenpe o medusing hein e aceo RFEM6Dlubal[40]( h ee-
dimensional ini eelemen analysisso wa e) o RhinoandG asshoppe .Basedon he
exis ingPa ame icFEMToolboxplugin o RFEM5, heRFEM6implemen si byde-
aul .Sobyha ing heG asshoppe ileandRFEMDlubalopenedsidebyside,andusing
hecomponen s ha a eshowninFigu e11, heconnec ionisimmedia e.Changesin
G asshoppe pa ame e sa eupda edins an lyinDlubalaswell.Howe e ,i mus be
emphasized ha he ans e edda aa emainlygeome ical( opology).Thede ini iono
sec ionsandma e ialmus bepe o medusing heexac e mso Dlubal o hep og am
op ocess hemco ec ly,andKa amba3Dcomponen sa eno compa ible.The e o e,
hisisa e yuse ul ea u ein e mso handling he amegeome y( hemaincomplexi y
o heses uc u es)bu somewha limi ed o he es (e.g.,modelinghollowglulamba s).
The emainingpa ame e s o hecomple ecalcula ionwillbede inedin he ini eele-
men p og amwhe e hecon olo se ingsisconside ablyhighe .
Figu e11.Sc eensho o Rhino7(le ),G ashoppe (cen e )andRFEM6( igh )in e connec ed.
123
4
5
6
Figu e 10. Sc eensho o he G asshoppe ile. (1) pa ame ic de ini ion; (2) pa ame e s; (3) ans o -
ma ion om geome y o s uc u e; (4) calcula ion; (5) isualiza ion; (6) hino iewe .
Be o e p oceeding, a b ie aside on he in e ope abili y be ween FEM so wa e and
G asshoppe . A es has been pe o med using he in e ace o RFEM 6 Dlubal [
40
] ( h ee-
dimensional ini e elemen analysis so wa e) o Rhino and G asshoppe . Based on he
Appl. Sci. 2024,14, 6400 16 o 19
3.2.3. Me ics: Nodes and Ba s
As a guideline, a b eakdown by componen s o he o al cos o he sys em is es ima ed.
These a e he app oxima e a e age alues [
44
]: ba s 30%, nodes 40%, p o ec ion and pain
10% and assembly 20%. F om hese da a, i can be deduced ha he cos o a space ame
is closely ela ed o he ype and numbe o join s (40% nodes+30% ba s). The e o e, in
he absence o a budge , he numbe o nodes can be aken as a guide o cos . In such a
case, economizing means ha he numbe o nodes pe squa e me e should be kep o
a minimum.
The g aphs om Figu e 15 show ha ames C1 and D1 a e he mos “expensi e” ones,
bo h in e ms o he numbe o nodes and numbe o ba s, while A3 and D2, he ligh ened
opologies, a e he mos cos -e icien ones. F ame A2 is in he middle o bo h ex emes.
As he span o he s uc u e inc eases, he wo lines ma ked on he g aphs main ain hei
ou line because he numbe o modules emains cons an . Howe e , nume ically speaking,
he s uc u e becomes “cheape ”. The clea es example is o compa e he alues o he
7
×
12.5 and 25
×
50 oo s. Wi hou going any u he , he A1 mesh needs 2.46 nodes/m
2
o co e 91 m2, while i only needs 0.2 nodes/m2 o 1200 m2.
By educing he densi y o elemen s wi h longe ba s, no only a g ea e load-bea ing
capaci y is achie ed, bu also ma e ial and, he e o e, cos is op imized. This is he ad-
an age ha space ames o e o e o he s uc u al sys ems, and ha is why hey a e so
compe i i e in la ge spans.
4. Conclusions
4.1. Topologies
One o he objec i es o he pape is o de ine he scope o each o he se en opologies,
hei s eng hs and limi a ions. A e analyzing he esul s, he ollowing conclusions
a e d awn:
•
G oup A (A1–A2–A3): These a e he mos balanced opologies, applicable in a ious
si ua ions. In his ega d, i is only logical ha hey a e he mos common ones used.
O he h ee, A1 is he wo s pe o me ; i s cubic module means ha wi h he g ea es
numbe o nodes pe squa e me e , i s ill has he g ea es de o ma ion.
•
On he o he hand, he semi-oc ahed al modulus p o ides A2 and A3 meshes wi h su -
icien s i ness wi hou a ec ing he mass oo much. Be ween he las wo, he e
is no ha much di e ence; A3 u ns ou o be a good al e na i e o A2 when
mass/economics is he de e mining ac o , wi hou se ious de imen in de o ma-
ions. In gene al, all h ee a e ela i ely simple geome y opologies and easy o i .
•
G oup D (D1–D2): hei e ahed al modulus makes hem ex emely igid. Especially
D1 is he p e e ed choice o la ge spans (o e 40–50 m). F om hese spans on, he
mesh s a s o be compe i i e: he node-ba /m
2
a io dec eases d as ically (which
makes hem mo e cos -e ec i e) and he deple ion a es go up (which indica es ha
he s uc u e is wo king). A u u e esea ch ask would be o u he analyze he limi s
o e ahed al meshes in la ge spans (abo e 50 m).
•
The D2 mesh is p esen ed as a good al e na i e o D1. Al hough he lowe laye
de aches a signi ican numbe o ba s o o m hexagons, i is s ill a igid mesh, compe -
i i e o i s ligh ness (wi h de o ma ions lowe han hose o mesh A3, also ligh ened).
One d awback ha can a ise is he di icul y in handling he hexagonal geome y.
I he p ojec does no con empla e he use o hese cha ac e is ic shapes om he
beginning, edges and join s can become an added complica ion.
