research article research on multidisciplinary optimization design of bridge...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 763545 10 pageshttpdxdoiorg1011552013763545

Research ArticleResearch on Multidisciplinary Optimization Design ofBridge Crane

Tong Yifei1 Ye Wei1 Yang Zhen1 Li Dongbo1 and Li Xiangdong2

1 Nanjing University of Science and Technology School of Mechanical Engineering 402 210094 Nanjing China2 Jiangsu Province Special Equipment Safety Supervision Inspection Institute LongJiang Building 107 Caochangmen StreetJiangsu Province 210000 Nanjing China

Correspondence should be addressed to Li Dongbo db tyfyahoocn

Received 17 February 2013 Accepted 7 May 2013

Academic Editor C Wu

Copyright copy 2013 Tong Yifei et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Bridge crane is one of the most widely used cranes in our country which is indispensable equipment for material conveying in themodern production In this paper the framework of multidisciplinary optimization for bridge crane is proposed The presentedresearch on crane multidisciplinary design technology for energy saving includes three levels respectively metal structures leveltransmission design level and electrical system design level The shape optimal mathematical model of the crane is established forshape optimization design of metal structure level as well as size optimal mathematical model and topology optimal mathematicalmodel of crane for topology optimization design of metal structure level is established Finally system-level multidisciplinaryenergy-saving optimization design of bridge crane is further carried out with energy-saving transmission design results feedbackto energy-saving optimization design of metal structure The optimization results show that structural optimization design canreduce total mass of crane greatly by using the finite element analysis and multidisciplinary optimization technology premised onthe design requirements of cranes such as stiffness and strength thus energy-saving design can be achieved

1 Introduction

Empirical design is often used for the structure design ofbridge crane which determines the design parameters ofbridge crane and furthermore improves the performanceThe traditional design method cannot work out accurateperformance data resulting in the safe coefficient of craneover the design requirements greatly which leads to the wasteof materials and energy consumption and so forth [1]

At present a simplified structure to reduce the weightand lightweight design-based heuristic algorithm is usuallyadopted to achieve energy saving most of which focuson single structural design improvement With the rapiddevelopment of finite element analysis (FEA) technique [2 3]the traditional design method is gradually replaced by finiteelement analysis and design There is quite a lot of finiteelement analysis software such as ANSYS ABAQUS andHyperWorks [4 5] However purely from structural designto reduce the weight of the crane has been very limitedand blindly to reduce the weight would be a security risk

On the other hand crane is a complex system composedof many subsystems among which there exist weak orstrong coupling relationships Thus crane energy-savingdesign is a multidisciplinary coupling engineering probleminvolving structural design mechanical transmission andelectrical control which is not a simple superposition andpermutations of various disciplines design Therefore it is ofurgent need frommultidisciplinary point of view of structuremechanical transmission and electrical control to study thesystem-level energy-saving design of crane

The present work was carried out in order to obtainsimulation data of the bridge crane In the next sectionthe framework of multidisciplinary optimization design isproposed In Section 3 FE model of double girder craneis developed using commercial program HyperWorks andthe loading and the results of finite element analysis aregiven and discussed Topology optimization and size opti-mization are further carried out and the results of metalstructural optimization are analyzed In Section 4 system-level multidisciplinary energy-saving optimization design

2 Mathematical Problems in Engineering

of bridge crane is further carried out with transmission-level design results feedback to energy-saving optimizationdesign of metal structure Finally research conclusions aresummarized

2 Multidisciplinary Optimization DesignFramework for Bridge Crane Energy Saving

The presented research on crane multidisciplinary designtechnology for energy saving includes three levelsrespectively energy-saving design of metal structuresenergy-saving transmission design and energy-savingelectrical system design Energy-saving design of metalstructure involves structural lightweight design and archcurve design of beam energy-saving transmission systemdesign involves dynamic loading transmission efficiency andcomponents lightweight and energy-saving electric systemdesign involves power loss

