• No se han encontrado resultados

Capítulo III: Evaluación Externa

3.5. La Industria Peruana de Café y sus Competidores

It was seen that the wall thickness at the intrados decreases with increase in the

internal pressure. Figure 6-4 shows the variation in maximum wall thickness with

increasing pressure. The minimum wall thickness with variation in internal pressure is

shown in figure 6-5. The minimum wall thickness at extrados decreases with increase in

3.08 3.09 3.1 3.11 3.12 3.13 3.14 0 1 2 3 4 5

Internal pressure (MPa)

T h ickn ess o f t u b e at i n tr ad o s ( m m) F = 12.9 kN F = 15.05 kN F = 17.2 kN F = 19.35 kN

Fig. 6-4 Comparison of maximum wall thickness at intrados at constant axial pull for increasing value of internal pressure

From the two curves it is seen both at extrados and at intrados the wall thickness reduced with increase in the axial pull. The change in wall thickness at both extrados and intrados both follow a linear pattern. The slope of the wall thickness change at the extrados is sharp when compared to the slope of wall thickness change at the intrados. This indicates with the increase in internal pressure the rate of reduction in wall thickness is greater at extrados than intrados.

2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.6 2.61 0 1 2 3 4 5

Internal pressure (MPa)

T h ickn ess o f t u b e at ext ra d o s ( m m) F = 12.9 kN F = 15.05 kN F = 17.2 kN F = 19.35 kN

Fig. 6-5 Comparison of maximum wall thickness at extrados at constant axial pull for increasing value of internal pressure

The cross section distortion of tube with variation in internal pressure is shown in figure 6-6. It was seen that the cross section distortion decreased with increase in the internal pressure. But with further increase in internal pressure the cross section distortion increased.

From the parametric study it can be concluded that with an optimum value of pressure

and axial pull wrinkling can be eliminated and the cross section of the tube can be

maintained circular. 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5

Internal pressure (MPa)

C ro s s s e c tio n d is tor ti on (% ) F = 12.9 kN F = 15.05 kN F = 17.2 kN F = 19.35 kN

Fig. 6-6 Comparison of cross section distortion at constant axial pull for increasing value of internal pressure

CONCLUSIONS

Stretch bending tends to minimize wrinkling and can reduce springback. By applying

fluid pressure during bending, the wrinkling tendency and cross section distortion of the

tube are reduced. Thus, this approach can be used for bending a thin walled tube over a

small die radius, which cannot be achieved with a traditional tube bending process.

In this paper, the problem of tube bending with internal pressure and axial stretching

has been investigated analytically and numerically. The objective of the study is to

develop a tool to accurately predict the wall thickness variation and cross section

distortion of the tube under different loading conditions. The analytical models were

developed based on the plastic deformation theory. For general tube bending processes

(without the additional tension and pressure), the analytical and FEA predictions agree

well with published experimental data. With additional tension and pressure loading, it is

found that the analytical and FEA results are in good agreement.

It was seen that internal pressure can alone remove wrinkling and provide a better

cross section, but the use of internal pressure alone is limited to the capacity of pressure

intensifier. And moreover beyond a certain value of internal pressure the cross section

distortion increases. In such cases combination of axial pull and internal pressure can be

used. From the parametric study it was seen that with increase in axial pull the rate of

decrease in wall thickness was greater at intrados and in the case of axial pull the rate of

obtained.

The contribution of the present work is that the developed analytical models can be

used to analyze tooling and process design in the early design stage. This is significant

since the commonly used FEA simulation requires extensive part modeling and

computation time.

The future work can include improvement in the analytical model by incorporating the

effect of the pressure die so a more accurate prediction of wall thickness can be made at

[1] Brewster, K., Sutter, K., Ahmetoglu, M.A., and Altan, T., 1996, “Hydroforming

Tube,” The Tube and Pipe Quarterly, 7(4), pp. 34-40.

[2] Denglar, K., 1996, “Exploring Internal High Pressure in Forming of Metal,” The

Fabricator, 7/8.

[3] Horton, F., 1997, “Using Forming Simulation in Development of Complex

Hydroformed Shapes,” Proceedings of the 2nd annual automotive tube conference,

Dearborn, Michigan, May 13-14, pp.173.

[4] Kim, J., Kang, S.J., and Kang, B.S., 2002, “Computational Approach to Analysis and

Design of Hydroforming Process for an Automobile Lower Arm,” Computers and

Structures, 80, pp. 1295-1304.

