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Effect of Defect on the Compressive Response of Sandwich Structures with Carbon Fiber

Macroscopic response of carbon-?ber pyramidal truss core panel taking account of local defect

Hongshuai Lei a,*,Xiaolei Zhu b,*,Haosen Chen b,Hualin Fan c,*,Mingji Chen d, Daining Fang a,b

a College of Engineering,Peking University,Beijing100871,China

b Department of Engineering Mechanics,Tsinghua University,Beijing100084,China

c College of Mechanics an

d Materials,Hohai University,Nanjing210098,China

d National Center for Nanoscienc

e and Technology,Beijing100190,China

a r t i c l e i n f o

Article history:

Received4January2015 Received in revised form

11March2015

Accepted29April2015 Available online8May2015

Keywords:

https://www.wendangku.net/doc/cf15133679.html,ttice truss

B.Mechanical performance D.Local defect a b s t r a c t

In present paper,the macroscopic responses of carbon-?ber pyramidal truss core panel subject to uni-axial compressive loading are investigated through experimental,theoretical and?nite element analysis (FEA)methods,taking account of local defect.The local defect is introduced in the form of missing strut for the unit cell.A theoretical model is proposed to predict the effect of defect on the compressive stiffness and ultimate strength of pyramidal truss core sandwich panel.To study the buckling and crushing behavior,a progressive damage model based on the Hashin failure criteria is implemented in ABAQUS software by means of a user subroutine VUMAT.The sensitivity of sandwich panel to the per-centage of missing struts,defect type,and defect spatial con?guration are respectively discussed. Comparing with the open-cell foam and honeycombs,the pyramidal truss has better defect tolerant than bending dominated construction.Moreover,the effects of defect type and defect spatial con?guration on the strength of pyramidal truss panel are signi?cant under the same percentage of missing struts.The numerical results reveal that the discrepancy can be up to14%and29%,respectively.The local defect should be considered in the design and application of pyramidal truss structure.

1.Introduction

Pyramidal truss structure has gained increasing attention in recent years due to their remarkable speci?c strength and stiffness as well as potential multifunctional advantages[1e6].In fact,it retains an open-cell construction and has lower density and higher porosity in contrast with the convenient lightweight construction. Several manufacturing processes have been developed to fabricate the truss core with metal or?ber material,such as investment cast method[7e9],deformation forming method[10,11],hot press molding method[6,12],and slot-?tting method[13,14].The macroscopic effective stiffness and strength have been systemati-cally investigated by theoretical,numerical and experimental methods.However,various types of defects[15e23],such as missing strut,stochastic dispersion of node and non-periodic microstructure,can be originated in the manufacture or practical applications.The lightweight truss construction composites are sensitive to local defects,thus the unexpected defects will result in crucial in?uence on the mechanical performance of lattice materials.

For the honeycombs construction,Silva and Gibson[15],Guo and Gibson[20],and Wang and McDowell[21]investigated the effect of missing cell walls on the elastic buckling strength,plastic collapse strength and initial yield strength,using the?nite element method(FEM).In the aspect of lattice truss,Wallach and Gibson [16]analyzed early the effect of removing truss core members on the effective modulus of octet-truss core structure using FEM.Their results revealed that the lattice truss construction was more tolerant to this type defect than convention foam.The compressive modulus and strength of structure decreased linearly with the fraction of ligaments removed.Hyun et al.[22]investigated the effect of geometry imperfections and material property imperfec-tions on the macroscopic response of wire-woven bulk Kagome truss core through FEM and experimental tests.The periodic boundary conditions were applied on the unit cell to avoid the

*Corresponding authors.

E-mail addresses:leihongshuai@https://www.wendangku.net/doc/cf15133679.html,(H.Lei),zhuxiaolei856028@126. com(X.Zhu),fhl02@https://www.wendangku.net/doc/cf15133679.html,(H.

Fan).Contents lists available at ScienceDirect Composites Part B

jou rn al homepage:https://www.wendangku.net/doc/cf15133679.html,/loc

ate/compositesb

https://www.wendangku.net/doc/cf15133679.html,/10.1016/https://www.wendangku.net/doc/cf15133679.html,positesb.2015.04.052

Composites Part B79(2015)311e321

boundary effect.The defect interaction and reinforcement for the Kagome truss construction were discussed by Zhu et al.[23] through theoretical and FEM.An analytical model was proposed to predict the interaction of two defects in lattice materials based on a single defect model.

It should be noted that,for the pyramidal truss structure,the published studies on the effect of local defect are less by far.Biagi and Bart-Smith[17]investigated the effect of unbound nodes be-tween the truss cores and face sheets on the compressive and shear performance through FEM,experimental and theoretical methods. They discussed the in?uences of percentage of unbound nodes and spatial con?guration,and obtained the upper and lower limit on stiffness and strength.A three-dimensional model of a9-cell core used for small scale simulation was created in Abaqus software,and meshed using continuum element.Recently,the effects of missing unit cell on the natural frequencies and the corresponding vibration modes of pyramidal truss core sandwich panel were studied by Lou et al.[12]through FEM.In fact,the missing strut of unit cell will lead to the degradation of stiffness and strength,thereby affecting the overall performance of construction.In our previous paper[24], a theoretical model was proposed,considering the strut bending and shear behavior,to describe the effect of missing struts on the overall stiffness and strength of pyramidal truss core sandwich panel.However,the in?uences of defect type and defect spatial con?guration were neglected.

