Open Access Prediction on Deflection of Z-Core Sandwich Panels in Weak Direction

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1 Send Orders for Reprints to 88 The Open Ocen Engineering Journl 20 6 (Suppl- M7) Open Access Prediction on Deflection of Z-Core Sndwich Pnels in Wek Direction Chen Cheng * School of Civil Environmentl Engineering nyng Technologicl University nyng Avenue Singpore Astrct: In Z-core sndwich pnel the sher stiffness of the sndwich pnel in the wek direction which is perpendiculr to the plcement of the Z-cores is much smller thn the ending stiffness ecuse the hollow section etween the two fcing pltes cnnot sustin sher ction Becuse of this fct the sher deformtion of Z-core sndwich pnel under ending in the wek direction cnnot e ignored Although the flexurl deformtion of Z-core sndwich pnel cn e clculted simply from em theory the sher deformtion is much more difficult to clculte due to the mutul ction etween the fcing pltes nd the Z-core stiffener Considering the contct etween the Z-core flnges nd the fcing pltes the sher deformtion of typicl segment in Z-core sndwich pnel is nlyzed sed on comptiility conditions By using Cstiglino s second theorem the equtions for clculting the deflection cused y sher ction of Z- core sndwich pnel under ending in wek direction re otined The overll deflection of the Z-core sndwich pnel is superposed y the deflections cused y flexurl nd sher ctions respectively The ccurcy of the presented equtions for clculting the deflection of Z-core sndwich pnel is finlly verified y compring the predicted results with experimentl results reported in corresponding reference It is found tht the predicted results from the presented eqution gree quite well with experimentl results which shows the reliility nd ccurcy of the proposed equtions Keywords: Z-core sndwich pnel ending ehvior wek direction sher deflection comptiility conditions ITRODUCTIO A steel sndwich pnel is consisted of two fcing pltes nd core etween them This structure hs high flexurl stiffness light weight nd especilly it hs high resistnce to dynmic nd lst lods Due to these dvntges it is widely used in ship nd offshore engineering such s ship nd offshore pltform decking or doule-skin vessels It is lso potentil for this structure to e used in uilding nd constructionl industries Coming with light weight mterils such s luminum the sndwich pnels cn e lso used in terrestril nd spce engineering For steel sndwich pnel different types re clssified ccording to the cores Such commonly used types include we-core C-core Z-core X-core V-core nd truss-core etc The cores re plced generlly in single direction which cuses the sndwich pnel of different stiffnesses in the two length directions In the direction of the core plcement the ending stiffness the sher stiffness nd the torsion stiffness re ll high However in the direction perpendiculr to the core plcement or so-clled trnsverse direction the sher stiffness is much weker The difference of the mechnicl properties of sndwich pnel in two directions mkes it difficult to nlyze this structure theoreticlly ecuse it is essentil to e composite structure In the literture mny efforts hve een mde to simplify sndwich pnel to e n equivlent orthotropic thick plte sed on providing the pproprite solutions of some fundmentl structurl *Address correspondence to this uthor t the School of Civil Environmentl Engineering nyng Technologicl University nyng Avenue Singpore 69798; Tel: Fx: E-mil: ChenChng@ntuedusg X properties Such erly representtive work ws conducted y Liove nd Btforf (948) [] nd Liove nd Huk (95) [2] Simplifying D sndwich pnel into 2D equivlent plte it is necessry to give ccurte solution of some elstic constnts such s the ending stiffnesses in two directions the twisting stiffnesses nd the sher stiffnesses in two directions Liove nd Huk (95) derived the elstic constnts for sndwich pnels with continuous corrugted core sed on the ssumption tht the cross section of the core-stiffeners is symmetricl out verticl plne Lter on mny reserchers pid much