[5] Kervick, R.J., and Springborn, R.K., 1966, Cold Bending and Forming Tube and

Other Sections, American Society of Tool and Manufacturing Engineers, Dearborn, MI. [6] Tarana, K., 2002, “Finite Element Simulation of the Tube Hydroforming Process –

Bending, Preforming and Hydroforming,” Journal of Materials Processing Technology,

127, pp. 401-408.

[7] Yang, J., Jeon, B., 2001, “The Tube Bending Technology of a Hydroforming Process

from an Automotive Part,” Journal of Materials Processing Technology, 111, pp. 175-

181.

[8] Miller, J.E., Kyriakides, S., Bastard, A.H., 2001, “On Bend-Stretch Forming of

Aluminum Extruded Tubes - I: Experiments,” International Journal of Mechanical

Aluminum Extruded Tubes - II: Analysis,” International Journal of Mechanical Sciences,

43(5), pp. 1319-1338.

[10] Li, H.Z., Fagerson, R., and Stelson, K.A., 1994, “A Method of Adaptive Control of

Rotary-Draw Thin Walled Tube Bending With Spring Back Compensation,”

Transactions of the North American Manufacturing Research, S.M.E, 22, pp. 25-28. [11] Brazier, L.G., 1927, “On the Flexure of Thin Cylindrical Shells and Other Sections,”

Proceedings of the Royal Society of London, 116, pp. 104-114.

[12] Zang, L.C., and Yu, T.X., 1987, “An Investigation of the Brazier Effect on a

Cylindrical Tube Under Pure Elastic-Plastic Bending,” International Journal of Pressure

Vessel and Piping, 30, pp.77-86.

[13] Pan, K., and Stelson, K.A., 1995, “On the Plastic Deformation of a Tube During

Bending,” Journal of Engineering for Industry, 117, pp. 494-500.

[14] Tang, N.C., 2000, “Plastic-Deformation Analysis in Tube Bending,” International

Journal of Pressure Vessel and Piping, 77(12), pp. 751-759.

[15] Corona, E., and Kyriakides, S., 1988, “On the Collapse of Inelastic Tubes Under

Combined Bending and Pressure,” International Journal of Solids and Structures, 24, pp.

505-535.

[16] Kyriakides, S., and Ju, G.T., 1992, “Bifurcation and Local Instabilities in

Cylinderical Shells Under Bending: Part 1 Experiments,” International Journal of Solids

and Structures, 29, pp. 1117-1142.

[17] Corona, E., and Vaze, S.E., 1996, “Buckling of Elastic-Plastic Square Tubes under

Engineering Materials and Technology, 123(4), pp. 430-435.

[19] Zhan, M., Yang, H., Jiang, Z.Q., Zhao, Z.S., Lin, Y., 2002, “A Study on a 3D FE

Simulation Method of the Bending Process of Thin –Walled Tube,” Journal of Materials

Processing Technology, 129, pp. 273-276.

[20] Dyau, J.Y., and Kyriakides, S., (1992), “On the Response of Elastic-Plastic Tubes

Under Combined Bending and Tension,” Journal of Offshore Mechanics and Arctic

Engineering, 114, pp.50-62.

[21] Zhu, H., and Stelson, K.A., 2002, “Distortion of Rectangular Tubes in Stretch

Bending,” Journal of Manufacturing Science and Engineering, 124, pp. 886-890.

[22] Duncan J. L., Hu J., and Marciniak Z., Mechanics of Sheet Metal Forming,

Butterworth-Heinemann, Woburn, MA.

[23] Hosford, W.F., and Caddell, R.M., 1983, Metal Forming Mechanics and Metallurgy,

Prentice-Hall Inc., Englewood Cliffs, NJ.

[24] LS-DYNA, May 1999, “Keyword User’s Manual,” Livermore Software Technology

Corporation, Livermore, CA.

[25] HyperMesh, 2001, “Altair HyperMesh Tutorials Version 5.0,” Altair Engineering

Inc., Troy, MI.

[26] Khodayari. G., 2002, “How the Material Influences the Bending for Hydroforming

Effects on Ovality, Springback, and Wall Thickness in Tubes,” The Tube and Pipe

Journal,

SIMULATION OF ROTARY DRAW TUBE BENDING USING LS-DYNA

Finite element analysis consists of three steps Pre-processing, processing and post-

processing. HyperMesh was used as pre-processor for the simulation. LS-DYNA was

used as the processor while post-processing was done using HyperView.