It can be found that,from the above mentioned publication,the ?nite element method has been widely used to evaluate the effect of defect on the macroscopic performance of lattice truss com-posite.The buckling and crushing behavior of lattice truss can be obtained by implementing various failure criteria.Actually,due to the discrepancy of boundary condition and manufacturing quality, the construction can exhibit different failure modes during the loading process.Xiong et al.[6]involved the failure behavior in pyramidal truss sandwich panel subject to edge compressive by experimental tests,and listed as three different failure modes,such as face sheet wrinkling,macro-buckling,and strut crushing.

The present work involves the effect of local defect on macro-scopic response of carbon-?ber pyramidal truss core sandwich panel subject to uniaxial compressive.The defect is introduced in the form of missing strut for the individual cell.A theoretical model is proposed to predict the overall stiffness and ultimate strength.A three-dimensional?nite element model containing4-cell is created according to experimental tests.The strut buckling and collapse behavior are simulated based on the Hashin failure criteria which is implemented in the ABAQUS software by means of a user subrou-tine VUMAT.The effects of the percentage of missing strut,defect type,and defect spatial con?guration are respectively discussed.

2.Experiments details

2.1.Materials and manufacturing

In present paper,unidirectional carbon?ber cloth(T300)was used to fabricate the face sheets and pyramidal lattice truss core, and the polymer used as matrix was Unsaturated Polyester Resin 189.The face sheets were?rstly manufactured using hot press molding method.32-ply carbon?ber cloth was stacked in the sequence of[0 /90 ],and the thickness of each cloth was0.125mm. The pressure was set as0.6MPa,and kept for half an hour at140 C. The truss core was fabricated through expendable pattern casting process,and the diameter of lattice strut was4mm.It should be mentioned that the?ber in strut is unidirectional along the axial direction.Finally,the face sheets and truss core were cemented together using the strong adhesive which was provided by CHN carbon?ber technology Co.Ltd,China.

As shown in Fig.1,three types of compressive samples con-taining4-cell were cut from the pyramidal truss core sandwich panel,including the perfect cell(Fig.1b),missing two-strut(Fig.1c) and missing four-strut(Fig.1d).The shape dimension of sample was listed in Table1,and the speci?c structures of three sample types were shown schematically in Fig.2.As seen,the solid circles denote the top nodes bound with upper face sheet,and the hollow circles are the base nodes bound with lower face sheet.Solid lines represent the carbon?ber strut connecting two nodes,and the dash lines represent the struts have been removed.

https://www.wendangku.net/doc/cf15133679.html,pressive tests

To evaluate the effect of defect on the macroscopic mechanical performance of pyramidal truss core panel,uniaxial compressive tests were conducted using Instron-3382servo-electric testing machine at the ambient temperature following the ASTM C365 standard,and three samples per type.The loading speed was set as 0.5mm/min.In fact,the three types were corresponding to the percentage of missing strut0.00%,12.5%,and25.00%.

3.Theoretical model

A theoretical model has been proposed in our previous paper

[24],based on the general elastic theory,to predict the effect of missing strut percentage on the overall stiffness and strength of truss core panel.Moreover,the bending and shear effects of strut were considered in contrast with traditional theoretical models. This was necessary to obtain accurate stiffness,especially for the lower relative density of truss core.

The compressive stiffness of pyramidal truss core with perfect unit cell was expressed as

Ee0Tzz?E s r sin4ut

l2t2e1tvT

E s sin2u cos2u(1)

where E s was the compressive stiffness of strut material.r was lattice relative density,u was the angle between the truss members and face sheet,and l were the length of strut.v was the Poisson's ratio.Note that,the mark‘(0)’denoted the unit cell was perfect in present study.‘(1)’and‘(2)’represented the unit cell missing one-strut and two-struts,respectively.

According to the geometrical relation,the compressive stiffness of truss core with defects can be obtained as

Ee1Tzz?

3Ee0Tzz

;Ee2Tzz?E

e0T

:(2)

For the ultimate strength of pyramidal truss core,it should be divided into two cases.One was the strut buckling failure.Ac-cording to the Euler buckling formulation,the ultimate strength can be expressed as

se0Tu?

p2d2E s

4l2

r(3)

Here,d was the diameter of strut.When the main failure mode was strut crushing,it would be expressed as

se0Tu?r a s cr sin2u(4)

where s cr was the ultimate compressive strength of strut material and a was a material constant depending on the manufacturing quality which can be obtained through the uniaxial compressive tests.For the truss core with defects,the ultimate compressive strength can be derived similar as Eq.(2)which can expressed as

H.Lei et al./Composites Part B79(2015)311e321 312

s e1T

u ?

3s cr ;s e2T

u ?