effort on deriving ccurte solutions of these elstic constnts such s the work reported in Refs [-8] Bsed on these closed-form solutions of the elstic constnts the sttic ehvior of sndwich pnels cn e nlyzed theoreticlly nd numericlly Cheng et l (2006) [9] evluted the ccurcy of some elstic constnts of sndwich pnels with vrious cores y using finite element nlysis Chng et l (2005) [0] studied the ending ehvior of corrugted-core sndwich pnels y using Mindlin-Reissner plte theory Romnoff et l ( ) [-] nlyzed the ending ehvior of we-core sndwich ems y using the solutions of elstic constnts Bunnic et l (200) [4] lso investigted the ehvior of corrugted core sndwich pnels y using finite element method In this pper Z-core sndwich pnel under ending in wek direction is studied The ending ehvior of the Z- core sndwich pnel is then ssessed from the lod versus deflection reltionship In clculting the deflection simplified theoreticl nlysis for deriving the sher deformtion is conducted nd closed form equtions for clculting the deflection of Z-core sndwich pnels re presented The ccurcy of the derived equtions is lso verified 20 Benthm Open

2 Prediction on Deflection of Z-Core Sndwich Pnels in Wek Direction The Open Ocen Engineering Journl 20 Volume 6 89 THEORETICAL AALYSIS Typicl Segment in Z-Core Sndwich Pnel As shown in Fig () Z-core sndwich pnel is consisted of series of Z-core stiffeners nd two fcing pltes which re clled top fcing plte nd ottom fcing plte respectively The Z-core stiffeners re connected to the top nd ottom fcing pltes y using lser spot weld or selftpping screws Generlly the Z-core stiffeners re plced only in one direction s it is shown in Fig () tht the Z- core stiffeners re plced long x-xis Due to this reson the sndwich pnel hs different stiffnesses in x- nd y- directions It is esy to see tht the direction in y-xis is the wek direction due to lck of strengthening of the Z-core As the fcing pltes re minly sujected to ending ction nd the Z-core stiffeners re used to resist the sher ction the sher stiffness in the wek direction is definitely weker Fig () A C-core sndwich pnel If Z-core sndwich pnel is sujected to uniform loding typicl segment s shown in Fig (2) cn e isolted to nlyze It is ssumed tht ech segment in Z-core sndwich pnel hs similr deformtion property to its djcent one or ech segment hs sme mechnism in deforming This ssumption mkes it resonle tht representtive typicl segment s shown in Fig (2) cn e studied nd the deformtion clcultion of this segment cn e lso pplicle for other segments In Fig (2) the length of the top nd the ottom fcing pltes of the segment is denoted y s This length is lso identicl to the distnce etween ny two djcent C-cores The distnce etween the mid-plne of the top nd ottom fcing pltes is denoted y h p Similrly h c is used to represent the distnce etween the mid-plnes of the two flnges of the Z-core The we of the Z-core stiffener is locted in the mid-point of the fcing pltes nd the position of the connection etween the fcing pltes nd the Z-core re descried y l l l c nd l d respectively It is noted tht the segment is still itself if it is rotted y 80 o l = l nd l c = l d However the segment in Fig (2) represents more generl model For revity yet more prcticl the thicknesses of the top nd the ottom fcing pltes re ssumed to e sme nd it is denoted y t p The thickness of the Z-core which hs constnt vlue is denoted y t z s If Z-core sndwich pnel is sujected to ending lod the pnel hs no xil forces in ny cross section in thickness direction Therefore only sher force nd ending moment exist in the cross section In the wek direction the ending moment is ssumed to e replced y couple of forces t the two fcing pltes s shown in Fig () However the ending moments t the left nd the right ends of the segment my e different in generl cse It is ssumed tht the ending moments t the left end nd t the right end re M nd M+ΔM respectively M is replced y n equivlent couple of forces nd M+ΔM is replced y couple of forces +Δ The following eqution cn e otined M = h p # % M +!M = +! ( ) h p Eq () lso indictes tht the following reltionship exists ()!M =! h p (2) The sher forces t two ends of the segment however re sme The sher force t ech end is sustined y the top nd the ottom fcing pltes It is ssumed tht the sher force t ech end is V If the directions of the sher forces t two ends of the segment re defined s shown in Fig () contct will exist t the ends of the flnge of the Z-core stiffener The contct forces re denoted y F c nd respectively Due to the contct prolem the sher force sustined y the top fcing plte is not equl to tht sustined y the ottom fcing plte It is ssumed tht the sher forces distriuted to the top nd the ottom fcing pltes re V2-ΔV nd V2+ΔV respectively To mke the segment in equilirium the following eqution must e stisfied ( V 2! V ) # s + ( V 2 + V ) # s = M () Eq () cn e simplified to the following eqution Vs =!h p (4)! cn e determined from the following equ- Then tion! = Vs h p (5) V2-!V V2+!V F c F c V2-!V V2+!V Fig () Equilirium of segment in wek rrngement +! +! l l c h z l d l Fig (2) Typicl segment in C-core sndwich pnel h p However the contct points re different if the sher forces t the two ends re defined s shown in Fig (4) Fig (5) nd Fig (5) shows the different deformtions when the sher forces t two ends of the segment re different The segment hs igger stiffness if it deforms s shown in Fig (5) nd such it is clled strong rrngement Accordingly Fig (5) shows wek rrngement of the segment Such

3 90 The Open Ocen Engineering Journl 20 Volume 6 Chen Cheng definitions on the strong nd wek rrngements re lso given y Fung nd Tn (998) The equiliriums of the typicl segment shown in Figs () nd (4) re in ccordnce with the deformtion in Figs (5) nd (5) respectively V2-!V V2+!V F c F c V2-!V V2+!V Fig (4) Equilirium of segment in strong rrngement +! +!! p +! p2 = 0 (6)! Q +! Q2 = 0 (7) (2) The reltive displcement etween the top fcing plte nd the ottom fcing plte should e equl t the two ends of the segment The following eqution must e stisfied ccording to this ssumption! =!! 4 (8) For the segment in strong rrngement similr comptiility conditions cn e ssumed except the positions of the contct points re different Eqs (6)-(8) cn e used to derive the solutions of the three unknowns F c nd! V!! p!! p2! Q! 4! Q2 Fig (6) Comptiility conditions () wek rrngement () strong rrngement Fig (5) Definition of wek nd strong rrngement If the sher force V nd the ending moments M nd M+ΔM re known only three unknowns in the segment shown in Fig () or in Fig (4) re necessry to e clculted nd they re F c nd!v The closed-form solutions of the three unknowns should e otined from comptiility conditions etween djcent segments Comptiility Conditions Between Adjcent Segments The comptiility conditions of the typicl segment in wek rrngement cn e shown in Fig (6) The following two ssumptions re mde: () There is no reltive displcement etween the fcing plte nd the Z-core flnge t contct points This ssumption is meningful since there will e no seprtion etween ny contct points due to compression ction This ssumption will produce the following two equtions: Comptiility Equtions As cn e seen from Eqs (6)-(8) the comptiility conditions re essentilly to clculte the reltive displcement t some criticl positions This cn e done y using Cstiglino s second theorem To do so the moment digrm of the segment in equilirium s shown in Figs ()-(4) is firstly drwn For revity the ending moment cn e divided into severl prts: = M V! ( ) + M (!V ) + M c ( ) + M d ( F c ) (9) Where M (V Δ) M (ΔV) M c () nd M d (F c ) re the moments cused y different lodings Wek Arrngement The moment digrms produced y M (V Δ) M (ΔV) M c () nd M d (F c ) for the Z-core sndwich segment in wek rrngement re shown in Figs (7)-(7d) respectively In ech moment digrm from Fig (7) to (7d) the segment is lwys in equilirium In Eq (6) to clculte! p +! p2 the moment digrm s shown in Fig (8) is generted Two unit lods in this figure re pplied t the contct point etween the top fcing plte nd the top Z-core flnge Then! p +! p2 cn e clculted from the following eqution ( ) d! p +! p2 = # EI M 0 (0) d ( ) mens the moment digrm y letting where M d 0 F c = nd = 0 ; E is the elstic modulus of the steel mteril I is the second moment of re out the mid-plne

