Elastic-plastic Collapse of a Cylindrical Pipe under External Rigid Body Loading

Chapter 11: Elastic-plastic Collapse of a Cylindrical Pipe under External Rigid Body Loading

11Elastic-plastic Collapse of a Cylindrical Pipe under External Rigid Body Loading

Summary 146

Introduction 147

Requested Solutions 147

FEM Solutions 147

Modeling Tips 152

Pre- and Postprocess with SimXpert 153

Input File(s) 210

MD Demonstration Problems

CHAPTER 11146

SummaryTitle Chapter 11: Elastic-Plastic Collapse of a Cylindrical Pipe under External Rigid

Body Loading

Contact features Rigid-deformable contact; Velocity controlled rigid bodies; Elastic perfectly plastic material; Nonlinear shell elements with large strain plasticity

Geometry Pipe Length = 24”; Pipe Diameter = 8”; Pipe Thickness = 0.4”

Material properties Elastic perfectly plastic material

Analysis type Quasi-static analysis using elastic perfectly plastic material, geometric nonlinearity, and nonlinear boundary conditions

Boundary conditions Both ends of pipe are constrained in all degrees of freedom

Applied loads Both rigid bodies are moving towards the pipe in y-direction with a velocity of 2 in/sec. for duration of 1 second.

Element type 4-node nonlinear thick shell element

FE results Plot of y-displacement and total plastic strain contours

+

R = 3

+

R = 4Move Down

V = -2 in

Move UpV = 2 in

Pipe

Rigid Body 1

Rigid Body 2

E 3.0610 psi= 0.3= y 36000 psi=

0.0 0.5 1.0 1.5 2.00

20000

40000

60000

80000

100000

Force Y Bottom

Force Y Top

Die Load [Lbf ]

Die Displacment [in]

147CHAPTER 11

Elastic-plastic Collapse of a Cylindrical Pipe under External Rigid Body Loading

IntroductionA model of a cylindrical pipe is subjected to crushing as rigid bodies above and below the pipe move inward towards each other. The model is created using 2-D nonlinear thick shell elements to model the pipe and rigid surfaces above and below the pipe. The problem attempts to quantify whether the movement of the external structures cause the plastic collapse of the pipe. Initial contact with the external structures is expected to cause elastic deformation of the steel pipe. Additional incremental movement potentially subjects the structure to stresses beyond the proportional limit of the material. The yield stress defines the onset of plastic strains that may initiate the collapse of the structure walls. This exercise illustrates several SOL 400 capabilities including large displacement analysis, contact analysis between rigid and deformable bodies, and large strain plasticity modeled with an elastic-perfectly plastic model.

Requested SolutionsThe large displacement elastic-plastic contact analysis is carried out using MD Nastran SOL 400 for this rigid to deformable problem. The application of the nonlinear thick shell element is demonstrated by using the nonlinear extension PSHLN1 option for the regular PSHELL option. The following results from SOL 400 model are compared with the results obtained from the Marc model.

• Contour plot for y-displacement• Contour plot for total equivalent plastic strain

FEM SolutionsA numerical solution has been obtained with MD R2Nastran’s SOL 400 for a 3-D representation of the deformable pipe structure and two semi-circular sections of rigid pipes sections. The details of finite element model, contact simulation, material, load, boundary conditions, and solution procedure are discussed in this chapter.

Finite Element and Contact ModelThe finite element mesh for the pipe contains 18 elements around the circumference and 18 elements along the length for a total of 324 elements. MD Nastran CQUAD4 elements with material ID 1 and thickness 0.4 inches are selected using the following PSHELL and PSHLN1 entries. The PSHLN1 entry enables SOL 400 to access the thick shell elements with large strain capabilities. The finite element model used for this simulation is shown in Figure 11-1.