1s cr :(5)

As know,the overall mechanical properties of composite depended crucially on the volume fraction of matrix and rein-forcement.Similarly,the performance of sandwich composite structure containing many unit cells depended on the volume fraction of each cell type,especially for the compressive modulus.Hence,the effective modulus of pyramidal lattice truss core panel can be calculated by the mixture rule,as follows:

D ?

m àn m D e0Ttn m

D eT

(6)

where m was the total number of truss core cell,and n was the

number of missing strut cell.Symbols D ,D (0),and D (.)represented the stiffness and ultimate strength of panel,perfect cell,and missing strut cell,respectively.4.Finite element analysis

It has been con ?rmed that the numerical simulation was an effective method to evaluate the macroscopic performance of composite.Actually,some researchers have adopted this method to investigate the lattice truss composite [12].For the pyramidal truss

core sandwich panel subject to compressive loading,the strut buckling and strut crushing are the main failure modes which have been demonstrated in experiment.To study the failure behavior of truss panel,the ?nite element model and failure criteria will be introduced in this section.4.1.Finite element model

According to the geometrical dimension of experimental sam-ple,a three-dimension pyramidal lattice truss panel FEA model containing 4-cell was established in Abaqus software (as shown in Fig.3).The material properties obtained through experimental tests were given in Table 2.The face sheets were modeled as a composite laminate and meshed with continuous shell elements (SC8R).The struts were meshed with linear reduced integration solid elements (C3D8R).Note that for the sandwich panel subject to compressive condition,the effect of interfacial bound strength between face sheets and core on the macroscopic response is slight.This can be attributed to the shear stress is very small in the di-rection 2and 3,which have been con ?rmed in [17].Therefore,the interface between face sheets and struts is tied together in our model,and it will maintain perfect during the loading process.

The low face sheet is ?xed referring to the experimental setup.In the case of buckling analysis,a uniaxial uniform load (500N)will be applied along the direction 1,to obtain the effect of defect on the eigenvalues of overall structure.The rotation and sliding in this direction will be restricted.For the structure crushing analysis,the strain increment only in direction 1will be adopted to improve the convergence and computational ef ?ciency.4.2.Buckling analysis

To investigate the imperfection sensitivity of a structure,an eigenvalue buckling analyses will be performed at ?rst.In fact,the eigenvalue buckling is generally used to estimate the critical load of a structure,which can provide helpful estimate of collapse mode shape.Moreover,the linear perturbation theory is usually

utilized

Fig.1.Fabricated carbon-?ber pyramidal truss core compressive samples.

Table 1

Shape dimensions of pyramidal lattice truss core sandwich panel.Category

Value Vertical height of core 30mm Diameter of strut 4.0mm Length of strut

42.42mm Angle between strut and face-sheet 45

Thickness of face-sheets 4.0mm Length of sample 100.0mm Width of sample 100.0mm Thickness of sample

38.0mm

H.Lei et al./Composites Part B 79(2015)311e 321313

for the buckling analysis.The basic theoretical equations are sum-marized brie ?y as following.

At the initial equilibrium state,the balance equation of system can be expressed as

e?K E t?K G Tf U g ?f P g (7)

where [K E ]and [K G ]are the stiffness matrix corresponding to initial state and various stress states,respectively.U is the node displacement vector,and P is the node stress vector.

Based on the energy theory,the eigenvalue equation can be derived as

e?K E tl i ?K G Tf f i g ?0

(8)

where l i are the eigenvalues;f i is the buckling mode shapes.i denote the i th buckling mode.The subspace iteration eigensolver is employed in present paper to obtain the eigenvalues.It should be mentioned that,the geometric imperfection seed can be deter-mined by analysis the changing trend of eigenvalues,which is a crucial material parameter in the following crushing analysis.It has been con ?rmed that the strut buckling would result in the local delamination in ?ber reinforced composite,thereby causing the reduction of overall stiffness and strength [6,12].4.3.Crushing analysis

When the ?ber reinforced material fails,it might be due to the matrix cracking,?ber fracture,?ber e matrix interfacial debonding,and their combinations [25].To effectively predict the damage initiation of ?ber reinforced composite,several failure criteria have been proposed in previous studies considering the failure modes,such as maximum stress/strain,Hashin,Hoffman,Tsai-Hill and Tsai-Wu criteria [26e 29].Among these criteria,Tsai e Hill and Tsai e Wu criteria cannot identify the detailed failure modes [30].Actually,the Hashin criteria still remain one of the most effective failure criteria in predicting different failure modes [30].Therefore,it will be utilized to describe the damage initiation of face sheets and truss core during crushing process.At the three-dimensional state,six failure modes should be considered,including ?ber ten-sion,?ber compression,matrix tension,matrix compression,ten-sile delamination,and compressive delamination.The speci ?c expressions are represented as follows.Tensile ?ber failure,s 11!0.

s 11X t

2t t 12S 12 2t t 13

S 13

2?1(9)

Compressive ?ber failure,s 11<0.

à s 11

X c

?1(10)

Tensile matrix failure,s 22ts 33!0.

s 22ts 33Y t 2t 1S 23

! t 223às 22s 33 t t 12S 12 2t t 13

S 13 2?1(11)

Compressive matrix failure,s 22ts 33<

Fig.3.FEA model of pyramidal truss core panel:(a)Sandwich panel and (b)four-cell

core.

Fig.2.Speci ?c construction of three type samples:(a)Perfect cell,(b)missing two-strut,and (c)missing four-strut.

H.Lei et al./Composites Part B 79(2015)311e 321

314

1 c "

Y c

à1

es22ts33Tt

s22ts33

23!

t223às22s33

t12

t13

(12)

Tensile delamination failure,s33!0.

s33 Z t 2

t13

S13

t13

S23

?1(13)

Compressive delamination failure,s33<0.

t13 S13 2

t13

S23

?1(14)

where s(including s11,s22and s33)and t(including t12,t13and t23)are the stress components of each integration point in FEA model.For the laminated composite,X t and X c are the tensile and compressive strength in the longitudinal direction(along the?ber direction).Y t and Y c are the tensile and compressive strength in the transverse direction(perpendicular to the?ber direction in-plane). Z denotes the tensile strength in the out-plane direction,and S denote the shear strength.These material parameters can be directly determined through experimental tests.When one of above indexes is greater than or equal to one,the composite may initiate to fail.

