finite element analysis of an aluminium alloy sheet in a v ... · finite element analysis of an...

International Journal of Theoretical and Applied Mechanics

ISSN 0973-6085 Volume 12 Number 2 (2017) pp 331-342

copy Research India Publications

httpwwwripublicationcom

Finite Element Analysis of an Aluminium Alloy Sheet

in a V-Die Punch Mechanism Considering Spring-

Back Effect

Shirish Ghimire1a Yogesh Emeerith2b Rohit Ghosh3c Sushovan Ghosh4d

1 2 3 4 BTech Students Department of Mechanical Engineering National Institute of Technology Durgapur 713209 WB India

Dr Rabindra Nath Barman5e

5 Assistant Professor Department of Mechanical Engineering National Institute of Technology Durgapur 713209 WB India

Abstract

Sheet metal parts are used to manufacture a wide range of products Bending

and cutting the sheets into appropriate shapes by means of the physical process

of shearing is the very first step in forming such a part The current work is an

attempt to provide the readers with an appropriate understanding regarding the

deformation behavior of an aluminium alloy sheet by performing the finite

element analysis (FEM) for two distinct die angles The metal sheet is

analyzed before fatigue failure and with the help of a software based analysis

the paper explores the phenomena of spring-back associated with the metal

sheet during its deformation while subjected to the set of V-die punch

designed with suitable dimensions The V-die punch as well as the alloy sheet

is modeled in Solidworks 130 and their dimensions have been taken from

practical standards Finite element analysis for the same is carried out in

ANSYS Workbench 160

Keywords Solidworks 130 ANSYS Workbench 160 V-die punch Finite

element analysis

332 Shirish Ghimire et al

1 Introduction

Blanking and punching are one of the oldest manufacturing operations Their

applications range from components of very light to heavy appliances and

machineries [1] Punching is a metal forming process that uses a punch press to force

a tool called a punch through the work piece to create a hole via shearing When a

specially shaped punch is used to create multiple usable parts from a sheet of material

the process is known as blanking [2]During blanking the part is subjected to

complex solicitations such as deformation hardening and crack initiation and

propagation The theoretical modeling of such processes is very difficult due to the

complexity in describing the different stages of the whole shearing process starting

with the elastic stage and ending with the total separation of the sheet metal [3] Small

punch test (SPT) Ball punch Test Disk Bend test as well as Shear Punch Test [4-9]

are the techniques developing to characterize the mechanical behavior of small

specimens The concept of the small V-die punching is based on placing a thin metal

sheet specimen on the die and then the v shaped punch is applied to get the desired

shape In this process the feed is applied to the metal sheet horizontally and the

punching is done vertically In order to get the stable punching and the good punching

edge quality of the al alloy and stainless steel alloy sheets [10] it is necessary to

choose a narrow punch-die clearance and the heat sheet before punching Reducing

the clearance my increase the bright zone and also reduce the fracture zone as well as

the fracture angle but if the clearance is reduced the punching force and the tooling

wear increases [11] An experimental investigation had been carried out to study the

effect of die angle on the quality of extruded product ie surface finish and hardness

of cold extruded aluminum The die angles used were 30 45 and 60 ordms [12] Similarly

deformation in copper was observed using ECAE technique under variable die angles

The die angles used were 90 ordm and 120 ordm for this research [13] J W PILARCZYK

and J MARKOWSKI studied the effect of die angle on strain and stress state in

process of drawing of steel for pre-stressed concrete keeping 8 12 and 18 ordm dies for

the process [14] Similarly five different die angles (15 30 45 60 and 90) were used

to investigate the extrusion behavior of wrought aluminum alloys [15] Spring-back is

a geometric change that a sheet metal experiences after it gets rid of the tool forces in

a punching process Spring-back effect results in slight displacement of the sheet

metal in the direction of the return stroke of the punch Spring-back has a very

significant role in sheet metal bending process It leads to some geometric changes in

the product A research work was carried out for reflecting the different parameters on

spring-back in U-die bending of different materials with different sheet thickness and

tip radius [16]If not correctly predicted and compensated for spring-back will cause

the final part shape to deviate from design specifications and to create assembly

problems [17] H Laurent conducted the Spring-back study of aluminum alloy in

warm forming conditions A split-ring test was used to analyze the influence of

temperature during forming over Spring-back The obtained experimental results were

compared to the numerical simulations [18] A research was done earlier which

studied the spring-back effect in both V-die and U-die punching mechanism Spring-

Finite Element Analysis of an Aluminium Alloy Sheet in a V-Die Punchhellip 333

back can only be controlled and minimized but quite difficult to be eliminated [19]

