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A static load is applied to the center of an ellipsoidal dome. Shell elements are used. Nodes at the base of the dome are constrained, and included in a NODFOR output database.

## Introduction

```LS-DYNA Implicit Workshop

Problem #9: Ellipsoidal Dome

Objectives
* Learn the behavior of different element formulations in
static implicit simulations.
* Learn how to minimize hourglass problems.

Problem Description
A static load is applied to the center of an ellipsoidal
dome. Shell elements are used. Nodes at the base of the
dome are constrained, and included in a NODFOR output database.

Input Filename: ellipse.k

Procedure
Copy the input file to your local directory. Using an editor,
view the input file and answer the following questions:

1. What is the maximum value of the applied load?

2. How many load steps are used?

3. What shell element formulation is used?

4. What hourglass control type is used?

Run the simulation, and postprocess the results
(Note: NODFOR file contains reaction forces at
constrained base nodes.)

5. What happens?

6. total reaction force: center displacement:

Repeat the simulation using the S/R Hughes-Liu shell
(ELFORM=6), and postprocess the results.

7. total reaction force: center displacement:

Repeat the simulation using the Fast Fully Integrated shell
(ELFORM=16), and postprocess the results.

8. total reaction force: center displacement:

9. What conclusion can you draw about the effect of hourglass
deformation on overall structural stiffness for this problem?

Concentrated applied loads are often responsible for initiating
hourglass deformation. Edit the input deck and replace the
single concentrated nodal load with pressure acting on the
the comments inside the input deck). Repeat the simulation
using the default shell.

10. What happens?

11. total reaction force: center displacement:```

## Keywords

```*CONTROL_HOURGLASS
*CONTROL_IMPLICIT_AUTO
*CONTROL_IMPLICIT_DYNAMICS
*CONTROL_IMPLICIT_GENERAL
*CONTROL_IMPLICIT_SOLUTION
*CONTROL_IMPLICIT_SOLVER
*CONTROL_TERMINATION
*DATABASE_BINARY_D3PLOT
*DATABASE_EXTENT_BINARY
*DATABASE_GLSTAT
*DATABASE_NODAL_FORCE_GROUP
*DATABASE_NODFOR
\$*DEFINE_CURVE
*DEFINE_CURVE
*ELEMENT_SHELL
*END
*KEYWORD
*MAT_elastic
*NODE
*PART
*SECTION_SHELL
*SET_NODE_LIST
*TITLE```

## Reduced Input

```  *KEYWORD
*TITLE
PINCHED ELLIPSE
\$
\$ A. Tabiei, March 99
\$ units; mm, s, ton, N
\$
*CONTROL_TERMINATION
1.0000
\$
\$========1=========2=========3=========4=========5=========6=========7=========8
\$
*CONTROL_IMPLICIT_GENERAL
\$   imflag       dt0      iefs   nstepsb      igso
1      0.01         0         0         0
\$
*CONTROL_IMPLICIT_SOLUTION
\$  nlsolvr    ilimit    maxref     dctol     ectol     rctol     lstol
0         0         0       0.0       0.0         0         0
\$    dnorm   divflag   inistif   nlprint
0         0         0         0
\$
*CONTROL_IMPLICIT_SOLVER
\$   lsolvr   prntflg    negeig
0         0         0
\$
*CONTROL_IMPLICIT_AUTO
\$    iauto    iteopt    itewin     dtmin     dtmax
1         0         0       0.0       0.0
\$
*CONTROL_IMPLICIT_DYNAMICS
\$    imass     gamma      beta
0       0.0       0.0
\$
\$========1=========2=========3=========4=========5=========6=========7=========8
\$
*DATABASE_EXTENT_BINARY
\$    neiph     neips    maxint    strflg    sigflg    epsflg    rltflg    engflg
1         1
\$   cmpflg    ieverp    beamip

*DATABASE_BINARY_D3PLOT
0.01
*DATABASE_GLSTAT
0.01
*DATABASE_NODFOR
0.01
*DATABASE_NODAL_FORCE_GROUP
2
*SET_NODE_LIST
2
1         7        13        19        25        31        37        48
54        60        66        72        78        84        91        97
103       109       115       121       127       206       212       218
224       230       236       242
\$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$
*CONTROL_HOURGLASS
4
\$
*MAT_elastic
\$      MID        RO         E        PR
1 7.890E-09 2.100E+05 3.000E-01
\$
*SECTION_SHELL
\$      SID    ELFORM
1         0
3.000E-00 3.000E-00 3.000E-00 3.000E-00
\$
*PART
SHELL
1         1         1
\$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$
\$      NID       DOF      LCID        SF
164         3         1      -1.0
\$
*DEFINE_CURVE
1
0.00000000000000E+00 00.000000000000E+00
1.00000000000000E+00 500000.00000000E+00
2.00000000000000E+00 500000.00000000E+00
\$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
\$
\$\$     LCID        SF                  N1        N2        N3        N4
\$         2      -1.0                 154       155       164       163
\$         2      -1.0                 155       156       165       164
\$         2      -1.0                 163       164       173       172
\$         2      -1.0                 164       165       174       173
\$
\$*DEFINE_CURVE
\$         2
\$0.00000000000000E+00 00.000000000000E+00
\$1.00000000000000E+00 7500.0000000000E+00
\$2.00000000000000E+00 7500.0000000000E+00
\$
\$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*END```