4 Prediction on Deflection of Z-Core Sndwich Pnels in Wek Direction The Open Ocen Engineering Journl 20 Volume 6 9 F c V2 V2 Vsh p!v!v F c V2 V2 () M (V Δ) Vsh p!v () M (ΔV)!V (c) M c () (d) M d (F c ) Fig (7) Moment digrms of segment in wek rrngement Fig (8) Moment digrm Similrly using the moment digrm M ( ) s shown in Fig (0) the following eqution cn e otined s well ( )!! +! 4 = EI M d# (5) # Sustituting the ove eqution into Eq (4) the following eqution cn e otined Sustituting Eq (0) into comptiility condition Eq (6) the following eqution cn e otined F c =! ( V + l c 2 #V )( s 2 l l c % ) ) () ( where! = E z I z EI is the rtio of ending stiffness of the Z-core stiffener nd the fcing pltes out their respective mid-plne in thickness direction ie for unit width plte long x-xis I z = t z 2 nd I = t p 2 Similrly the comptiility condition t the contct point etween the ottom fcing plte nd the ottom Z-core flnge cn e clculted from the following eqution ( ) d! Q +! Q2 = # EI M 0 (2) d where M d 0 ( ) is shown in Fig (9)!V = (# 8 +# 9 ) V 2 # +# 2 +# +# 4 +# 5 +# 6 +# 7 # 8 # 9 (6) ( s where! = 2 + l ) ( s 2 = 2 l ) ( s = 2 l ) ; ( s! 4 = 2 + l )! 8 = l c 4 5 = l s2 6 = l s2 7 = h z s2 ; + ( s 2 # l # l c )2 9 = l d 4 + ( s 2 # l # l d )2 Fig (9) Moment digrm ( 0) M d From Eq (7) the following eqution cn e otined =! ( V + l d 2 + V )( s 2 # l # l d % ) ) () ( Comptiility condition Eq (8) cn e trnsformed into the following formt!! +! 4 = 0 (4) Fig (0) Moment digrm From Eqs () () nd (6) it is esy to find tht the three unknowns F c nd!v cn e clculted once the vlue of sher force V t two ends of the segment is known The steps cn e generlized s follows () From Eq (6) the vlue of! V cn e clculted when the vlue of sher force V is known (2) Sustituting the vlues of V nd! V into Eqs () nd () the vlues of F c nd cn e otined Strong Arrngement Using the sme method the equtions for clculting the three unknowns F c nd F c =! ( V + #V )( + l % 2

5 92 The Open Ocen Engineering Journl 20 Volume 6 Chen Cheng )( s 2 + 2l ) Vsh z + #Vs ) cn lso e otined The detiled 2!h p! () clculting process is not repeted nd the derived equtions re listed s follows F c =! ( V + l 2 + #V )( s 2 + 2l ) Vsh z + #Vs ) % 2!h p! () (7) =! ( V + l 2 + #V )( s 2 + 2l ) Vh 2 z #Vs ) % 2h p! ()!V = (# 8 # 9 +# +# 2 ) V 2 + ( # 9 2 # 0 +# +# 4 ) Vh z h p (8) # +# 2 +# +# 4 +# 5 +# 6 +# 7 # 8 2# 9 # 0 # 2# 2 # (9) In Eq (9) the expressions of the constnts re listed s follows: ( s! = 2 + l ( s ) 2 = 2 l ) ( s = 2 + l ) ( s 4 = 2 l ) ;! 5 = l s2 = l s2 6 = h z s2 7 8 = l + 4 ( s 2 + 2l ; )2! 9 = l s + 4 ( s 2 + 2l ) 0 = l s = l + 4 ( s 2 + 2l ; )2 = l s + 4 ( s 2 + 2l ) = l h z + 8 ( s 2 + 2l ) 4 = l sh z + 8 Sher Deformtion in Verticl Direction After the vlues of the unknowns cn e clculted the sher deformtion of the segment shown in Figs () nd (4) cn e nlyzed To clculte Z-core sndwich pnel under ending only the deformtion in verticl direction is nlyzed which is shown in Fig () The sher deformtion in verticl direction Δ s of this segment is clculted from the following eqution! s =! + +! +! 4 2!! 4 Fig () Sher deformtion of segment! (20) To clculte Δ s moment digrm M s shown in Fig (2) is generted Then Δ s is otined from the following eqution! s = # 2 EI Md (2) Fig (2) Moment digrm M Coming with Eqs () () nd (6) the verticl displcement Δ s cused y sher ction for the Z-core sndwich pnel in wek rrngement cn e clculted from the following eqution! s = V 2EI (!V 6EI ( 4EI * s 2 + l % + s # 2 ( l % + s # 2 + l % + s # 2 ( l % - # + ( + ) s 2 h z + s2 2 h z + )h )h * s 2 + l % + s # 2 ( l % ( s # 2 + l % ( s # 2 ( l % - (22) + # * 2 s F c l c 2 ( l ( l % c # + F l 2 s c2 d 2 ( l ( l %- d # + For the Z-core sndwich pnel in strong rrngement the sher deformtion cn e lso otined in the similr wy nd it is listed s follow * s! s = V 2 + l % + s # 2 ( l % + s # 2 + l % s # 2 ( l % - + # 2EI ( + ) s 2 h z + s2 2 h z + )h )h +!V * s 6EI 2 + l % + s # 2 ( l % ( s # 2 + l % ( s # 2 ( l % - (2) + # + * 2 s F 4EI c l 2 + 2l % # + F l 2 s c ) + F l 2 s c l % # + F l 2 s- c2 + ) If Z-core sndwich pnel is consisted of n typicl segments then the totl verticl displcement of the sndwich pnel w S is clculted from the following eqution w s = n! s (24) As the fcing pltes nd the Z-core stiffener in ending ehve in plne strin stte the elstic modulus E in ll ove equtions should e replced y E * nd E * = E! v 2 ( ) where v is Poisson s rtio Bending Deformtion in Verticl Direction For Z-core sndwich pnel under ending in wek direction the ending deformtion cn e clculted simply from em theory However the second moment of re of the Z-core sndwich pnel in wek direction I s is clculted from the following eqution

6 Prediction on Deflection of Z-Core Sndwich Pnels in Wek Direction The Open Ocen Engineering Journl 20 Volume 6 9 I s = 2 t h 2 p p (25) Eq (25) is otined sed on the ssumption tht the ending moment is sustined y the top nd the ottom fcing pltes while the Z-core stiffeners do not er ny ending moment CASE STUDY Verifiction Through Experimentl Results To verify the presented method in clculting the verticl deformtion of Z-core sndwich pnels under ending in wek direction n experimentl model reported y Fung nd Tn (998) is used to ssess the ccurcy of this method The sic dimensions of the Z-core sndwich pnel cn e found in Fig () The pnel is 495 mm in width nd 2000 mm in length with 6 Z-sections s core stiffeners t nominl spcing of 0 mm The fcing pltes nd the Z-sections re connected through self-tping screws The other dimensions cn e found in Tle point just under the we of the Z-core stiffener The pnel is sujected to line lod t the midspn nd thus it is threepoint ending model s shown in Fig (4) In experimentl test this pnel ws tested in its wek rrngement The reltionship etween the pplied lod nd the deflection t the midspn is otined from test mesurement Fung nd Tn (998) presented the reltionship etween the pplied lod P nd the deflection t the midspn w s follows () for the first specimen in wek rrngement P = 4596w (26) In Eq (26) the units of P nd w re mm nd mm or km nd m respectively (2) for the second pnel in strong rrngement P = 996w (27) The overll deflection of ech Z-core sndwich pnel under three-point ending is consisted of two prts: the deflection cused y ending w nd the deflection produced y sher w s The ending deflection is clculted from the following eqution w = (! v2 ) PL 48EI s (28) where L = 2000 mm nd 0 for the first nd the second Z-core sndwich pnels respectively Fig () Z-core sndwich pnel specimen Tle Dimensions of the Z-Core Sndwich Pnel Prmeter Pnel s (mm) 00 l (mm) 265 l (mm) 240 l c (mm) 240 l d (mm) 265 h p (mm) 04 h z (mm) 000 v 0 E (mm 2 ) E c (mm 2 ) t p (mm) 20 t c (mm) 20 The pnel is plced on two roller erings t the ends to simulte n idel simply supported oundry conditions The supporting centres of the rollers re ssumed to e t the Fig (4) Loding scheme on the Z-core sndwich pnel specimen Using Eqs (2) nd (24) the sher deflection w s cn lso e clculted The vlues of n in Eq (24) for the two pnels re 75 nd 55 respectively The vlues of n re not 8 nd 6 for the first nd for the second pnels respectively ecuse the supporting positions t two ends of the pnels re locted t the we of the Z-core stiffeners s cn e seen in Fig (4) which mkes the end Z-core stiffener only hs hlf length The predicted totl deflection of the pnel w is the sum of w nd w s If line lod with vlues of 0928 mm nd 92 mm is pplied to the first nd the second pnels the deflections t the midspn of the sndwich pnels re generlized in Tle 2 w e in Tle 2 denotes the experimentl vlue of the deflection t midspn From Tle 2 it cn e seen tht the deflection of the two Z-core sndwich pnels is minly dominnt y the sher deformtion while the ending deflection is much smller The predicted result of the reltionship etween the lod nd the displcement t the mid-point of the pnel cn e clculted from the presented equtions nd they re generlized s follows