PSHELL 1 1 .4 1 1PSHLN1 1 1 1 NO ++ C4 DCT L


CHAPTER 11148

Figure 11-1 Finite Element Model used with MD Nastran Simulation

In defining the contact model, the primary pipe section is modeled as a deformable body and the two external pipe structures are modeled as rigid bodies. Elements comprising the deformable pipe structure are used to generate a deformable contact body with ID 4 using the following BCBODY and BSURF entries. Contact body IDs 5 and 6 are used to define the velocity controlled rigid bodies for the two semicircular sections of rigid pipes. The geometry profiles of the rigid surfaces are defined using 3-D NURB surfaces that describe the true surface geometry and most accurately represent the curved surfaces.

BCBODY 4 3D DEFORM 4 0BSURF 4 1 2 3 4 5 6 7...BCBODY 5 3D RIGID 0 1 0 0 0. 0. 0. 0. 0. -2. 0. RIGID 0 1 CONTACT_TOP NURBS -13 10 4 4 50 50 0 -2. 8.1 -5.5 -2. 8.1 -4.66667...BCBODY 6 3D RIGID 0 1 0 0 0. 0. 0. 0. 0. 2. 0. RIGID 0 1 CONTACT_BOTTOM NURBS -13 10 4 4 50 50 8 0. -7.1 -5.5 0. -7.1 -4.66667...

Furthermore, the following BCTABLE entries identify how these bodies can touch each other. BCTABLE with ID 0 is used to define the touching conditions at the start of the analysis. This is a mandatory option required in SOL 400 for contact analysis and is flagged in the case control section through the optional BCONTACT = 0 option. The BCTABLE with ID 1 is used to define the touching conditions for later increments in the analysis, and it is flagged using BCONTACT = 1 in the case control section.

BCTABLE 0 2 SLAVE 4 0. 0. 0. 0. 0 0. 0 0 0 MASTERS 5 SLAVE 4 0. 0. 0. 0. 0 0. 0 0 0 MASTERS 6

149CHAPTER 11


BCTABLE 1 2 SLAVE 4 0. 0. 0. 0. 0 0. 0 0 0 MASTERS 5 SLAVE 4 0. 0. 0. 0. 0 0. 0 0 0 MASTERS 6

MaterialThe isotropic elastic and elastic-perfectly plastic material properties of the deformable body are defined using the following MAT1 and MATEP options.

MAT1 1 3.+7 .3MATEP 1 Perfect36000. Isotrop Addmean

The following NLMOPTS entry enables large strain formulation using additive plasticity with mean normal return.

NLMOPTS,LRGS,1

Loading and Boundary ConditionsBoth ends of the pipe are constrained in all degrees of freedom using the following entries. In addition to this, the top and bottom rigid surfaces are given velocity vectors of –2 inches per second, and +2 inches per second, respectively in the y-direction. This causes the upper structure to be pushed down onto the top of the pipe section and the lower structure to be pushed up into the bottom of the pipe section at a rate of 2 inches per second for a total time of 1 second. The velocities of these rigid bodies are defined in the BCBODY section.

SPCADD 2 1FORCE 1 1 0 1.-16 1. 0. 0.SPC1 1 123456 1 THRU 18SPC1 1 123456 343 THRU 360

Solution ProcedureThe nonlinear procedure used is defined through the following NLPARM entry:

NLPARM 1 100 PFNT 0 500 UPV NO

where 100 indicates the total number of increments; PFNT represents Pure Full Newton-Raphson Technique wherein the stiffness is reformed at every iteration; KSTEP = 0 in conjunction with PFNT indicates that the program automatically determines if the stiffness needs to be reformed after the previous load increment is completed and the next load increment is commenced. 500 is the maximum number of allowed recycles for every increment and if this were to be exceeded, the load step would be cut-back and the increment repeated. UPV indicates that convergence will be checked on displacements (U) and residuals (P) and V stands for vector component which will do a maximum component check. NO indicates that intermediate output will not be produced after every increment. The second line of NLPARM is omitted here which implies that default convergence tolerances of 0.01 will be used for U and P checking.