However a new technique was proposed to eliminate the spring-back of high-strength

steel (HSS) sheets in the U-bending process In this technique spring-back is

eliminated using counter-punch [20] The reason die angle change is to compensate

for spring-back [21] Friction plays a major role in metal forming processes because

of its direct interaction with die and work-piece Friction creates obstacles in the free

movement and significantly affects the deformation of the work-piece The co-

efficient of friction should be specified at the die-work interface [22] It was also seen

that the punch load increases significantly with the increase in co-efficient of friction

[23] PANKAJ TOMAR also investigated the effect of friction at the die-billet

interface for a commercially pure aluminum However this study was done for

hydrostatic extrusion of aluminum [24] In this analysis we are considering that metal

sheets are homogeneous and neglecting the surface roughness

2 Design Specification

To carry out this study a 5mm thick plate of aluminum alloy was used as the sheet

material Structural Steel was used as the preferred material for both die and punch

The dimensions used in the study for the die and the punch are tabulated below


ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm

Table 21 dimensions for a 90ordm punch Table 22 dimensions for a 90ordm die

ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm


3 Objectives

The objective of this study is to compare the deformations in the aluminum steel sheet

obtained for two different die angles incorporating the spring-back effect with a

software based analysis and to have an idea regarding the effective die-angle for the

v-die punching process The spring-back effect reduces with increase in die-angle and

the objective of this study is to validate this fact and choose a suitable die for the v-die

punching mechanism out of the two die angles used (90ordm and 120ordm) The study is

carried out with the help of finite element method in the ANSYS Workbench 160

software

4 Computational Investigation of V-die punching

41 Model geometry

The following assumptions are made for the purpose of the present study

ITEMS VALUES

Length 7970 mm

Width 1921 mm

Depth 1970 mm

Nose Fillet 2 mm

ITEMS VALUES

Length 7572 mm

Width 1921 mm

Depth 1970 mm

Nose

Fillet

2 mm


To simplify the process we have taken the steady loading condition under plain

strain condition since in the usual blanking operation the punch-die clearance is

very small

It is a quasi-static process and hence the effect of plain strain rate is neglected

The sheet metal is considered as the nonlinear plastic material while the die and

punch is the rigid bodies

In this case we have compared the mechanical properties of the aluminium and

stainless steel so our focus is only the simulation of the sheet metal So we

neglect the properties of punch amp die

In this study the Cartesian co-ordinate system is placed at the midpoint of the sheet

metal We have done our study based on this co-ordinate system The positive and

negative sign only indicates the position of the element with respect to this coordinate

system

Fig 41 V-die punch model in Ansys 160

42 FEM (Finite Element Method)

Numerical methods provide a general tool to analyze arbitrary geometries and loading

conditions Among this numerical analysis FEM (Finite Element Analysis) is used

most extensively [25] This kind of analysis requires the generation of the large

amount of data to obtain the more accurate results and consumes huge investment of

the computer resources and engineering time [26] FEM is the good choice to analyze

the sheet metal punching processes since it helps to eliminate the need for the time

and cost consuming experiments to optimize the parameters [27] The finite element

method gives an appropriate solution with an accuracy that mainly depends on the

type of element chosen and the number of elements We used the FEM to simulate the

punching process in ANSYS 150 which is capable of solving the nonlinear behavior

of the materials deformations and stress-strain accurately


43 Meshing

To perform the finite element method correctly we have to divide the metal sheet into

very small elements ie mesh elements and then the simulation is done respectively

There are different types of method to perform the meshing process like Tetrahedron

Hex dominant Sweep Multizone etc We in this study choose the Tetrahedron

method In this study 16804 elements and 31142 nodes are considered The details of

the meshing process are shown the figure below To get the accurate result we divide

the sheet metal into mesh element of sizing 1mm

Table 43 Meshing

ELEMENTS VALUES

Meshing method Tetrahedron

Elements 16804

Nodes 31142

Mesh element sizing 1 mm

Minimum edge

length

05 mm

Fig 43 Meshed model V-die punch model


44 Simulation

441 Result and discussion for 90 ordm die

The Total deformation and the directional deformations along x y and z axes are

shown in the following fig The analysis is performed by considering two nonlinear

metal sheets of 5mm thickness when subjected to a load of 550 MPa at STP

Fig 4411 total deformation for a 90ordm die

Fig 4412 directional deformation for 90 ordm die

Time is plotted along x axis and the variation of the total deformation is plotted along

the y- axis From this graphs it is observed that the total deformation for both the

metals increases almost uniformly and itrsquos parabolic in nature

Table 441 total and directional deformation for a 90 ordm die

Die-angle ITEMS VALUES

90 ordm

1 Total deformation 10048 mm (max) 038139 mm

(min)