In addition optimal design of lifting findings dynamicloading and components lightweight are feedback to struc-ture lightweight design for further design optimization Alsoarch curve can reduce climbing energy consumption therebyreducing motor power losses The arch curve optimizationresults need feedback for electrical energy saving The multi-disciplinary optimization design can be illustrated as shownin Figure 1

3 Energy-Saving Optimization Design ofMetal Structure Level of Bridge Crane

31 Development of FE Model of Double Girder Crane Take abridge crane used in a practical project as the research objectwhich is a 50 t-315m double girder crane whose materialparameter and usage are as follows

(i) material ordinary carbon steel Q235(ii) length of the crane (119897) 315m(iii) maximum lifting height 12m(iv) hoisting speed 78mmin(v) moving speed of the car 385mmin(vi) moving speed of the cart 873mmin

And according to the GBT 3811-2008 ldquocrane designstandardrdquo the working level of car is M5 and the workinglevel of cart is M6 [6]

32 Geometric Modeling of Double Girder Crane Accordingto the engineering drawing geometric model of the bridgecrane is established by PROE whose structure componentsinclude the up and down plates of end girders the side platesof end girders up and down plates of main girders the sideplates of main girders multiple belly boards feet frame andvarious connection boards The simplified geometric modelis shown as Figure 2

33 Model Processing Import the geometric model of bridgecrane into HyperMesh and clear it Owing to that each plate

is thin partition the plates with shell elements for finiteelement simulation analysis The shell elements should becreated on the middle surface of the geometry A group ofmiddle surfaces should be constructed by using ldquomidsurfacerdquopanel The imported model contains some connectivity erroror some other defects so the operations as follows should becarried out after importing file model

(1) Delete the unsheared surfaces(2) Fill the gaps (repair the missed surfaces)(3) Set the tolerance values of geometric cleaning(4) Combine the red free edges with ldquoequivalencerdquo(5) Delete the repeated surfaces

34 Mesh Partitioning of Double Girder Crane Welds con-nections between each board are taken place of the rigidconnections and mesh elements are created on extractionmidsurface [7] The calculation capacity and calculation effi-ciencymust be considered whenmesh partitioningThe finerthe elements meshed are the more accordant the partitionedmodel is with the actual condition while computing time andmemory usage will be increased largely After taking all theabove factors into account synthetically set the element sizeas 50mmtimes 50mm for finite element analysis The spot weldsare used to simulate the connections between the end andmain girders [8]

Due to that the bridge crane structure is symmetrical takehalf of the model as research object in order to reduce thecomputing time and memory usage The FE model of bridgecranes is shown in Figure 3

35 Loading and Static Analysis Both end girders and maingirders are processed as simply supported beams [9ndash11]Loading is illustrated as in Figure 4

Constraint loadings of the crane are described as follows

themovement in 119909 119910 119911 directions and the rotation in119911 direction of position 1 are restrainedthe movement in 119910 119911 direction and the rotation in 119911direction of position 4 are restrainedthe movement in 119911 direction and the rotation in 119909 119910direction of positions 2 3 are restrained because of thesymmetry

The loadings on both of the main girders are as follows

(i) rated hoisting loading 119875119876 = 50 t(ii) the car mass is 15765 t(iii) self-vibration load factor Φ1 = 11(iv) lifting dynamic load factor Φ2 = 114(v) horizontal inertial force of crane as volume force

acceleration is 032ms2(vi) cart gravity as volume force

L0 L1 L2 L3 and L4 denote the loadings on differentpositions of one main girder respectively called five work