Once the damage initial criteria in Eqs.(9)e(14)is satis?ed,the stress variables of integration point should be updated to re?ect the material damage.In general,a material stiffness degradation rule will be introduced to describe the structure failure progres-sive process.Until now,most of the published material degra-dation models belong to one of three general categories: instantaneous unloading,gradual unloading and constant stress at failure material point[31].For the instantaneous unloading model,the material stiffness is directly reduced to zero when the failure occurs.It is easy to realize by programming,however,it is not realistic,as the material can retain some load carrying ca-pacity after failure.In fact,the material property degradation is extremely depending on the failure mode.Taking account of the distinction between the above mentioned six failure modes,Tan [32]assumes the stiffness degradation associated with damage due to compressive loads is different from that under tensile loads,and the speci?c stiffness degradation parameters are given in Table3.This stiffness degradation rule has been widely used in the investigation of composite progressive failure[30e35].It means when the failure criteria are satis?ed,the state variable will be updated and the material stiffness is reduced according to the rule.According to the Hashin criteria and stiffness degrada-tion rule,a user subroutine VUMAT was developed which can be implemented in the ABAQUS/Explicit software,to control the initiation and propagation of local damage.

The?ow chart of the?nite element analysis is shown in Fig.4, which can be summarized as:(1)Establish the FEA model according to the geometrical dimension of sample,and de?ne the material parameters;(2)Create the?rst analysis step and choose buckle and linear perturbation in procedure type.Apply a uniform load in the upper face sheets,and the?le is named as buckling analysis.In this step,we can obtain ten eigenvalues and the reasonable geometric imperfection seed;(3)Create the second analysis step and named as crushing.And then,de?ne a displacement increment in upper face sheet.Edit the?le keywords and add the imperfection through parameter de?nition.The effect of mode shape would be considered in crushing analysis process;(4)Call the user subroutine VUMAT. The Hashin damage initiation criteria are used to judge whether some elements have failed.If no failure is detected,the applied displacement is increased and the analysis continues.Update the stress variables,when the criteria is satis?ed,the stiffness will degraded.Parallel calculations are implemented on a high-performance computer to improve the computational ef?ciency. 5.Results and discussion

https://www.wendangku.net/doc/cf15133679.html,paring of experimental,theoretical,and FEA results

Three samples per type,having the same strut spatial con?gu-ration,were experimentally tested and the corresponding compressive stress vs strain curves were shown in Fig.5by solid dots.By comparing each panel type,it can be found the effect of defect is signi?cant on the mechanical performance.As seen,the ultimate strength and overall stiffness of pyramidal truss core sandwich panel decreased by approximate30%in contrast with perfect cell.Observing the response curves,we can found that the panels exhibit a linear elastic behavior in the initial stage until core yield.There almost no plastic yield process after the compressive stress increases to peak value.In fact,a slow degradation of truss core is followed which is called as densi?cation process.At this stage,the struts have crushed.In our pervious paper[24],it has been con?rmed by analyzing the failure morphologies.

Table2

Mechanical properties of laminate and strut.

Laminate X t?1975MPa;X c?1925MPa;Y T?74MPa;Yc?167MPa;S12?45MPa;

n12?0.34;n13?0.34;n23?0.52;

E11?129GPa;E22?9.5GPa;E33?9.8GPa;G12?4.7GPa;G13?4.7GPa;G23?3.2GPa

Strut X t?500MPa;X c?480MPa;Y t?20Mpa;Y c?40MPa;Z t?20MPa;Z c?40MPa;

S12?12MPa;S13?12MPa;S23?7MPa;n12?0.34;n13?0.34;n23?0.52;

E11?34.0GPa;E22?2.4GPa;E33?2.5GPa;G12?1.2GPa;G13?1.2GPa;G23?1.0GPa;

Table3

Stiffness degradation of?ber reinforced composite used in VUMAT.

Failure mode E11E22E33G12G13G23n12n13n23 Tensile?ber failure0.07e e0.070.07e0.070.07e Compressive?ber failure0.07e e0.070.07e0.070.07e Tensile matrix failure e0.2e0.2e0.20.2e0.2 Compressive matrix failure e0.4e0.4e0.40.4e0.4 Tensile delamination failure e e0.2e0.20.2e0.20.2 Compressive delamination failure e e0.2e0.20.2e0.20.2

H.Lei et al./Composites Part B79(2015)311e321315

In Fig.5,the hollow dots curves are the simulation results ob-tained by our established FEA model and VUMAT subroutine.It should be noted that the geometric imperfection seed,which was implemented in the crushing analysis process,can be calculated as 0.03by comparing of FEA and experimental results for the perfect cell panel.In Fig.5(b)and (c),the FEA result curves of missing two-strut and missing four-strut panel are obtained based on the same imperfection seed.As can be seen,the trends of simulation curves are in agreement with experimental results.