7 94 The Open Ocen Engineering Journl 20 Volume 6 Chen Cheng () for the first pnel in wek rrngement P e = 4256w (29) (2) for the second pnel in strong rrngement Tle 2 P e = 827w (0) Comprison Between Experimentl nd Predicted Results Prmeter Pnel Pnel 2 P (mm) w e (mm) w (mm) w s (mm) w (mm) Figs (5) nd (5) show the comprison of the lod versus displcement of the two pnels etween predicted nd experimentl fitting results The comprison shows the presented equtions cn provide resonly good estimtion for the ending ehviour of Z-core sndwich pnels P () P () Predicted result Experimentl result w (mm) () Pnel in wek rrngement Predicted result Experimentl result w (mm) () Pnel 2 in strong rrngement Fig (5) Comprison of the lod-displcement reltionship for the pnel specimens A reltive error etween the results clculted from the theoreticl method in this study nd the experimentl mesurement is defined s follow e = P! P e 00% () P From Eq () the clculted reltive errors re -74% nd -65% respectively The vlues of the errors for the two models re oth negtive nd it mens the predicted lod is smller thn the experimentlly mesured lod Therefore the predicted results re sfe It cn e seen tht the vlues of the errors re cceptle nd the ccurcy nd reliility of the presented equtions re ensured COCLUSIOS The ending ehvior of Z-core sndwich pnel is studied nd equtions for predicting the sher deformtion of Z- core sndwich pnel in wek direction with wek nd strong rrngements re derived Through cse study the following two conclusions cn e mde: The presented equtions in this study re ccurte nd relile in clculting the deflection of Z-core sndwich pnel under ending in its wek direction 2 For Z-core sndwich pnel under ending in wek direction the sher deformtion is much igger thn the flexurl deformtion COFLICT OF ITEREST The uthor(s) confirm tht this rticle content hs no conflicts of interest ACKOWLEDGEMET Declred none REFERECES [] C Liove nd SB Btdorf A generl smll deflection theory for flt sndwich pltes ACA Tech ote 526 t Advisory Com for Aeronutics Wshingtong DC 948 [2] C Liove nd RE Huk Elstic constnts for corrugted-core sndwich pltes ACA Tech ote 2289 t Advisory Com for Aeronutics Wshingtong DC 95 [] T ordstrnd LA Crlsson nd HG Allen Trnsverse sher stiffness of structurl core sndwich Composite Struct vol 27 pp [4] TC Fung KH Tn nd TS Lok Sher stiffness D Qy for C-core sndwich pnels J Struct Eng ASCE vol 22 pp [5] TC Fung nd KH Tn Sher stiffness for Z-core sndwich pnels J Struct Eng ASCE vol 24 pp [6] TC Fung KH Tn nd TS Lok Elstic constnts for Z-core sndwich pnels J Struct Eng ASCE vol 20 pp [7] TS Lok nd QH Cheng Elstic stiffness properties nd ehvior of truss-core sndwich pnel J Struct Eng ASCE vol 26 pp [8] P Kujl nd A Klnc Anlyticl nd numericl nlysis of non-symmetricl ll steel sndwich pnels under uniform pressure lod In interntionl design conference design Durovnik pp [9] YB Sho ST Lie nd SP Chiew Sttic strength of tuulr T- joints with reinforced chord under xil compression Adv Struct Eng vol pp [0] WS Chng E Ventsel T Kruthmmer nd J John Bending ehvior of corrugted-core sndwich pltes Composite Struct vol 70 pp [] J Romnoff nd P Vrst Bending response of we-core sndwich ems Composite Struct vol 7 pp

8 Prediction on Deflection of Z-Core Sndwich Pnels in Wek Direction The Open Ocen Engineering Journl 20 Volume 6 95 [2] J Romnoff nd P Vrst Bending response of we-core sndwich pltes Composite Struct vol 8 pp [] J Romnoff P Vrst nd A Klnc Stress nlysis of homogenized we-core sndwich ems Composite Struct vol 79 pp [4] Bunnic P Crtrud nd T Quesnel Homogeniztion of corrugted core sndwich pnels Composite Struct vol 59 pp Received: Septemer Revised: Octoer 0 20 Accepted: Octoer Chen Cheng; Licensee Benthm Open This is n open ccess rticle licensed under the terms of the Cretive Commons Attriution on-commercil License ( licensesy-nc0) which permits unrestricted non-commercil use distriution nd reproduction in ny medium provided the work is properly cited