Mathematical Problems in Engineering 3

Energy-saving design of bridge crane

Energy-saving design of metal structures

Energy-saving transmission design

Energy-saving electrical system design

(a) Overall framework of multidisciplinary energy-saving design

Energy-saving design of metal

structure

Lightweight design of structure

Arch curve design of

crane girder

Shape and distribution of

ribs

Optimization of thickness

Design of crosssection with

variablethickness

Optimization of height and

width

Beam design

Analysis of different arch

curve

Size optimization

Topology optimization

Shapeoptimization

Comprehensive optimization

Dynamic Feedbackloading

coefficient

(b) Energy-saving design of metal structure level

Energy-saving design of

transmission system

Dynamic load coefficient

Transmission efficiency

Hoisting dynamic load

coefficient

Horizontal dynamic load

coefficient

Hoisting mechanism

Car

Crane dolly

Crane dolly lightweight

design

Latest production at abroad

Dynamic simulation

Comparison of the new and old

transmission schemes

Components lightweight

Hoisting mechanism

Operation mechanism

(c) Energy-saving design of transmission design level


electric system

Generator power loss

in climbing situation

Generator power loss in

hoisting situation

Series resistance speed

Voltage regulator for motor stator

VVVF

FeedbackPower loss

Energy feedback

(d) Energy-saving design of electrical system design level

Figure 1 Multidisciplinary optimization design framework for energy saving


Table 1 Five work conditions description

Workconditions

Cart gravity(ms2)

Car mass(t)

Self-vibrationfactor

Horizontalinertial force ofcrane (ms2)

Rated loading(t)

Lifting moveload factor

Loadposition

1 98 15765 11 032 50 114 Middle of thebeam

2 98 15765 11 032 50 114 Left end ofthe beam

3 98 15765 11 032 50 114 Right end ofthe beam

4 98 15765 11 032 50 114 Left 14 of thebeam

5 98 15765 11 032 50 114 Right 14 ofthe beam

Figure 2 Geometric model of double girder crane

Figure 3 Finite element model

conditions and the magnitude of the loadings (L0 L1 L2 L3and L4) is 3222485KN Five work conditions are calculatedin finite analysis as in Table 1

According to the requirements of the crane design inGBT 3811-2008 ldquocrane designrdquo combined with actual usagerequirements for the stiffness of the crane girder are asfollows

119891 le1

800119904 (1)

where 119891 is the deflection displacement 119904 is the span of thecrane [12]

And requirements for the stress of the crane girder are asfollows

(i) material Q235(ii) yield stress 120590119904 235MPa(iii) allowable stress [120590] le 100MPa defined by engineer-

ing design

L12

1

3

4

L2L3 L4L0

y

z

x

Figure 4 Loadings illustration

After loading on different locations of themain girder theresults of finite element analysis are shown in Figures 5 and 6

Analyz and compar different conditions of loads to obtainthe conclusions that when loading on the middle of the maingirder the maximum displacement of 403mm appears onthe middle of the main girder and the maximum stress of916MPa occurs on themiddle of themain girders Accordingto the results of FEA the total mass of the initial model is189 t

36 Structural Optimization of Double Girder Crane

361 Shape Optimization The shape optimal mathematicalmodel is established as follows which takes the minimumvolume as objective function the height and width of thecrane as design variables and the scopes of stress strainenergy and modal as constraints

Min 1198811015840 (119883) = 1198811015840 (Height1015840Width1015840)

Design variables minus5 le Height1015840le 20

minus5 leWidth1015840 le 20

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(2)


zx

y

gt359e+01lt359e+01lt315e+01lt271e+01lt227e+01lt183e+01lt140e+01lt956e+00lt517e+00lt785eminus01

SUB39-load0Displacements

Max = 403e+01Min = 785eminus01

Max node 39096

Min node 1033975

Figure 5 Displacement cloud

zx

y


SUB39-load0Von Mises stress

Max = 916e+01Min = 123eminus01Max node 37752

Min node 76938

Figure 6 Stress cloud

where 1198811015840(119883) denotes the volume fraction 119862119895 denotes thetotal strain energy of the crane under the 119895th load 119870denotes the stiffness matrix of the system 119891 denotes theload 119906 denotes the node displacement vector under the load119891 120590 denotes the stress 119865 denotes the natural frequencyObjective function 1198811015840(119883) constraint function 119862119895 and 120590 canbe obtained from structural response of the finite elementanalysis