2 Directional deformation 10046 mm (max) 038129 mm

(min)

Fig 4411 total deformation for 90

ordm die



In a similar way the deformation and the directional deformations for 120 ordm die along

x y and z axes are shown in the following fig The analysis is performed by

considering two nonlinear metal sheets of 5mm thickness when subjected to a load of

550 MPa at STP

Fig 4421 Total deformation for 120ordm die

Fig 4422 Directional deformation for 120 ordm die


the y- axis From this graph it is observed that the total deformation for both the




120 ordm


(min)


(min)


44 Conclusion

From this analysis we can see that the total deformation on the sheet metal for 90 ordm

die is greater than that in case of 120 ordm die Total deformation on the sheet metal for a

90 ordm die is 10048 mm (max) and that when die angle equals to 120 ordm is 61095 mm

(max) Similarly the directional deformation on the sheet metal for a 90 ordm die is

10046 mm (max) in the vertical direction and that when using a 120 ordm die is 61094

mm (max) Hence we see that the deformation in the 90 ordm die is much greater than

that in the 120 ordm die After removal of the tool the final directional deformation on the

metal sheet for a 90 ordm die is 80578 mm and that when using a 120 ordm die is 51489 mm

For the 90 ordm die a reduction of 19882 mm for directional deformation from the

initials and a reduction of 09605mm for the 120 ordm die is obtained Hence we

understand that the phenomena of spring back produces different effects for different

die anglesWith the increase in die-angle the spring-back effect is reduced In the

present study it is found that the spring-back effect for 120 ordm die is lesser than that for

the 90 ordm die which validates the concept of spring back phenomena in the context of

variable die angles In addition to that the spring-back effect being an unwanted

effect deformation in the 120 ordm die is the desired deformation and hence 120 ordm die

would be the preferred one

Table 44 Conclusion Table

ITEM NAME

For 90 ordm die For 120 ordm die

Maximum Total Deformation 10048 mm 61095 mm

Maximum Directional Deformation along y-axis

(initial)

10046 mm 61094 mm

Directional Deformation with Spring-back effect 80578 mm 51489 mm

Reduction in Directional Deformation 19882 mm 09605 mm

45 FUTURE SCOPE OF WORK

Further investigation is needed to explore more parameters and operating conditions

to develop a general model for more material types by using the combination of

various techniques A combination of techniques can be used in order to achieve a

higher level of verification and to reduce the cost of the necessary experimental effort

It is recommended to experimentally perform the punching process that combines the

optimal set of parameters and monitor its output quality


REFERENCES

[1] FW Timmerbil Werkstatt Maschin 46 (1956) 58ndash66

[2] httpsenwikipediaorgwikiPunching

[3] F Faura J Loacute pez C Luacute is MA Sebastiaacuten and Blanking of stainless

steel tool life equation model in T Altan (Ed) Advanced Technology of

Plasticity vol II Columbus OH 1996 pp 655ndash663

[4] Russell biagi hilary bart smithldquoimperfection sensetivity of pyramidal core

sandwich structurerdquo international journal of solids and structures 44 (2007)

4690ndash4706

[5] Sisheng yang xiang ling yangyan zheng rongbiao ma ldquocreep life analysis by

an energy model of small punch

creeptestrdquojournalhomepagewwwelseviercomlocatematdes

[6] Wen chun jiang b yang bywang h chen jm gong ldquoexperimental and

numerical study on the residual stress in a lattic truss sandwich atructure

effect of geometrical dimension of punching dierdquojournal homepage

wwwelseviercomlocatematdes

[7] Pusit mitsomwang shigeru nagasawardquoeffect of mechanical conditions on

cutting characteristics of polycarbonate sheet subjected to straight punchdie

shearingrdquo (ICTP) 2014 19-24 October 2014 Nagoya Congress Center

Nagoya Japan Procedia Engineering 81 ( 2014 ) 1145 ndash 1150

[8] Soumya subramoniana taylan altanan bogdan ciocirlanb craig campbellb

ldquooptimum selection of variable punch-die clearance to improve tool life in

blanking non-symmetric shapesrdquo (IJMTM) journal homepage

wwwelseviercomlocateijmactool

[9] E falconnet jchambert h makich g monteil ldquoprediction of abrasive punch

wear in copper alloy thin

sheetblankingrdquojournalhomepagewwwelseviercomlocatewear

[10] L komgrit h hamasaki r hino fyoshida ldquoelimination of springback of high

strength steel sheet by using additional bending with counter punchrdquo

(JMPT)journalhomepagewwwelseviercomlocatejmatprotec

[11] Debayan das saurav rajgadia anush karki ankit basnet pawan jaiswal rakesh

jaiswal anupam raj jha rabindra nath barman ldquodesign and finite element

analysis of connecting rod using solidworks and ansys workbenchrdquo (ijreat)