Preprocessing gives the description about the geometry, material property and boundary

conditions. HyperMesh provides different types of collectors to store information; like

component collector to store the information about the geometry, material collector to

store information about material property and load collector to store information about

the loads and boundary conditions. The entire preprocessing has been divided into three

steps:

a. Creating collectors

b. Creating geometry

c. Applying boundary condition

d. Applying control cards and data base cards

1 Creating collectors

Four types of collectors are created: material (Mat), property (Prop), component (Comp)

The tooling for rotary draw tube bending consists of six parts (five rigid parts and one

tube) and hence six material collectors were created. All the collectors are named

according to the part. The rigid toolings were specified MAT 20 which is the default rigid

material for LD-DYNA. MAT24 (LINEAR _PEICEWISE_PLASTICITY) was used as

the material model for the tube. Each material must be assigned material property: -

Young’s modulus, density, Poisson’s ratio. It is essential that units should be consistent

because LS-DYNA understands a consistent set of units. The units chosen for simulation

are:

Table A-1: Units used in simulation

Mass Ton Force Newton Pressure MPa Time Second

The material property specified for all the rigid tools are listed in the table 111.The other

important thing which needs to be specified is the translational and the rotational

constraint of the rigid body.

1.1.1 Bend die: It was specified a translation in X and Y direction and rotation about

the Z axis.

1.1.3 Wiper die: It was constrained to translate and rotate in all the directions.

1.1.4 Mandrel: It was constrained to translate and rotate in all the directions.

1.1.5 Pressure die: It has been given translation degree of freedom in X and Y

direction and was constrained to rotate in all directions.

1.2 Property collector

Six shell sections were created, one for each part. Each section is assigned to the

corresponding material. Shell element, thickness and NIP (number of integration points)

were specified for each shell segment.

Four nodded, Belytschko-Tsay shell element with 5 NIP having a thickness of 2.858 mm

was specified for the tube.

Four nodded, Belytschko-Tsay shell element with 2 NIP was considered for the rigid

1.3 Component collector

Six component collectors were created and corresponding materials are assigned to each

of them.

1.4 Load collector

Two load collectors (bend die rotation and pressure die movement) were created one for

the bend die movement and the other one for the pressure die movement. Prescribed

Boundary (PRS BOUN) was selected as the load type.

2 Creating Geometry

Here a brief description is provided for modeling al the six parts.

2.1 Bend Die

The bend die consists of two parts: a circular part and a straight part where the clamp die

holds the tube. Hence the modeling was done in two steps. The first step was modeling of

2.1.1 Circular part

User control torus was used to model the circular part. For this first the nodes were

created for selecting the center of the die, major direction and normal direction. Radius

and angle of major and minor axis and the element density were specified to get the final

model.

2.1.2 Straight part

Modeling of the straight part was done using the user controlled cylinder. Nodes were

created for selecting the major direction and the center of the cylinder. Radius, angle of

the cylinder and the element density was used to complete the modeling.

2.2 Clamp die

Modeling of clamp die was done using user controlled cylinder. Similar to the modeling

of the straight portion of the bend die.

2.3 Pressure die

Modeling of clamp die was done using user controlled cylinder. Similar to the modeling

2.4 Wiper die

Modeling of clamp die was done using user controlled cylinder, similar to the modeling

of the straight portion of the bend die.

2.5 Mandrel

A plug mandrel is used for the simulation. The modeling procedure for the mandrel is

same as the clamp die .The only difference is that instead of span angle of 180o , span

angle of 360o is specified.

2.6 Tube

Modeling of clamp die was done using user controlled cylinder similar to the modeling of

the mandrel.

3 Boundary Condition

3.1 Contact

For defining the contact between different surface pair’s two different types of contact

algorithm are chosen

3.1.1 Contact_surface_to_surface

This is used to define the surface contact between tube-bend die, tube–pressure die, tube–

wiper die, and tube–mandrel. Contact option is specified by selecting master surface and

the slave surface. The rigid body is always selected as the master surface and the blank

(which is finely meshed) is always selected as the slave surface.

The coefficient of static and dynamic friction between the Tube-bend-die is specified as

0.10 and the coefficient of static friction between the tube-pressure die, tube-wiper die,

tube –mandrel is specified as 0.5

3.1.2 Constrained_extra_nodes_set

A node set is made of all the nodes of the tube towards the clamp side and they are added

3.2 Pressure

A pressure of 50 MPa is applied to the pressure die for which elements of pressure die are

selected. In a shell element, pressure always acts in the direction of the normal, so a

negative value of magnitude must be specified to change the direction of pressure.