•
B1: I can be a good al e na i e o A2 mesh. The me ics (numbe o ba s and nodes)
a e be e , and o wha is sa ed in elemen s, he de o ma ions do no inc ease so much.
•
The only doub ha may come up is (as in he D2) he geome y i sel . As he ba s a e
no a anged pa allel o he edges, ba s o special leng hs a ise o inish o he mesh,
p oblems ha g oup A can a oid.
•
C1: O he se en opologies, C1 is he one ha beha es he wo s in gene al. I ends
o des abilize easily, and i is com o able up o a 20–25 m span. Beyond his limi ,
Appl. Sci. 2024,14, 6400 17 o 19
i becomes e y limi ed. I is also he opology ha needs mo e nodes and ba s pe
squa e me e (sligh ly mo e han D1). In gene al, i seems ha he geome y is no
app op ia e o gene a ing a s uc u al space ame.
I should be men ioned ha in o de o analyze he beha io o he opologies, he
s uc u e has been pushed o he limi . Some o he esul s collec ed in his pape , al hough
complying wi h he s anda ds, a e qui e igh ( he de lec ions o he suppo s on h ee
sides and he deple ion indices). In he de elopmen o he calcula ion, he esul s should
be handled mo e loosely, al hough o he pu pose o his academic wo k, hey a e he
app op ia e ones.
Al hough he scope o he wo k has been la meshes, he applica ion o he sys em
could be ex apola ed om he plane o he cu ed su ace and analyze, o ins ance,
cylind ical o sphe ical meshes. This is a ield o be explo ed in u u e p ojec s.
4.2. Suppo Dis ibu ions
Ano he objec i e o he wo k is o analyze he epe cussion o he di e en suppo s
on he beha io o he s uc u e. Fo his pu pose, h ee cases ha e been conside ed:
pe ime e suppo , 3-sided suppo and ou punc ual suppo s. The ollowing conclusions
ha e been eached:
In gene al, he dis ibu ion o suppo s has a g ea in luence on he s uc u al beha io
o he mesh, he change being less no iceable in he s i e meshes ( hose o g oup D).
Suppo s dis ibu ed in an o de ly and symme ical manne bene i he analyzed opologies.
They do no ole a e misma ches and asymme ies well. Clea ly, he pe ime e con inuous
suppo is he mos s able o all, al hough i is also limi ing in he p ojec . The ou punc ual
suppo s o e he designe g ea e eedom.
The suppo on h ee sides is he mos limi ing. I is clea ha he ec angula p o-
po ion (1/2) is no adequa e in ha case. Ano he u u e di ec ion o he s udy would
be o op imize he a io o he oo o imp o e he alues o he h ee-sided suppo . This
would mean ha ing o pa ame e ize he la ices di e en ly, so ha changing he numbe o
modules does no a ec he o e all dimensions o he oo . In his way, di e en a ios o
1/2 could be es ed, using galapagos ( i ness: a ow, genomes: numbe o modules on he x
and yaxis) o ind he op imal a io.
4.3. Using G asshoppe and Ka amba
Unde s anding how in o ma ion is handled be ween componen s is he mos di icul
pa o G asshoppe , as i is a majo shi om wo king wi h ac ual geome y o handling
lis s o da a. Fundamen al concep s such as “g a ” and “ la en” become he co ne s one
o modeling. The p og am is e y powe ul and use ul. The gene ic algo i hm becomes
an ally o ob ain esul s wi hou ha ing o manually es he pa ame e s, al hough he
condi ions mus be well de ined o a oid undesi ed esul s. I is also impo an o limi he
numbe o a iables so ha he algo i hm does no ake oo long o app oach he answe
(especially in hese ypes o long iles).
4.4. Final Conclusion
Al hough a wo k low is p oposed a he han speci ic nume ical esul s, he case
s udies illus a e how much in o ma ion his so wa e can p o ide and he eby demons a e
hei u ili y. In summa y, a pa ame ic analysis and p e-dimensioning ool has been c ea ed
o p ojec la double-laye spa ial meshes. A cus omizable and expandable “g aphical
sp eadshee ” ha accompanies he designe du ing he p elimina y design phase.
Au ho Con ibu ions: Concep ualiza ion, M.M.-U., F.G.-Q. and J.A.B.-M.; Da a cu a ion, F.G.-Q.
and J.M.R.-M.; Fo mal analysis, M.M.-U. and F.G.-Q.; Funding acquisi ion, F.G.-Q. and J.M.R.-
M.; In es iga ion, M.M.-U.; Me hodology, M.M.-U. and F.G.-Q.; P ojec adminis a ion, J.M.R.-M.;
Resou ces, F.G.-Q., J.M.R.-M. and J.A.B.-M.; So wa e, M.M.-U. and F.G.-Q.; Supe ision, F.G.-Q.,
J.M.R.-M. and J.A.B.-M.; Valida ion, F.G.-Q., J.M.R.-M. and J.B.A.; Visualiza ion, M.M.-U., F.G.-Q.,
Appl. Sci. 2024,14, 6400 18 o 19
J.M.R.-M. and J.B.A.; W i ing—o iginal d a , M.M.-U.; W i ing— e iew and edi ing, M.M.-U., F.G.-Q.
and J.M.R.-M. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch was unded by: 1. HAZI and he Basque Coun y Go e nmen , Vice-Minis y
o Ag icul u e, Fishe ies and Food Policy in he ame o he Timbe S uc u es, Cons uc ion and
Design Mas e . 2. Uni e si y o he Basque Coun y. A chi ec u e Depa men . 3. Fundación Tecnalia
Resea ch and Inno a ion.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : The da a p esen ed in his s udy a e a ailable in he a icle.
Con lic s o In e es : The au ho s decla e no con lic s o in e es .
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au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