Volume 3 Issue 4 Aug-Sept 2015 ISSN 2320 ndash 8791

[12] International Journal of Emerging Technology and Advanced Engineering

wwwijetaecom (ISSN 2250-2459 Volume 2 Issue 7 July 2012)

Experimental Evaluation of Effect of Die Angle on Hardness and Surface

Finish of Cold Forward Extrusion of Aluminum G A ChaudhariSR

Andhale NG Patil


[13] Effect of die angle on the deformation texture of copper processed by equal

channel angular extrusion WH Huang a L Chang b PW Kao a CP

Chang wwwelseviercomlocatemsea Materials Science and Engineering

A307 (2001) 113ndash118

[14] J W Pilarczyk J Markowski FEM Analysis Of Effect Of Die Angle On

Strain And Stress State In Process Of Drawing Of Steel For Prestressed

Concrete

[15] Extrusion Characteristics Dependence of Wrought Aluminium Alloy on

Extrusion Variables S O Adeosun Akpan E I Gbenebor O P American

Journal of Materials Science 2013 3(4) 77-83 DOI

105923jmaterials2013030403

[16] Investigating Springback effect in U-Die Bending Process by varying different

Parameters Jaydeep R Shah12 S K Sharma1 B C Patel$1 Associate

professor Mechanical Department $Assistant Professor Mechanical

Department Research Scholar Mechanical Department

[17] Creep and anelasticity in the springback of aluminum JF Wang a RH

Wagoner a WD Carden b DK Matlock c F Barlat Elsevier

International journal of plasticity

[18] Mechanical Behavior and Springback Study of an Aluminum Alloy inWarm

Forming Conditions H Laurent1 2 J Coumler1 2 R Gr`eze1 P Y Manach1

A Andrade-Campos3 M C Oliveira2 and L FMenezes2 International

Scholarly Research Network ISRN Mechanical Engineering Volume 2011

Article ID 381615

[19] A Comprehensive Review of Experimental Approaches Used in the

Measurement of Springback 1AB Abdullah 2SM Sapuan 1Z Samad and

2NA Aziz

[20] Elimination of springback of high-strength steel sheet by usingadditional

bending with counter punchL Komgritablowast H Hamasakic R Hinoc F

Yoshidac Journal of Materials Processing Technology 229 (2016) 199ndash206

elsevier

[21] httpwwwthefabricatorcomarticlebendingbending-basics-why-do-die-

angles-changer

[22] Prediction of coefficient of friction for Aluminum Billet Ajay Kumar Kaviti

Om Prakash and P Vishwanath Kumar Scholars Research Library Archives

of Applied Science Research 2011 3 (4)328-335

[23] The effect of friction coefficient on punch load and thickness reduction in

deep drawing process Sadık Olguner A Tolga Bozdana INTERNATIONAL

JOURNAL OF MATERIALS Volume 3 2016


[24] Theoretical Investigation of Friction at DieBillet Interface in Hydrostatic

Extrusion of Commercially Pure Aluminum PANKAJ TOMAR SCIENCE

DIRECT

[25] An Application of Finite Element Method and Design of Experiments in the

Optimization of Sheet Metal Blanking Process Emad Al-Momani Ibrahim

Rawabdeh

[26] Haydn ng wadley norman a fleck anthony g evans ldquofabrication and

atructural performance of periodic cellular metal sandwich structuresrdquo

Composite scienceand technology 63 (2003) 2331-2343

[27] S Maiti A Ambekar U Singh P Date and K Narasimhan ldquoAssessment of

influence of some process parameters on sheet metal blankingrdquo Journal of

Materials Processing Technology Vol 102 2000 249-256


1 Introduction

Blanking and punching are one of the oldest manufacturing operations Their

applications range from components of very light to heavy appliances and

machineries [1] Punching is a metal forming process that uses a punch press to force

a tool called a punch through the work piece to create a hole via shearing When a

specially shaped punch is used to create multiple usable parts from a sheet of material

the process is known as blanking [2]During blanking the part is subjected to

complex solicitations such as deformation hardening and crack initiation and

propagation The theoretical modeling of such processes is very difficult due to the

complexity in describing the different stages of the whole shearing process starting