CHAPTER 11150

ResultsThe contour of displacement in y-direction and total equivalent plastic strain in the pipe section from SOL 400 simulations are shown in Figure 11-2 and Figure 11-3, respectively. Similar plots from the Marc simulations are shown in Figure 11-4 and Figure 11-5, respectively. It is clear from these figures that the predictions from the SOL 400 matches closely with the prediction from Marc.

Figure 11-2 Y-Displacement Contours from SOL 400 Model

Figure 11-3 Total Equivalent Plastic Strain Contours from SOL 400 Model

151CHAPTER 11


Figure 11-4 Y-Displacement Contours from Marc Model

Figure 11-5 Total Equivalent Plastic Strain Contours from Marc Model


CHAPTER 11152

Modeling Tips• PSHLN1 entry in conjunction with regular PSHELL entry allows the users to make use of the thick shell

element which is capable of handling large strain elasto-plastic applications problems. Users should also make use of the NLMOPTS,LRGS,1 option to flag the large strain behavior of these element.

• Adding the parameter,

PARAM,CDBMSG05,5

after the BEGIN BULK option will output a num-11m.t19 file that has the contact information available for postprocessing in either Mentat or Patran. With this information, you can plot the normal contact force on the rigid bodies (Die Forces) versus the Die Displacement as shown in Figure 11-6. The step shaped response is due to the local collapsing of the curvature of the pipe elements. Using more elements would require smaller step sizes.

Figure 11-6 Die Load versus Die Displacement

• It is possible to make use of load controlled rigid body in place of the velocity controlled rigid body for this problem. In such case, you should apply necessary displacement boundary condition at the control node of rigid bodies to simulate its movement in y-direction.

0.0 0.5 1.0 1.5 2.00

20000

40000

60000

80000

100000

Force Y Bottom

Force Y Top

Die Load [Lbf ]

Die Displacment [in]

153CHAPTER 11


Pre- and Postprocess with SimXpert

Specify the Model Units

a. Tools: Options

b. Select Units Manager

c. For Basic Units, specify the model units:

Length = mm; Mass = kg; Time = s; Temperature = kelvin, Force = N

d. Click OK

a

b c

d


CHAPTER 11154

Create a Part for the Pipe

a. Assemble tab

b. Select Create Part

c. For Title, specify pipe

d. Click OK

e. Observe pipe in the Model Browser Tree

ab

c

d

e

155CHAPTER 11


Create Curves for the Pipe

a. Geometry tab: Curve/Arc

b. Select Arc

c. Select Circle

d. Select Dir-Radius

e. For X,Y,Z Input, enter -12,0,0

f. Click OK

g. For Circle,1 Radius, enter 4

h. Click OK

i. Fill

a

b

c

d

e

f

g

h

i


CHAPTER 11156

Create Curves for the Pipe (continued)


b. Select Arc

c. Select Circle

d. Select Dir-Radius

e. For X,Y,Z Input, enter -7.2,0,0; click OK

f. For X,Y,Z Input, enter 7.2,0,0; click OK

g. For X,Y,Z Input, enter 1.2,0,0; click OK

e

f

g

157CHAPTER 11


Create Mesh for the Pipe

a. Meshing tab

b. Select 2-3-4-Line Mesh

c. For Curves, select 2 curves

d. For On curve 1: enter 18

e. For On curve 2, enter 3

f. Leave On curve 3 and 4 blank

g. Click OK

a

b

c

de

f

g

c

de

f

g


CHAPTER 11158

Create Mesh for the Pipe (continued)

a. Meshing tab






g. Click OK

g

f

ed

c

b

a

159CHAPTER 11


Create Mesh for the Pipe (continued)

a. Meshing tab






g. Click OK

a

b

g

fe

d

c


CHAPTER 11160

Merge Equivalent Nodes

a. Node/Elements tab

b. Select Equivalence

c. For Entities, select Select All

d. Click OK

a

b

d

c

161CHAPTER 11


Merge Equivalent Nodes (continued)

a. Node/Elements tab

b. Check for any other coincident nodes by repeating the previous step.