Internal pressure in the tube is also specified in the same way.

3.3 Checking Penetration

Penetration check is done so as to check if the master segment would penetrate in the

slave segment during the simulation. To avoid penetration two things have to be kept in

mind:

The normal should be opposite to each other.If both the normal point towards each other

then normal of one of the surface should be reversed.

The slave surface (tube) should have a finer mesh than the master surface (rigid part). If

3.4 Displacement Boundary condition

3.4.1 Bend die

Rotation about Z axis and the load curve are specified The load curve is a curve between

the time and angle (in radians)

3.4.2 Pressure die

Translation in X axis and the load curve are specified. The load curve is a curve between

INPUT DECK FOR ROTARY DRAW TUBE BENDING *KEYWORD

$$ Units Ton, N, MPa, sec $$

*CONTROL_TERMINATION

$$ ENDTIM ENDCYC DTMIN ENDENG ENDMAS 0.0365 0 0.0 0.0 0.0

*CONTROL_SHELL

$$ WRPANG ITRIST IRNXX ISTUPD THEORY BWC MITER PROJ 20.0 2 0 1 2 2 1 0 *CONTROL_HOURGLASS $$ IHQ QH 2 0.1 *CONTROL_BULK_VISCOSITY $$ Q2 Q1 1.5 0.06 *CONTROL_DAMPING 250 .001 .995 *CONTROL_CONTACT

$$ SLSFAC RWPNAL ISLCHK SHLTHK PENOPT THKCHG ORIEN 0.1 1.0 2 2 1 1 1

$$ URSTR USRFRC NSBCS INTERM XPENE SSTHK ECDT TIEDPRJ 0 0 10 0 4.0 1 0 0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 *CONTROL_OUTPUT

$$ NPOPT NEECHO NREFUP IACCOP OPIFS IPNINT IKEDIT 1 3 1 0 0.0 0 100 0

*CONTROL_ENERGY

$$ HGEN RWEN SLNTEN RYLEN 2 2 2 2

$$

$$DATABASE_OPTON… Control Cards for ASCII output $$ $$ *DATABASE_GLSTAT 1.0000E-04 *DATABASE_BINARY_D3PLOT $$ DT/CYCL LCDT BEAM NPLTC 3.0000E-03 0 0 0 *DATABASE_BINARY_D3THDT $$ DT/CYCL LCID 0.0 0 *DATABASE_EXTENT_BINARY

$$ NEIPH NEIPS MAXINT STRFLG SIGFLG EPSFLG RLTFLG ENGFLG 0 0 3 0 1 1 1 1

$$ CMPFLG IEVERP BEAMIP DCOMP SHGE STSSZ 0 0 0 1 1 1

$$

$$MATERIAL PROPERTIES $$

*MAT_RIGID

1.0 0 0

0.0 0.0 0.0 0.0 0.0 0.0 *MAT_RIGID

$HMNAME MATS 3matrigid.1

37.8300E-09 207000.0 0.3 0.0 0.0 0.0 1.0 7 4

0.0 0.0 0.0 0.0 0.0 0.0 *MAT_RIGID

$HMNAME MATS 4matrigid.2

47.8300E-09 207000.0 0.3 0.0 0.0 0.0 1.0 7 7

0.0 0.0 0.0 0.0 0.0 0.0 *MAT_RIGID

$HMNAME MATS 5matrigid.3

57.8300E-09 207000.0 0.3 0.0 0.0 0.0 1.0 6 7

0.0 0.0 0.0 0.0 0.0 0.0 *MAT_PIECEWISE_LINEAR_PLASTICITY $HMNAME MATS 2MAT24_2

28.9000E-09 210000.0 0.3 210.0 900.0 0.0 0.0 0.0 0 0

$$ HM Entries in Stress-Strain Curve = 8

0.0 0.000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $$ $$PART PROPERTIES $$ *PART_INERTIA

$HMNAME COMPS 1die 0 0 $HMCOLOR COMPS 1 7 1 1 3 0 0 0 0 100.0 100.0 0.07.6500E-05 0 9.82 5.49-2.500E-04 16.62.8900E-04 24.3 0.0 0.0 0.0 0.0 0.0 0.0 *CONSTRAINED_RIGID_BODIES 1 9 1 11 *CONSTRAINED_EXTRA_NODES_SET 9 3 *PART