The comparison of effective modulus is shown in Fig.6and Table 4,between experimental,theoretical,and FEA results.The theoretical results are calculated by Eqs.(1)e (6),and the material parameters required for calculation can be found in Table https://www.wendangku.net/doc/cf15133679.html,paring these re-sults,although some slight discrepancy can be found,especially be-tween theoretical and experimental,but we believe it was acceptable.The discrepancies are mainly due to two possible reasons:one is the theoretical model neglect the in ?uence of strut spatial con ?guration;

and the other is that the strut performance maybe not stable for the manufacturing and processing.Therefore,through the comparison,the theoretical model and FEA model presented in this paper can be used to predict the changing trend of effective modulus with the in-crease of missing strut percentage.5.2.Effect of percentage of missing struts

For the lattice truss composite structure,it has been known that the strut volume faction plays an important role in determining the mechanical properties of overall structure.This is mainly due to the strut is the main load-bearing structure.Thus,the missing strut will affect the macroscopic response which has been con ?rmed by tests.To investigate the defect tolerance of pyramidal truss core sand-wich panel,the mechanical performance is discussed with the percentage of missing struts in the range from 0to 50%.

Fig.7illustrates the speci ?c panel construction with various percentages of missing struts,from perfect cell (0%)to missing eight-strut (50%).In fact,for the panel missing 50%of struts,it will become a new construction different with pyramidal truss.The compressive stress vs strain curves are shown in Fig.8,predicted by the presented FEA model.As seen,due to the increase of percentage of missing struts,the macroscopic response of sandwich panel tends to not smooth especially at the elastic stage.An obvious yield platform can be found after the stress increases to the peak value.To clarify the reason,the ?rst eigenvalues and mode shapes of overall panel are listed in Fig.9,under various percentages of missing struts.Owing to the changing of defect,the eigenvalues decrease from 116.94to 59.12.The reduction is approximately 50%and almost equal to the percentage of defect.The reduction of eigenvalue indicates the critical buckling load and overall stiffness have been obviously decreased,which cause the buckling will gradually tend to main failure mode.The experimental failure mode has been discussed in previous paper,and it is agreement with our FEA results.In fact,Cui et al.[36]obtained the similar phenomenon in the investigation on the imperfect lattice materials through FEM.Additionally,through comparing the buckling morphology between perfect cell panel and missing eight-strut panel,the critical failure location has also been obviously changed from single strut to global strut.For the panel with 50%defect volume fraction,the maximum failure strain has increased by 30%in contrast with that of perfect cell.The stresses in densi-?cation stage also decrease remarkably more than 60%owing to the reduction of struts percentage.

The effect of percentage of missing struts on the compressive stiffness and ultimate strength is shown in Figs.10and 11,including the FEA results and theoretical results.As seen,they exhibit the similar changing tendency that as a linear decrease with the per-centage of missing struts.The compressive stiffness of missing eight-strut panel is degenerated to 133.36MPa,almost reduction by 54.1%in contrast with that of perfect cell panel.The ultimate strength is remarkable decreased by almost 55%,from 2.5MPa to 1.12MPa.This can be attributed to the missing of load bearing struts.It should be mentioned that the reduction trend of compressive stiffness obtained in present paper is agreement with the experimental results in Refs.[16,17]and FEA results in Ref.[37].Furthermore,for the missing three-strut and missing ?ve-strut panel,the ultimate strengths are slightly higher than that of missing two-strut and missing four-strut.We consider this is mainly due to the in ?uence of defect type and spatial con ?guration which will be discussed in the subsequently section.

The defect tolerance is an essential material performance for lattice truss.Thus,the comparison of compressive stiffness ratio between pyramidal and previous lightweight structures is shown in Fig.12,changing with the percentage of missing struts.It can

Fig.4.Flow chart of ?nite element analysis.

H.Lei et al./Composites Part B 79(2015)311e 321

316

found that the compressive stiffness ratio of octet truss,honey-comb,and open-cell foam,sharply decrease with the increasing of defect in contrast with that of pyramidal truss core.It indicates the pyramidal truss construction has better defect tolerant.The result also testi?es the conclusion that stretching dominated lattice ma-terial is more tolerant to missing members than bending domi-nated cellular material[16].5.3.Effect of defect type

For the pyramidal truss unit cell,we assume that there are only two defect types.One is the unit cell missing one strut,and the other is missing two struts.The speci?c con?guration and force state have been analyzed in our previous paper through theoretical. Under the same percentage of missing strut,various defect

types https://www.wendangku.net/doc/cf15133679.html,parison of compressive stress vs strain curves between experimental and FEA results:(a)Perfect cell panel,(b)missing two-strut panel,and(c)missing four-strut

panel.

https://www.wendangku.net/doc/cf15133679.html,parison of effective moduli between experimental,theoretical,and FEA results:(a)Compressive stiffness,and(b)ultimate strength.

H.Lei et al./Composites Part B79(2015)311e321317

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恰恰相反，非常刺激。 https://www.wendangku.net/doc/cf15133679.html, But onthecontrary, lazy. 却恰恰相反，懒洋洋的。 https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, I hate it! 恰恰相反，我不喜欢！ https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, the club gathers every month. 相反，俱乐部每个月都聚会。 https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, I'm going to work harder. 我反而将更努力工作。 https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, his demeanor is easy and nonchalant. 相反，他的举止轻松而无动于衷。 https://www.wendangku.net/doc/cf15133679.html, Too much nutrition onthecontrary can not be absorbed through skin. 太过营养了反而皮肤吸收不了. https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, I would wish for it no other way. 正相反，我正希望这样 Provided by jukuu Onthecontrary most likely pathological. 反之很有可能是病理性的。 https://www.wendangku.net/doc/cf15133679.html, Onthecontrary, it will appear clumsy. 反之，就会显得粗笨。 https://www.wendangku.net/doc/cf15133679.html,