c. Click OK

a


CHAPTER 11162

Merge Equivalent Nodes (continued)

a. Quality tab

b. Select Fix Elements

c. Select Normal

d. For Element Verify Normals 1: Mode, select Show Normals

e. Select Select All

f. Click OK

g. For Element Verify Normals 1: Mode, select Hide Normals

h. Select Select All

i. Click OK

ih

g

fe

d

cb

a

163CHAPTER 11


Save the Intermediate File

a. File tab

b. Select Save As

c. For File name: enter ch11.SimXpert

d. Click Save

dc

b

a


CHAPTER 11164

Create a Part for the Upper-right Body

a. Assemble tab


c. For Title, specify upper_rigid

d. Click OK

e. Observe upper_rigid in the Model Browser Tree

ab

c

d

e

165CHAPTER 11


Create Surface for Upper-rigid Body (continued)


b. Select Arc

c. Select 3 Points

d. For X,Y,Z Input, enter -2,8.1 -5.524.1 -5.568.1.5

e. Click OK

f. Click OK

fe

d

c

b

a


CHAPTER 11166


a. Geometry tab:

b. Select Sweep

c. For X,Y,Z Input, enter 0 0 1

d. For Sweep Direction screen, enter Vector

e. For Axis, select Z

f. Click OK

a

b

c

d

e

f

167CHAPTER 11



a. Geometry tab:

b. Select Sweep

c. For Entities screen select the CURVE/5

d. For Length of Sweep, enter 10

e. Click OK

e

dc

b

a


CHAPTER 11168

Create a Part for the Lower-rigid Body

a. Assemble tab


c. For Title, specify lower_rigid

d. Click OK

e. Observe lower_rigid in the Model Browser Tree

ab

c

d

e

169CHAPTER 11


Create Surface for Lower-rigid Body (continued)


b. Select Arc

c. Select 3 Points

d. For X,Y,Z Input, enter -5.5 -3 -4.1 -5.5 -6 -7.1 -5.5

e. Click OK

f. Click OK

a

b

c

d

ef


CHAPTER 11170


a. Geometry tab:

b. Select Sweep

c. For X,Y,Z Input, enter 0 0 1

d. For Sweep Direction screen, enter Vector

e. For Axis, select Z

f. Click OK

a

b

c d

e

f

171CHAPTER 11


Create Surface for Lower-rigid Body (continued)

a. Geometry tab:

b. Select Sweep

c. For Entities screen select the CURVE/5

d. For Length of Sweep, enter 10

e. Click OK

e

dc

b

a


CHAPTER 11172

Define Material Data

a. Materials and Properties tab:

b. Select Isotropic

c. For Isotropic Material screen, select steel

d. For Young’ Modulus, enter 3e7

e. For Poisson’s Ratio, enter 0.3

f. Click Advanced

g. Click Add Constitutive Model, Elasto Plastic

g

f

e

d

c

b

a

173CHAPTER 11


Define Material Data (continued)