$HMNAME COMPS 2tube $HMCOLOR COMPS 2 6

2 2 2 0 0 0 0 *PART

$HMNAME COMPS 4pressure $HMCOLOR COMPS 4 7

4 1 5 0 0 0 0 *PART

$HMNAME COMPS 7wiper $HMCOLOR COMPS 7 6

7 1 4 0 0 0 0

$HMNAME COMPS 9clamp $HMCOLOR COMPS 9 3

9 1 1 0 0 0 0 *PART

$HMNAME COMPS 11diepart $HMCOLOR COMPS 11 7 11 1 1 0 0 0 0 $$ $$SECTION PROPERTIES $$ *SECTION_SHELL

$HMNAME PROPS 1shell section 1 2 1.0 5 0.0 0.0 0 7.01 7.01 7.01 7.01 0.0

$HMNAME PROPS 2shell-tube 2 2 1.0 5 0.0 0.0 0 2.858 2.858 2.858 2.858 0.0 $$ $$BOUNDARY CONDITION $$ *BOUNDARY_PRESCRIBED_MOTION_RIGID $HMNAME LOADCOLS 1boundary $HMCOLOR LOADCOLS 1 7

1 7 2 1 -1.0 01.0000E+28 0.0 *BOUNDARY_PRESCRIBED_MOTION_RIGID

$HMNAME LOADCOLS 2PrescribedMtnRgd 2 $HMCOLOR LOADCOLS 2 1

4 2 2 3 -1.0 01.0000E+28 *CONTACT_SURFACE_TO_SURFACE

$HMNAME GROUPS 4contact-tube-prseeure $HMCOLOR GROUPS 4 1

2 11 3 3 0 0.05 0.05 0.0 0.0 20.0 1 1.0 1.0 0.0 0.0 1.0 1.0 1.0 *CONTACT_SURFACE_TO_SURFACE

$HMNAME GROUPS 5contact-tube-wiper $HMCOLOR GROUPS 5 1

2 4 3 3 0

0.05 0.05 0.0 0.0 20.0 1 0.0 0.0 1.0 1.0 0.0 0.0 1.0 1.0 1.0 1.0 *CONTACT_SURFACE_TO_SURFACE

$HMNAME GROUPS 7tube-die $HMCOLOR GROUPS 7 1 2 1 3 3 0 0.10 0.10 0.0 0.0 0.0 1 1.0 1.0 0.0 0.0 1.0 1.0 1.0 *CONTACT_SURFACE_TO_SURFACE 2 9 3 3 0.1 0.1 0.0 0.0 0.0 1 1.0 $$

$$VECTORS AND CURVE $$

$HMNAME VECTORCOL 1auto1

$HMCOLOR VECTORCOL 1 1

1 100.0 100.0 0.0 100.0 100.0 -10.0 *DEFINE_CURVE $HMNAME CURVES 1curve1

$HMCOLOR CURVES 1 1 $HMCURVE 1 1 curve1 1 0 1.0 1.0 0.0 0.0 0 0.0 0.0 3.00000000000000E-03 0.1309 6.00000000000000E-03 0.261799 0.009 0.392699 0.012 .522599 0.015 .654498 0.018 .785398 0.021 .916298 0.024 1.047198 0.027 1.178098 0.030 1.308997 0.033 1.439897 0.036 1.570796 0.0365 1.701696 *DEFINE_CURVE $HMNAME CURVES 4curve1.1

$HMCOLOR CURVES 4 1

$HMCURVE 1 1 curve1 tube

2 0 1.0 1.0 0.0 0.0 0

0.0 5.0 0.0365 5.0 *DEFINE_CURVE $HMNAME CURVES 2curve2

$HMCOLOR CURVES 2 1 $HMCURVE 1 1 curve2 3 0 1.0 1.0 0.0 0.0 0 0.0 0.0 3.00000000000000E-03 10.0 0.011 15.0 0.020 20.0 0.0365 25.0 *DEFINE_CURVE $HMNAME CURVES 4curve1.1

$HMCOLOR CURVES 4 1

$HMCURVE 1 1 curve1 Pressure

4 0 1.0 1.0 0.0 0.0 0 0.0 50.0 0.0365 50.0 *DEFINE_CURVE 5 0 1.0 1.0 0.0 0.0 0 0.0 0.0 0.001 300.0 0.045 300.0 *NODE 4 239.04 100.0 32.2 5 238.76563632066 108.73039383535 32.2 6 237.94362807076 117.42633279478 32.2