Use OptiStruct Solver to optimize the girder by selectingmorph optimization tool the optimization results of themaingirder are shown as follows

Volume = 227E + 09mm3 Mass = 179 tHeight1015840 = minus036 Width1015840 = 12

After shape optimization

Height= 1724mm + 036 times 50mm = 1742mmWidth = 600 mm minus 12 times 50mm = 540mmHeightWidth = 1724540 = 319

By analyzing the results of finite element analysis thestructure performance (including strength stiffness andmodal) after topology optimization meets the requirementsof crane design specifications greatly which are shown inFigures 7 and 8

Analyze and compare different conditions of loads toobtain the conclusions that when loading on themiddle of the

main girder the maximum displacement of 429mm appearson the middle of the main girder and the maximum stress of986MPa occurs on the middle of the main girders The totalmass of themodel after shape optimization is 179 t which hasreduced by 53

Compare the maximum displacement and maximumstress before and after topology optimization the result isgiven as in Table 2

The analysis results shown in Table 2 show that structureperformance of the various plates some materials of whichhave been reasonably removed meets the design require-ments as well Meanwhile the total mass of structure is 179 twhich has reduced by 1 t

362 Size Optimization Furth optimizing of the structureafter shape optimization was carried out in our researchTaking the minimum volume as the objective function thethicknesses of the plates as the design variables the scopesof the stress strain energy and modal as constraints the sizeoptimal mathematical model is established as follows

Min 119881 (119883) = 119881 (1199091 1199092 11990918)

ST 119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5


zx

y


S39-load0 [10]Displacements


Min node 1033975


zx

y


S39-load0 [10]Von Mises stress


Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)

where 119883 = 1199091 1199092 11990918 denotes the thicknesses of plates119881(119883)denotes the total volumeof the crane the rest of variableparameters are denoted as above Use theOptiStruct Solver tooptimize girders by size optimization tool The optimizationresults of the thicknesses of the plates are shown in Table 3

By analyzing the results of size optimization the struc-ture performance (including strength stiffness and modal)after topology optimization meets the requirements of cranedesign specifications greatly The results of finite elementanalysis after size optimization are shown in Figures 9 and10

The maximum displacement of 441mm appears on themiddle of themain girder and themaximum stress of 99MPaoccurs on the end of the main girders The total mass of themodel after size optimization is 173 t which has reduced by85

The comparison of initial model and final model is shownin Table 4

From the analysis results shown in Table 4 it can befound easily that the structure performance after shape and

size optimization meets the requirements of crane designspecifications greatly Moreover after size optimization thetotal mass of the main girder changes into 173 t which hasbeen reduced by 16 t

363 Topology Optimization Furth optimizing of the struc-ture after shape and size optimization was carried outThe topology optimal mathematical model is establishedas follows which takes the minimum volume fraction asobjective function the material density of each element asdesign variables and the scopes of stress strain energy andmodal as constraints

Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)

where119883 = 1199091 1199092 119909119899 denotes the material density of eachelement are and the rest of variable parameters are denotedas above


Table 2 Comparison of the stress and displacement

Load step Before AfterStress (MPa) Displacement (mm) Stress (MPa) Displacement (mm)

L0 916 403 986 429L1L2 802 872L3L4 745 744

Table 3 Comparison of the thicknesses before and after optimiza-tion

Main optimal size Before (mm) After (mm)Upper plates 24 207Under plates 24 234Inside plates 6 6Outside plates 6 6Small ribbed plates 8 95Big ribbed plates 8 56

Use OptiStruct Solver to optimize the girder by selectingtopology optimization tool the optimization results of themain girder are shown in Figures 11 and 12