英语造句

一般过去式时间状语：yesterday just now (刚刚) the day before three days ag0 a week ago in 1880 last month last year 1. I was in the classroom yesterday. I was not in the classroom yesterday. Were you in the classroom yesterday. 2. They went to see the film the day before. Did they go to see the film the day before. They did go to see the film the day before. 3. The man beat his wife yesterday. The man didn’t beat his wife yesterday. 4. I was a high student three years ago. 5. She became a teacher in 2009. 6. They began to study english a week ago 7. My mother brought a book from Canada last year. 8.My parents build a house to me four years ago . 9.He was husband ago. She was a cooker last mouth. My father was in the Xinjiang half a year ago. 10.My grandfather was a famer six years ago. 11.He burned in 1991

学生造句--Unit 1

●I wonder if it’s because I have been at school for so long that I’ve grown so crazy about going home. ●It is because she wasn’t well that she fell far behind her classmates this semester. ●I can well remember that there was a time when I took it for granted that friends should do everything for me. ●In order to make a difference to society, they spent almost all of their spare time in raising money for the charity. ●It’s no pleasure eating at school any longer because the food is not so tasty as that at home. ●He happened to be hit by a new idea when he was walking along the riverbank. ●I wonder if I can cope with stressful situations in life independently. ●It is because I take things for granted that I make so many mistakes. ●The treasure is so rare that a growing number of people are looking for it. ●He picks on the weak mn in order that we may pay attention to him. ●It’s no pleasure being disturbed whena I settle down to my work. ●I can well remember that when I was a child, I always made mistakes on purpose for fun. ●It’s no pleasure accompany her hanging out on the street on such a rainy day. ●I can well remember that there was a time when I threw my whole self into study in order to live up to my parents’ expectation and enter my dream university. ●I can well remember that she stuck with me all the time and helped me regain my confidence during my tough time five years ago. ●It is because he makes it a priority to study that he always gets good grades. ●I wonder if we should abandon this idea because there is no point in doing so. ●I wonder if it was because I ate ice-cream that I had an upset student this morning. ●It is because she refused to die that she became incredibly successful. ●She is so considerate that many of us turn to her for comfort. ●I can well remember that once I underestimated the power of words and hurt my friend. ●He works extremely hard in order to live up to his expectations. ●I happened to see a butterfly settle on the beautiful flower. ●It’s no pleasure making fun of others. ●It was the first time in the new semester that I had burned the midnight oil to study. ●It’s no pleasure taking everything into account when you long to have the relaxing life. ●I wonder if it was because he abandoned himself to despair that he was killed in a car accident when he was driving. ●Jack is always picking on younger children in order to show off his power. ●It is because he always burns the midnight oil that he oversleeps sometimes. ●I happened to find some pictures to do with my grandfather when I was going through the drawer. ●It was because I didn’t dare look at the failure face to face that I failed again. ●I tell my friend that failure is not scary in order that she can rebound from failure. ●I throw my whole self to study in order to pass the final exam. ●It was the first time that I had made a speech in public and enjoyed the thunder of applause. ●Alice happened to be on the street when a UFO landed right in front of her. ●It was the first time that I had kept myself open and talked sincerely with my parents. ●It was a beautiful sunny day. The weather was so comfortable that I settled myself into the

英语句子结构和造句

高中英语~词性~句子成分~语法构成第一章节：英语句子中的词性 1.名词：n. 名词是指事物的名称，在句子中主要作主语.宾语.表语.同位语。 2.形容词;adj. 形容词是指对名词进行修饰~限定~描述~的成份，主要作定语.表语.。形容词在汉语中是（的）.其标志是: ous. Al .ful .ive。. 3.动词：vt. 动词是指主语发出的一个动作，一般用来作谓语。 4.副词：adv. 副词是指表示动作发生的地点. 时间. 条件. 方式. 原因. 目的. 结果.伴随让步. 一般用来修饰动词. 形容词。副词在汉语中是（地）.其标志是：ly。 5.代词：pron. 代词是指用来代替名词的词，名词所能担任的作用，代词也同样.代词主要用来作主语. 宾语. 表语. 同位语。 6.介词：prep.介词是指表示动词和名次关系的词，例如：in on at of about with for to。其特征：

介词后的动词要用—ing形式。介词加代词时，代词要用宾格。例如：give up her（him）这种形式是正确的，而give up she（he）这种形式是错误的。 7.冠词：冠词是指修饰名词，表名词泛指或特指。冠词有a an the 。 8.叹词：叹词表示一种语气。例如：OH. Ya 等 9.连词：连词是指连接两个并列的成分，这两个并列的成分可以是两个词也可以是两个句子。例如：and but or so 。 10.数词：数词是指表示数量关系词，一般分为基数词和序数词第二章节：英语句子成分主语：动作的发出者，一般放在动词前或句首。由名词. 代词. 数词. 不定时. 动名词. 或从句充当。谓语：指主语发出来的动作，只能由动词充当，一般紧跟在主语后面。宾语：指动作的承受着，一般由代词. 名词. 数词. 不定时. 动名词. 或从句充当. 介词后面的成分也叫介词宾语。定语：只对名词起限定修饰的成分，一般由形容

六级单词解析造句记忆MNO

M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官，地方法官，治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.１．放大，扩大；２．夸大，夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.１．重要性，重大；２．巨大，广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女，年轻姑娘，未婚女子 a.首次的，初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的，壮丽的，庄严的，高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.１．［Ｍ－］陛下（对帝王，王后的尊称）；２．雄伟，壮丽，庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意，怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.１．恶性的，致命的；２．恶意的，恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.（由许多商店组成的）购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.