8 234.67180272332 134.5778419114 32.2 9 232.23489802567 142.96572289789 32.2 10 229.2761225979 151.18403780527 32.2 11 225.80715337487 159.2003526992 32.2 12 221.84168079329 166.9830308471 32.2 .. .. 16541 212.99138814707 173.64545454545 -18.92907341988 16542 208.42550134103 184.03636363636 -9.979602790705 16543 212.99138814707 184.03636363636 -18.92907341988 *ELEMENT_SHELL 58 1 189 187 188 188 62 1 200 199 201 201 113 1 233 228 229 229 184 1 272 273 292 292 201 1 309 242 310 310 221 1 122 323 123 123 246 1 330 336 329 329 .. .. 14907 11 15533 15534 15540 15538 14908 11 15538 15540 15539 15537 $$ $$ NODE SETS $$ *SET_NODE_LIST $HMSET

$NODES OF TUBE CONSTRAINED TO CLAMP 3 0.0 0.0 0.0 0.0 9760 9761 9762 9763 9764 9765 9766 9767 9768 9769 9770 9771 9772 9773 9774 9775 9776 9777 9778 9779 9780 9781 9782 9783 9784 9785 9786 9787 9788 9789 9790 9791 9792 9793 9794 9795 9796 9797 9798 9799 9800 9801 9802 9803 9804 9805 9806 9807 9808 9809 9810 9811 9812 9813 9814 9815 .. .. 11283 11284 11285 11286 11287 11288 11289 11290 11291 11292 11293 11294 11295 11296 11297 11298 11299 11300 11301 11302 11303 11304 11305 11306 11307 11308 11309 11310 11311 11312 11313 11314 *SET_NODE_LIST $HMSET

$NODES TO WHICH AXIAL PULL IS APPLIED 4 0.0 0.0 0.0 0.0 9928 9929 9930 9931 9932 9933 9934 9935 9936 9937 9938 9939 9940 9941 9942 9943 9944 9945 9946 9947 9948 9949 9950 9951 9952 9953 9954 9955 9956 9957 9958 9959 9960 9961 9962 9963 9964 9965 9966 9967 9968 9969 9970 $$ $$LOAD APPLIED $$

$$ HMNAME LOADCOLS 2PrescribedMtnRgd 2 $$ PRESSURE APPLIED TO PRESSURE DIE

4 -1.0 0.0 16037 16036 16041 16040 4 -1.0 0.0 16036 16024 16023 16041 4 -1.0 0.0 16040 16041 16016 16015 4 -1.0 0.0 16041 16023 16017 16016 4 -1.0 0.0 16038 16037 16040 16042 4 -1.0 0.0 16042 16040 16015 16014 4 -1.0 0.0 16001 16039 16043 16002 .. .. 4 -1.0 0.0 16410 16318 16319 16408 4 -1.0 0.0 16369 16370 16411 16395 4 -1.0 0.0 16370 16371 16410 16411 4 -1.0 0.0 16395 16411 16409 16394 4 -1.0 0.0 16411 16410 16408 16409 *LOAD_SEGMENT

$$ HMNAME LOADCOLS 2PrescribedMtnRgd 2 $$ INTERNAL PRESSURE APPLIED TO TUBE

2 -1.0 0.0 10847 10852 10848 10846 2 -1.0 0.0 10827 10826 10852 10847 2 -1.0 0.0 10729 10728 10850 10851 2 -1.0 0.0 9825 10729 10851 9826 2 -1.0 0.0 10851 10850 10848 10849 2 -1.0 0.0 9826 10851 10849 9827 2 -1.0 0.0 10845 10850 10728 10727 2 -1.0 0.0 10846 10848 10850 10845 .. .. 2 -1.0 0.0 15113 15177 15173 15114 2 -1.0 0.0 15166 15178 15147 15146 2 -1.0 0.0 15178 15177 15148 15147 2 -1.0 0.0 15165 15174 15178 15166 2 -1.0 0.0 15174 15173 15177 15178 *LOAD_NODE_SET

$HMNAME LOADCOLS 2PrescribedMtnRgd 2 $HMCOLOR LOADCOLS 2 1

4 2 5 1.0 *END

VITA

Rohit Agarwal

HIG 79 Sector E

Aliganj, Lucknow, India

August 12, 1979...Born, Kanpur, U.P., India

2001 – 2004...M.S. Mechanical Engineering,

Texas A&M University, USA

1996 - 2000...B.E. Mechanical Engineering,

Bangalore University, India