By analyzing the results of topology optimization thestructure performance (including strength stiffness andmodal) after topology optimization meets the requirementsof crane design specifications greatly The results of finiteelement analysis after topology optimization are shown inFigures 13 and 14

Analyze and compare different conditions of loads toobtain the conclusions that when loading on themiddle of themain girder the maximum displacement of 399mm appearson the middle of the main girder and the maximum stress of99MPa occurs on the end of the main girdersThe total massof the model after topology optimization is 158 t which hasreduced by 164



37 Overall Stability Analysis of Main Girder Accordingto the requirements of ldquothe crane design manualrdquo for boxsection structure ldquowhen aspect ratio (heightwidth) denotedby hb⩽ 3 or 3lt hb⩽ 6 amp l119887 le 95(235120590s) the lateralbuckling stability of the flexural components do not needverifyrdquo

In our research the results are as follows

before optimization h= 1724mm b= 600mm hb=287 so hb⩽ 3after optimization h= 1742mm b= 540mm hb=319 and l= 31500mm lb= 583 120590119904 = 253MPa so3lt hb⩽ 6 amp 119897119887 le 95(235120590119904)

Therefore lateral buckling stability conforms to thedesign requirements

4 System-Level MultidisciplinaryEnergy-Saving Optimization Design ofBridge Crane

Energy-saving transmission design is researched by ourresearch group in dynamic simulation and speed regulationof hoistingmechanismaswell as optimization and innovationof transmission mechanism scheme reported in the literature[13 14] Thus self-vibration load factor in Section 34 isreduced from 114 to 111 under VVVF and the car massin Section 34 is reduced from 15765 t to 144 t System-level multidisciplinary energy-saving optimization designof bridge crane can be further carried out with energy-saving transmission design results feedback to energy-savingoptimization design of metal structure By repeating theabove modelling and analysis in Section 3 the system-levelmultidisciplinary energy-saving optimization results areshown in Table 6

5 Conclusions

The framework of multidisciplinary energy-saving optimiza-tion design of bridge crane is proposed And the structure-level optimization design of bridge crane by using finiteelement analysis technology is discussed in this paper indetailThis research seeks to getmore reasonable lightweightand energy-saving structure on the basis of insuring theperformances of crane and to provide the design referencefor bridge crane The main results of this research can beconcluded as follows

(1) the results of finite element analysis show that theconcentrated stress occurs on the middle of maingirders under full load

(2) for the cranes which meet the design requirementsshape optimization is researched The total massof the structure after shape optimization changesinto 179 t176 t (optimization design of metal struc-turesystem-level multidisciplinary energy-savingoptimization) and it is reduced by 1 t13 t comparedwith the initial model

(3) size optimization is researched after shape optimiza-tion The total mass of the structure after size opti-mization changes into 173 t167 t and it is reduced by16 t22 t


Table 4 Comparing the stress and displacement

Load step Initial model Final modelStress (MPa) Displacement (mm) Stress (MPa) Displacement (mm)

L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108

Table 6 System-level multidisciplinary energy-saving optimization results

Optimization method Mass after optimization (t) Percentage decrease189

Shape optimization 176 688Size optimization 167 1164Topologyoptimization 158 1640

zx

y

gt393e+01lt393e+01lt345e+01lt297e+01lt250e+01lt202e+01lt154e+01lt106e+01lt580e+00lt101e+00


Max = 441e+01Min = 101e+00Max node 22190

Min node 1033975


zx

y




Min node 76938



z

x

y

gt890eminus01lt890eminus01lt780eminus01lt670eminus01lt560eminus01lt450eminus01lt340eminus01lt230eminus01lt120eminus01lt100eminus02

Design [32]Element density


43388 nodes share maxFirst max 146

4955 nodes share minFirst min 4438

Figure 11 Density graph of the side plate

z

x

y






Figure 12 Density graph of the belly board

z

x

y




Min node 1033975


ZX

Y




Max node 1192098



(4) topology optimization based on densitymethodologyis used after shape and size optimization The totalmass of the structure after topology optimizationchanges into 158 t158 t and it is reduced by 31 t31 tcompared with the initial model