with the elastic stage and ending with the total separation of the sheet metal [3] Small

punch test (SPT) Ball punch Test Disk Bend test as well as Shear Punch Test [4-9]

are the techniques developing to characterize the mechanical behavior of small

specimens The concept of the small V-die punching is based on placing a thin metal

sheet specimen on the die and then the v shaped punch is applied to get the desired

shape In this process the feed is applied to the metal sheet horizontally and the

punching is done vertically In order to get the stable punching and the good punching

edge quality of the al alloy and stainless steel alloy sheets [10] it is necessary to

choose a narrow punch-die clearance and the heat sheet before punching Reducing

the clearance my increase the bright zone and also reduce the fracture zone as well as

the fracture angle but if the clearance is reduced the punching force and the tooling

wear increases [11] An experimental investigation had been carried out to study the

effect of die angle on the quality of extruded product ie surface finish and hardness

of cold extruded aluminum The die angles used were 30 45 and 60 ordms [12] Similarly

deformation in copper was observed using ECAE technique under variable die angles

The die angles used were 90 ordm and 120 ordm for this research [13] J W PILARCZYK

and J MARKOWSKI studied the effect of die angle on strain and stress state in

process of drawing of steel for pre-stressed concrete keeping 8 12 and 18 ordm dies for

the process [14] Similarly five different die angles (15 30 45 60 and 90) were used

to investigate the extrusion behavior of wrought aluminum alloys [15] Spring-back is

a geometric change that a sheet metal experiences after it gets rid of the tool forces in

a punching process Spring-back effect results in slight displacement of the sheet

metal in the direction of the return stroke of the punch Spring-back has a very

significant role in sheet metal bending process It leads to some geometric changes in

the product A research work was carried out for reflecting the different parameters on

spring-back in U-die bending of different materials with different sheet thickness and

tip radius [16]If not correctly predicted and compensated for spring-back will cause

the final part shape to deviate from design specifications and to create assembly

problems [17] H Laurent conducted the Spring-back study of aluminum alloy in

warm forming conditions A split-ring test was used to analyze the influence of

temperature during forming over Spring-back The obtained experimental results were

compared to the numerical simulations [18] A research was done earlier which

studied the spring-back effect in both V-die and U-die punching mechanism Spring-




















ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm


ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm


3 Objectives








software


41 Model geometry


ITEMS VALUES

Length 7970 mm

Width 1921 mm

Depth 1970 mm

Nose Fillet 2 mm

ITEMS VALUES

Length 7572 mm

Width 1921 mm

Depth 1970 mm

Nose

Fillet

2 mm




very small










system















43 Meshing








Table 43 Meshing

ELEMENTS VALUES


Elements 16804

Nodes 31142


Minimum edge

length

05 mm



44 Simulation












90 ordm


(min)


(min)


ordm die






550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh


























ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm


ITEMS VALUES

Length 2950 mm

Width 3303 mm

Depth 1970 mm

Fillet 2 mm

Die opening 23 mm


3 Objectives








software


41 Model geometry


ITEMS VALUES

Length 7970 mm

Width 1921 mm

Depth 1970 mm

Nose Fillet 2 mm

ITEMS VALUES

Length 7572 mm

Width 1921 mm

Depth 1970 mm

Nose

Fillet

2 mm




very small










system















43 Meshing








Table 43 Meshing

ELEMENTS VALUES


Elements 16804

Nodes 31142


Minimum edge

length

05 mm



44 Simulation












90 ordm


(min)


(min)


ordm die






550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh










very small










system















43 Meshing








Table 43 Meshing

ELEMENTS VALUES


Elements 16804

Nodes 31142


Minimum edge

length

05 mm



44 Simulation












90 ordm


(min)


(min)


ordm die






550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh








43 Meshing








Table 43 Meshing

ELEMENTS VALUES


Elements 16804

Nodes 31142


Minimum edge

length

05 mm



44 Simulation












90 ordm


(min)


(min)


ordm die






550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh








44 Simulation












90 ordm


(min)


(min)


ordm die






550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh












550 MPa at STP








120 ordm


(min)


(min)


44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh








44 Conclusion



















ITEM NAME




(initial)

10046 mm 61094 mm











REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh








REFERENCES








4690ndash4706






























Andhale NG Patil





A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh











A307 (2001) 113ndash118



Concrete




105923jmaterials2013030403












Article ID 381615



2NA Aziz




elsevier


angles-changer










DIRECT



Rawabdeh










DIRECT



Rawabdeh







finite element analysis of an aluminium alloy sheet in a v ... · finite element analysis of an...

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