base on的例句

意见应以事实为根据. 3 来自辞典例句 192. The bombers swooped ( down ) onthe air base. 轰炸机突袭空军基地. 来自辞典例句 193. He mounted their engines on a rubber base. 他把他们的发动机装在一个橡胶垫座上. 14 来自辞典例句 194. The column stands on a narrow base. 柱子竖立在狭窄的地基上. 14 来自辞典例句 195. When one stretched it, it looked like grey flakes on the carvas base. 你要是把它摊直, 看上去就象好一些灰色的粉片落在帆布底子上. 18 来自辞典例句 196. Economic growth and human well - being depend on the natural resource base that supports all living systems. 经济增长和人类的福利依赖于支持所有生命系统的自然资源. 12 1 来自辞典例句 197. The base was just a smudge onthe untouched hundred - mile coast of Manila Bay. 那基地只是马尼拉湾一百英里长安然无恙的海岸线上一个硝烟滚滚的污点. 6 来自辞典例句 198. You can't base an operation on the presumption that miracles are going to happen. 你不能把行动计划建筑在可能出现奇迹的假想基础上.

英语造句大全

英语造句大全English sentence 在句子中，更好的记忆单词！ 1、(1)、able adj. 能句子：We are able to live under the sea in the future. (2)、ability n. 能力句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地句子：His calculation is accurately. 3、(1)、act v. 扮演句子：He act the interesting character. （2）、actor n. 演员句子：He was a famous actor. (3)、actress n. 女演员句子：She was a famous actress. (4)、active adj. 积极的句子：He is an active boy. 4、add v. 加句子：He adds a little sugar in the milk. 5、advantage n. 优势句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n.

(完整版)主谓造句

主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2．体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英： 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。

初中英语造句

【it's time to和it's time for】 ——————这其实是一个句型,只不过后面要跟不同的东西. ——————It's time to跟的是不定式（to do）.也就是说,要跟一个动词,意思是“到做某事的时候了”.如： It's time to go home. It's time to tell him the truth. ——————It's time for 跟的是名词.也就是说,不能跟动词.如： It's time for lunch.(没必要说It's time to have lunch) It's time for class.(没必要说It's time to begin the class.) They can't wait to see you Please ask liming to study tonight. Please ask liming not to play computer games tonight. Don’t make/let me to smoke I can hear/see you dance at the stage You had better go to bed early. You had better not watch tv It’s better to go to bed early It’s best to run in the morning I am enjoy running with music. With 表伴随听音乐 I already finish studying You should keep working. You should keep on studying English Keep calm and carry on 保持冷静继续前行二战开始前英国皇家政府制造的海报名字 I have to go on studying I feel like I am flying I have to stop playing computer games and stop to go home now I forget/remember to finish my homework. I forget/remember cleaning the classroom We keep/percent/stop him from eating more chips I prefer orange to apple I prefer to walk rather than run I used to sing when I was young What’s wrong with you There have nothing to do with you I am so busy studying You are too young to na?ve I am so tired that I have to go to bed early

The Kite Runner-美句摘抄及造句

《The Kite Runner》追风筝的人--------------------------------美句摘抄 1.I can still see Hassan up on that tree, sunlight flickering through the leaves on his almost perfectly round face, a face like a Chinese doll chiseled from hardwood: his flat, broad nose and slanting, narrow eyes like bamboo leaves, eyes that looked, depending on the light, gold, green even sapphire 翻译：我依然能记得哈桑坐在树上的样子，阳光穿过叶子，照着他那浑圆的脸庞。他的脸很像木头刻成的中国娃娃，鼻子大而扁平，双眼眯斜如同竹叶，在不同光线下会显现出金色、绿色，甚至是宝石蓝。 E.g.: A shadow of disquiet flickering over his face. 2.Never told that the mirror, like shooting walnuts at the neighbor's dog, was always my idea. 翻译：从来不提镜子、用胡桃射狗其实都是我的鬼主意。E.g.:His secret died with him, for he never told anyone. 3.We would sit across from each other on a pair of high

翻译加造句

一、翻译 1. The idea of consciously seeking out a special title was new to me., but not without appeal. 让我自己挑选自己最喜欢的书籍这个有意思的想法真的对我具有吸引力。 2.I was plunged into the aching tragedy of the Holocaust, the extraordinary clash of good, represented by the one decent man, and evil. 我陷入到大屠杀悲剧的痛苦之中，一个体面的人所代表的善与恶的猛烈冲击之中。 3.I was astonished by the the great power a novel could contain. I lacked the vocabulary to translate my feelings into words. 我被这部小说所包含的巨大能量感到震惊。我无法用语言来表达我的感情（心情）。 4，make sth. long to short长话短说 5.I learned that summer that reading was not the innocent(简单的) pastime(消遣) I have assumed it to be., not a breezy, instantly forgettable escape in the hammock(吊床)，( though I’ ve enjoyed many of those too ). I discovered that a book, if it arrives at the right moment, in the proper season, will change the course of all that follows. 那年夏天，我懂得了读书不是我认为的简单的娱乐消遣，也不只是躺在吊床上，一阵风吹过就忘记的消遣。我发现如果在适宜的时间、合适的季节读一本书的话，他将能改变一个人以后的人生道路。二、词组造句 1. on purpose 特意，故意 This is especially true here, and it was ~. (这一点在这里尤其准确，并且他是故意的) 2.think up 虚构，编造，想出 She has thought up a good idea. 她想出了一个好的主意。 His story was thought up. 他的故事是编出来的。 3. in the meantime 与此同时助记：in advance 事前in the meantime 与此同时in place 适当地... In the meantime, what can you do? 在这期间您能做什么呢？ In the meantime, we may not know how it works, but we know that it works. 在此期间，我们不知道它是如何工作的，但我们知道，它的确在发挥作用。 4.as though 好像，仿佛 It sounds as though you enjoyed Great wall. 这听起来好像你喜欢长城。 5. plunge into 使陷入 He plunged the room into darkness by switching off the light. 他把灯一关，房