(5) multidisciplinary optimization design by means offinite element analysis and dynamic simulation notonly can assure stiffness strength and other perfor-mances requirements of the crane but also can greatlyreduce the use of materials by lightweight design

Acknowledgments

This work was financially supported by National Founda-tion of General Administration of Quality Supervision andInspection (2012QK178) program of Science Foundation ofGeneral Administration of Quality Supervision and Inspec-tion of Jiangsu Province (KJ103708) and ldquoexcellence plans-zijin starrdquo Foundation of Nanjing University of Science Thesupport is gratefully acknowledged

References

[1] N Zhaoyang R Yongxin R Chengao et al ldquoANSYS applicationin design of the main beam of cranerdquoMachinery for Lifting andTransportation vol 5 pp 31ndash33 2008

[2] M Styles P Compston and S Kalyanasundaram ldquoFiniteelement modelling of core thickness effects in aluminiumfoamcomposite sandwich structures under flexural loadingrdquoComposite Structures vol 86 no 1ndash3 pp 227ndash232 2008

[3] C Nucera and F L Scalea ldquoHigher-harmonic generation anal-ysis in complex waveguides via a nonlinear semianalytical finiteelement algorithmrdquoMathematical Problems in Engineering vol2012 Article ID 365630 16 pages 2012

[4] L Kwasniewski H Li J Wekezer and J Malachowski ldquoFiniteelement analysis of vehicle-bridge interactionrdquo Finite Elementsin Analysis and Design vol 42 no 11 pp 950ndash959 2006

[5] Y Li Y Pan J Zheng et al ldquoFinite element analysis withiterated multiscale analysis for mechanical parameters of com-posite materials with multiscale random grainsrdquo MathematicalProblems in Engineering vol 2011 Article ID 585624 19 pages2011

[6] D Qin YWang X Zhu J Chen and Z Liu ldquoOptimized designof the main beam of crane based on MSC1PatranNastranrdquoMachinery for Lifting and Transportation vol 7 pp 24ndash26 2007

[7] D Hongguang B Tianxiang S Yanzhong and Y Sikun ldquoTheoptimum design of single girder bridge-crane based on FEMrdquoSteel Construction vol 2 pp 46ndash48 2009

[8] L Hui Y Haipeng and L Huixin ldquoThe malfunction about thebridge crane girder based on FEMrdquo Construction Machineryvol 2 pp 67ndash69 2007

[9] W Fumian ldquoDiscussion about the static stiffness design of thebridge crane and the related problemsrdquo Machinery for Liftingand Transportation vol 12 pp 42ndash44 2009

[10] Z Zhang ldquoThe application of ANSYS into optimizing designof main beam in joist portal cranerdquo Machinery Technology andManagement on Construction vol 8 pp 91ndash93 2009

[11] Y Menglin Q Dongchen L Zhuli and W Y Jia ldquoResearch onstructure optimization design of bridge crane box beamrdquoDesignand Research vol 4 pp 23ndash24 2008

[12] GBT3811-2008 Crane design standard[13] L Shuishui F Yuanxun and B Tingchun ldquoIntroduction for

new hoisting mechanism of a cranerdquo Machinery Design ampManufacture no 5 pp 275ndash276 2012

[14] F Yuanxun B Tingchun and L Shuishui ldquoCo-simulating onlifting dynamic load of bridge crane based on ADAMS andMATLABrdquo Heavy Machinery no 5 pp 30ndash32 2011

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of bridge crane is further carried out with transmission-level design results feedback to energy-saving optimizationdesign of metal structure Finally research conclusions aresummarized