a. Materials and Properties tab: Isotropic

b. Click Perfectly Plastic

c. For Initial Yield Stress, enter 36000

d. Click OK

d

c

b

a


CHAPTER 11174

Define Property Data

a. Materials and Properties tab

b. Select Shell

c. For Name, specify pipe_prop

d. Select Entities pipe from Model Browser

e. For Material, specify steel

f. For Part Thickness, enter 0.4

g. Click OK

g

fe

d

c

ba

d

175CHAPTER 11



a. Materials and Properties tab

b. Select Shell

c. For Name, specify pipe_prop

d. Select Entities pipe from Model Browser

e. For Material, specify steel

f. For Part Thickness, enter 0.4

g. Click OK

g

fe

d

c

ba

d


CHAPTER 11176


a. Materials and Properties tab: Shell

b. Select Non Linear

c. For Membrane material, specify steel

d. For Bending material, specify steel

e. For Analysis type, specify IS

f. For Corner elements keyword, enter 4

g. For Element structural behavior, enter DCT

h. For Integration scheme, enter L

i. Click OK

ihgf

ed

cb

a

177CHAPTER 11


Define Contact Body for Pipe

a. LBCs tab

b. Select Deformable Body

c. For Name, specify deform_pipe

d. For Pick Entities, select pipe from Part in the Model Browser

e. Click OK

e

d

c

ba

d


CHAPTER 11178

Define Contact Body for Upper-rigid Body

a. LBCs tab

b. Select Rigid Body

c. For Name, specify rigid_top

d. For Pick Entities, select SURFACE/1 (upper-rigid body)

e. Click Motion

e

dc

b

a

179CHAPTER 11


Define Contact Body for Upper-rigid Body (continued)

a. LBCs tab: Rigid Body

b. For Velocity, specify X: 0; Y: -2; Z: 0

c. Click Body

c

b

a


CHAPTER 11180



b. For Inward Normals, click Reverse

c. Click Display

d. Click Preview

d

cb

a

181CHAPTER 11




b. Click Animate

c. Verify rigid_top is moving down

d. Click Exit

d

c

b

a


CHAPTER 11182

Define Contact Body for Lower-rigid Body

a. LBCs tab

b. Select Rigid Body

c. For Name, specify rigid_bottom

d. For Pick Entities, select SURFACE/2 (lower-rigid body)

e. Click Motion

ed

c

b

a

183CHAPTER 11


Define Contact Body for Lower-rigid Body (continued)


b. For Velocity, specify X: 0; Y: 2; Z: 0

c. Click Body

c

b

a


CHAPTER 11184



b. For Inward Normals, click Reverse

c. Click Display

d. Click Preview

d

cb

a

185CHAPTER 11




b. Click Animate

c. Verify rigid_bottom is moving up

d. Click Exit

d

c

b

a


CHAPTER 11186

Define Contact Table

a. LBCs tab

b. Select Table

c. Click twice on T to disable self contact of the pipe

d. Click OK

d

c

b

a

187CHAPTER 11


Define Boundary Conditions

a. LBCs tab

b. Select Fixed

c. For Name, specify fix

d. Select nodes at left and right edges of the pipe

e. Click OK

e

dd

c

ba


CHAPTER 11188

Create SimXpert Analysis File

a. Right click on FileSet

b. Select Create new Nastran job

c. For Job Name, enter pipe-crush

d. For Solution Type, select SOL 400

e. For Solver Input File, specify the fine name and its path

f. Unselect Create Default Layout

g. Click OK

g

fe

d

c

ba

189CHAPTER 11


Create SimXpert Analysis File (continued)

a. Right click on Load Case

b. Select Create Global Loadcase

c. Click OK

c

ba


CHAPTER 11190


a. Right click on Loads/Boundaries

b. Select Select Contact Table

c. For Selected BCTable, enter BCTABLE_1

d. Click OK

d

c

b

a

191CHAPTER 11



a. Right click on Load Cases

b. Select Create Loadcase

c. For Name (Title), enter subcase-1

d. Click OK

a

b

c

d


CHAPTER 11192


a. Right click on Loadcase Control

b. Select Subcase Nonlinear Static Parameters

c. For Stiffness Update Method, select Pure Full Newton (PFNT)

d. For Maximum Iterations for each Load Inc, enter 500

e. Unselect Default Tolerance Setting

f. Check Displacement Error; for Displacement Tolerance, enter 0.01

g. Check Load Error; for Load Tolerance, enter 0.01

h. Check Vector Component Method

i. From the Intermediate Output Control pull down menu,

select Every computed load increment (YES)