改写句子练习2标准答案

The effective sentences:(improve the sentences!) 1.She hopes to spend this holiday either in Shanghai or in Suzhou. 2.Showing/to show sincerity and to keep/keeping promises are the basic requirements of a real friend. 3.I want to know the space of this house and when it was built. I want to know how big this house is and when it was built. I want to know the space of this house and the building time of the house. 4.In the past ten years,Mr.Smith has been a waiter,a tour guide,and taught English. In the past ten years,Mr.Smith has been a waiter,a tour guide,and an English teacher. 5.They are sweeping the floor wearing masks. They are sweeping the floor by wearing masks. wearing masks,They are sweeping the floor. 6.the drivers are told to drive carefully on the radio. the drivers are told on the radio to drive carefully 7.I almost spent two hours on this exercises. I spent almost two hours on this exercises. 8.Checking carefully,a serious mistake was found in the design. Checking carefully,I found a serious mistake in the design.

用以下短语造句

M1 U1 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： add up (to) be concerned about go through set down a series of on purpose in order to according to get along with fall in love (with) join in have got to hide away face to face 1 We’ve chatted online for some time but we have never met ___________. 2 It is nearly 11 o’clock yet he is not back. His mother ____________ him. 3 The Lius ___________ hard times before liberation. 4 ____________ get a good mark I worked very hard before the exam. 5 I think the window was broken ___________ by someone. 6 You should ___________ the language points on the blackboard. They are useful. 7 They met at Tom’s party and later on ____________ with each other. 8 You can find ____________ English reading materials in the school library. 9 I am easy to be with and _____________my classmates pretty well. 10 They __________ in a small village so that they might not be found. 11 Which of the following statements is not right ____________ the above passage? 12 It’s getting dark. I ___________ be off now. 13 More than 1,000 workers ___________ the general strike last week. 14 All her earnings _____________ about 3,000 yuan per month. 二.用以下短语造句： 1.go through 2. no longer/ not… any longer 3. on purpose 4. calm… down 5. happen to 6. set down 7. wonder if 三. 翻译： 1.曾经有段时间，我对学习丧失了兴趣。（there was a time when…） 2. 这是我第一次和她交流。（It is/was the first time that …注意时态） 3.他昨天公园里遇到的是他的一个老朋友。（强调句） 4. 他是在知道真相之后才意识到错怪女儿了。（强调句） M 1 U 2 一. 把下列短语填入每个句子的空白处（注意所填短语的形式变化）： play a …role (in) because of come up such as even if play a …part (in) 1 Dujiangyan(都江堰) is still ___________in irrigation(灌溉) today. 2 That question ___________ at yesterday’s meeting. 3 Karl Marx could speak a few foreign languages, _________Russian and English. 4 You must ask for leave first __________ you have something very important. 5 The media _________ major ________ in influencing people’s opinion s. 6 _________ years of hard work she looked like a woman in her fifties. 二.用以下短语造句： 1.make (good/full) use of 2. play a(n) important role in 3. even if 4. believe it or not 5. such as 6. because of

英语造句

English sentence 1、(1)、able adj. 能句子：We are able to live under the sea in the future. (2)、ability n. 能力句子：Most school care for children of different abilities. (3)、enable v. 使。。。能句子：This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子：We must have the accurate calculation. (2)、accurately adv. 精确地句子：His calculation is accurately. 3、(1)、act v. 扮演句子：He act the interesting character.（2）、actor n. 演员句子：He was a famous actor. (3)、actress n. 女演员句子：She was a famous actress. (4)、active adj. 积极的句子：He is an active boy. 4、add v. 加句子：He adds a little sugar in the milk. 5、advantage n. 优势句子：His advantage is fight. 6、age 年龄n. 句子：His age is 15. 7、amusing 娱人的adj. 句子：This story is amusing. 8、angry 生气的adj. 句子：He is angry. 9、America 美国n. 句子：He is in America. 10、appear 出现v. He appears in this place. 11. artist 艺术家n. He is an artist. 12. attract 吸引 He attracts the dog. 13. Australia 澳大利亚 He is in Australia. 14.base 基地 She is in the base now. 15.basket 篮子 His basket is nice. 16.beautiful 美丽的 She is very beautiful. 17.begin 开始 He begins writing. 18.black 黑色的 He is black. 19.bright 明亮的 His eyes are bright. 20.good 好的 He is good at basketball. 21.British 英国人 He is British. 22.building 建造物 The building is highest in this city 23.busy 忙的 He is busy now. 24.calculate 计算 He calculates this test well. 25.Canada 加拿大 He borns in Canada. 26.care 照顾 He cared she yesterday. 27.certain 无疑的 They are certain to succeed. 28.change 改变 He changes the system. 29.chemical 化学药品