2 Multidisciplinary Optimization DesignFramework for Bridge Crane Energy Saving

The presented research on crane multidisciplinary designtechnology for energy saving includes three levelsrespectively energy-saving design of metal structuresenergy-saving transmission design and energy-savingelectrical system design Energy-saving design of metalstructure involves structural lightweight design and archcurve design of beam energy-saving transmission systemdesign involves dynamic loading transmission efficiency andcomponents lightweight and energy-saving electric systemdesign involves power loss

In addition optimal design of lifting findings dynamicloading and components lightweight are feedback to struc-ture lightweight design for further design optimization Alsoarch curve can reduce climbing energy consumption therebyreducing motor power losses The arch curve optimizationresults need feedback for electrical energy saving The multi-disciplinary optimization design can be illustrated as shownin Figure 1

3 Energy-Saving Optimization Design ofMetal Structure Level of Bridge Crane

31 Development of FE Model of Double Girder Crane Take abridge crane used in a practical project as the research objectwhich is a 50 t-315m double girder crane whose materialparameter and usage are as follows

(i) material ordinary carbon steel Q235(ii) length of the crane (119897) 315m(iii) maximum lifting height 12m(iv) hoisting speed 78mmin(v) moving speed of the car 385mmin(vi) moving speed of the cart 873mmin

And according to the GBT 3811-2008 ldquocrane designstandardrdquo the working level of car is M5 and the workinglevel of cart is M6 [6]

32 Geometric Modeling of Double Girder Crane Accordingto the engineering drawing geometric model of the bridgecrane is established by PROE whose structure componentsinclude the up and down plates of end girders the side platesof end girders up and down plates of main girders the sideplates of main girders multiple belly boards feet frame andvarious connection boards The simplified geometric modelis shown as Figure 2

33 Model Processing Import the geometric model of bridgecrane into HyperMesh and clear it Owing to that each plate

is thin partition the plates with shell elements for finiteelement simulation analysis The shell elements should becreated on the middle surface of the geometry A group ofmiddle surfaces should be constructed by using ldquomidsurfacerdquopanel The imported model contains some connectivity erroror some other defects so the operations as follows should becarried out after importing file model

(1) Delete the unsheared surfaces(2) Fill the gaps (repair the missed surfaces)(3) Set the tolerance values of geometric cleaning(4) Combine the red free edges with ldquoequivalencerdquo(5) Delete the repeated surfaces

34 Mesh Partitioning of Double Girder Crane Welds con-nections between each board are taken place of the rigidconnections and mesh elements are created on extractionmidsurface [7] The calculation capacity and calculation effi-ciencymust be considered whenmesh partitioningThe finerthe elements meshed are the more accordant the partitionedmodel is with the actual condition while computing time andmemory usage will be increased largely After taking all theabove factors into account synthetically set the element sizeas 50mmtimes 50mm for finite element analysis The spot weldsare used to simulate the connections between the end andmain girders [8]

Due to that the bridge crane structure is symmetrical takehalf of the model as research object in order to reduce thecomputing time and memory usage The FE model of bridgecranes is shown in Figure 3

35 Loading and Static Analysis Both end girders and maingirders are processed as simply supported beams [9ndash11]Loading is illustrated as in Figure 4

Constraint loadings of the crane are described as follows

themovement in 119909 119910 119911 directions and the rotation in119911 direction of position 1 are restrainedthe movement in 119910 119911 direction and the rotation in 119911direction of position 4 are restrainedthe movement in 119911 direction and the rotation in 119909 119910direction of positions 2 3 are restrained because of thesymmetry

The loadings on both of the main girders are as follows

(i) rated hoisting loading 119875119876 = 50 t(ii) the car mass is 15765 t(iii) self-vibration load factor Φ1 = 11(iv) lifting dynamic load factor Φ2 = 114(v) horizontal inertial force of crane as volume force

acceleration is 032ms2(vi) cart gravity as volume force

L0 L1 L2 L3 and L4 denote the loadings on differentpositions of one main girder respectively called five work








structure



crane girder


ribs



variablethickness


width

Beam design


curve

Size optimization


Shapeoptimization



coefficient



transmission system




coefficient


coefficient

Hoisting mechanism

Car

Crane dolly


design


Dynamic simulation




Hoisting mechanism

Operation mechanism



electric system




hoisting situation



VVVF

FeedbackPower loss

Energy feedback





Workconditions

Cart gravity(ms2)