j. Click Apply

k. Click Close

a

bc

d

e

f

g

h

i

jk

193CHAPTER 11



a. Double click on Loadcase Control

b. Select Stepping Procedure Parameters

c. For Number of Steps, enter 100

d. Click Apply

e. Click Close

a

bc

d

e


CHAPTER 11194



b. Select Select Lbcs

c. Select fix from the Model Browser

d. Click OK

dc

c

b

a

195CHAPTER 11




b. Select Select Contact Table

c. Select BCTABLE_1 from the Model Browser

d. Click OK

d

c

c

b

a


CHAPTER 11196


a. Right click on Output Request

b. Select Nodal Output Requests

c. Select Create Displacement Output Request

d. Click Suppress Print

e. Click OK

e

d

c

ba

197CHAPTER 11




b. Select Nodal Output Requests

c. Select Create Contact Output Request


e. Click OK

e

d

c

ba


CHAPTER 11198



b. Select Elemental Output Requests

c. Select Create Nonlinear Stress Output Request


e. Click OK

e

d

c

b

a

199CHAPTER 11



a. Double click on Solver Control

b. Select Solution 400 Nonlinear Parameters

c. Structural Damping Coefficient, select Large Disp and Follower Force

d. Click Apply

e. Creep Analysis Type, select Additive Plasticity for Large Strain Formulation

f. Click Apply

g. Click Close (not shown)

f

e

d

c

b

a


CHAPTER 11200


a. Double click on Solver Control

b. Select Output File Properties

c. Nastran DB Options, select Master/DBALL

d. Binary Output, select OP2

e. Click Apply

f. Click Close (not shown)

e

d

cb

a

201CHAPTER 11



a. File: Save

b. Select pipe-crush

c. Select Run

b

c

a


CHAPTER 11202

Attach the SimXpert Analysis Results File

a. File tab

b. Select Attach Results

c. File path, enter *.Master

d. Attach Options: click Results or click Both to get both model and results data which

enables postprocessing without using model data from SimX database

e. Click OK

e

e

d

d

c

b

a

c

203CHAPTER 11


Attach the SimXpert Analysis Results File (continued)

a. Results: Deformation

b. Deformation tab: Deformed display scaling, check True

c. Plot Data tab: Plot type select Deformation

d. Results entities: Results cases: select last increment

e. Results entities: Results type: select Displacements, Translational

f. Click Update

fe

d

c

b

a


CHAPTER 11204


a. Animation tab

b. Results cases: select SC1:Step 1 (selects all increments)

c. Results entities: Results type: select Displacements, Translational

d. Click Update

dc

b

a

205CHAPTER 11



a. Animation tab

b. Click Pause icon to stop animation

a


CHAPTER 11206


a. Results: Fringe

b. Animation tab

c. Results entities: Results cases: select SC1:Step 1 (selects all increments)

d. Results entities: Results type: select Nonlinear Strains, Plastic Strain

e. Fringe tab: Display settings tab: select Element edges

f. Label attributes, select color of labels

g. Click Update

g

f

e

dc

b

a

207CHAPTER 11



a. Use shift + Right click on the mouse to rotate the model in SimXpert to view results in

various parts of the pipe


CHAPTER 11208


a. Results: Fringe

b. Animation tab: click Pause icon to stop animation

c. Plot Data tab: Results type: Contact Status: select Normal contact force

d. Click Update

dc

b

a

209CHAPTER 11



a. Use shift + Right click on the mouse to rotate the model in SimXpert to view results in

various parts of the pipe


CHAPTER 11210

Input File(s)File Description

nug_11m.dat MD Nastran SOL 400 input

ch11.SimXpert SimXpert input file

ch11.bdf Associated MD Nastran SOL 400 input from SimXpert

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch011/nug_11m.dat

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch011/ch11.SimXpert

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch011/ch11.bdf

Elastic-plastic Collapse of a Cylindrical Pipe under External Rigid Body Loading

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