Car mass(t)



Rated loading(t)


Loadposition




4 98 15765 11 032 50 114 Left 14 of thebeam

5 98 15765 11 032 50 114 Right 14 ofthe beam





119891 le1

800119904 (1)




ing design

L12

1

3

4

L2L3 L4L0

y

z

x






Min 1198811015840 (119883) = 1198811015840 (Height1015840Width1015840)



119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(2)


zx

y




Max node 39096

Min node 1033975


zx

y




Min node 76938













Min 119881 (119883) = 119881 (1199091 1199092 11990918)

ST 119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5


zx

y




Min node 1033975


zx

y




Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)








Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)





L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















structure



crane girder


ribs



variablethickness


width

Beam design


curve

Size optimization


Shapeoptimization



coefficient



transmission system




coefficient


coefficient

Hoisting mechanism

Car

Crane dolly


design


Dynamic simulation




Hoisting mechanism

Operation mechanism



electric system




hoisting situation



VVVF

FeedbackPower loss

Energy feedback





Workconditions

Cart gravity(ms2)

Car mass(t)



Rated loading(t)


Loadposition




4 98 15765 11 032 50 114 Left 14 of thebeam

5 98 15765 11 032 50 114 Right 14 ofthe beam





119891 le1

800119904 (1)




ing design

L12

1

3

4

L2L3 L4L0

y

z

x






Min 1198811015840 (119883) = 1198811015840 (Height1015840Width1015840)



119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(2)


zx

y




Max node 39096

Min node 1033975


zx

y




Min node 76938













Min 119881 (119883) = 119881 (1199091 1199092 11990918)

ST 119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5


zx

y




Min node 1033975


zx

y




Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)








Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)





L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Workconditions

Cart gravity(ms2)

Car mass(t)



Rated loading(t)


Loadposition




4 98 15765 11 032 50 114 Left 14 of thebeam

5 98 15765 11 032 50 114 Right 14 ofthe beam





119891 le1

800119904 (1)




ing design

L12

1

3

4

L2L3 L4L0

y

z

x






Min 1198811015840 (119883) = 1198811015840 (Height1015840Width1015840)



119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(2)


zx

y




Max node 39096

Min node 1033975


zx

y




Min node 76938













Min 119881 (119883) = 119881 (1199091 1199092 11990918)

ST 119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5


zx

y




Min node 1033975


zx

y




Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)








Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)





L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










zx

y




Max node 39096

Min node 1033975


zx

y




Min node 76938













Min 119881 (119883) = 119881 (1199091 1199092 11990918)

ST 119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5


zx

y




Min node 1033975


zx

y




Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)








Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)





L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










zx

y




Min node 1033975


zx

y




Max node 30255

Min node 76938


119870119906 = 119891

120590 le 100MPa

119865 ge 3

(3)








Min 1198811015840 (119883) = 1198811015840 (1199091 1199092 119909119899)

119862119895 =1

2119906119879

119895 119891119895 le 11 times 107119869 119895 = 1 5

st 119870119906 = 119891

120590 le 100MPa

119865 ge 3

(4)





L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra












L0 916 403 986 429L1L2 802 872L3L4 745 744














5 Conclusions








L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra












L0 916 403 99 441L1L2 802 844L3L4 745 883



L0 916 403 976 439L1L2 802 90L3L4 745 108




zx

y




Min node 1033975


zx

y




Min node 76938



z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










z

x

y







z

x

y







z

x

y




Min node 1033975


ZX

Y




Max node 1192098





Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article research on multidisciplinary optimization design of bridge...

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