# Linear — Welcome to LS-DYNA Examples

The center node of a plate moves in the normal direction. Two other nodes that are neighbors to the center node are constrained such that their displacement in the normal direction is identical.

## Introduction

```*CONSTRAINED_LINEAR
Linearly Constrained Plate
LS-DYNA Manual Section: *CONSTRAINED_LINEAR

BOUNDARY_PRESCRIBED_MOTION_NODE
DEFINE_CURVE

Example: Linearly Constrained Plate

Filename: constrained.linear.plate.k

Description:
The center node of a plate moves in the normal direction. Two other nodes that
are neighbors to the center node are constrained such that their displacement
in the normal direction is identical.

Model:
The plate is made of an elastic material measuring 40 * 40 * 2 mm3 and contains
64 Hughes-Liu shell elements. The center node displacement increases linearly.
At the termination time, 0.0005 seconds, the displacement is 15 mm. The degree
of freedom in the z-direction for the two nodes is identical.

Input:
A load curve defines the magnitude of the prescribed displacement of the
center node (*BOUNDARY_PRESCRIBED_MOTION_NODE, *DEFINE_CURVE). A linear
constraint card defines the coupling of the displacement in the z-direction
between the two nodes (*CONSTRAINED_LINEAR). Two equal coefficients with
opposite signs control the displacement.

Reference:
Schweizerhof, K. and Weimar, K.```

## Keywords

```*BOUNDARY_PRESCRIBED_MOTION_NODE
*CONSTRAINED_LINEAR
*CONTROL_CONTACT
*CONTROL_HOURGLASS
*CONTROL_SHELL
*CONTROL_TERMINATION
*DATABASE_BINARY_D3PLOT
*DATABASE_BINARY_D3THDT
*DATABASE_EXTENT_BINARY
*DATABASE_HISTORY_NODE
*DATABASE_NODOUT
*DEFINE_CURVE
*ELEMENT_SHELL
*END
*KEYWORD
*MAT_ELASTIC
*NODE
*PART
*SECTION_SHELL
*TITLE```

## Reduced Input

```  *KEYWORD
*TITLE
Linear Constraint Equations
\$
\$  LSTC Example
\$
\$
\$   Units: mm, s
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
\$\$\$\$  Control Ouput
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
\$...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8
\$
*CONTROL_TERMINATION
\$   endtim    endcyc     dtmin    endneg    endmas
0.0005
\$
*CONTROL_CONTACT
\$   slsfac    rwpnal    islchk    shlthk    penopt    thkchg     orien
0.1                   2
\$
\$   usrstr    usrfac     nsbcs    interm    xpenen

\$
*CONTROL_HOURGLASS
\$      ihq        qh
4
\$
*CONTROL_SHELL
\$   wrpang    itrist     irnxx    istupd    theory       bwc     miter
1
\$
\$
*DATABASE_BINARY_D3PLOT
\$       dt      lcdt
0.00002
\$
*DATABASE_BINARY_D3THDT
\$       dt      lcdt
0.00001
\$
*DATABASE_EXTENT_BINARY
\$    neiph     neips    maxint    strflg    sigflg    epsflg    rltflg    engflg
1
\$
\$   cmpflg    ieverp    beamip

\$
\$
*DATABASE_HISTORY_NODE
\$      id1       id2       id3       id4       id5       id6       id7       id8
\$...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8
40        41        42
\$
*DATABASE_NODOUT
\$       dt
0.00001
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
\$\$\$\$  Constraints and Boundary Conditions
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
\$...>....1....>....2....>....3....>....4....>....5....>....6....>....7....>....8
\$
\$\$\$\$  nodes 40 and 42 are constrained to have identical z-direction motion
\$
*CONSTRAINED_LINEAR
\$      num
2
\$
\$      nid      dofx      dofy      dofz    dofrx      dofry     dofrz      coef
40                             1                                    1.00
42                             1                                   -1.00
\$
\$
\$\$\$\$  node 41 is displaced in the z-direction according to load curve 1
\$
*BOUNDARY_PRESCRIBED_MOTION_NODE
\$      nid       dof       vad      lcid        sf       vid
41         3         2         1       1.0
\$
*DEFINE_CURVE
\$     lcid      sidr      scla      sclo      offa      offo
1
\$
\$           abscissa            ordinate
0.0                 0.0
0.0005               -15.0
0.0015               -15.1
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
\$\$\$\$  Define Parts and Materials
\$
\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$
\$
*PART
Impacted Material
\$      pid       sid       mid     eosid      hgid    adpopt
1         1         1         0         0         0
\$
\$
\$\$\$\$\$\$  Materials
\$
*MAT_ELASTIC
\$      mid        ro         e        pr        da        db         k
1   2.00e-8  100000.0     0.300
\$
\$
\$\$\$\$\$\$  Sections
\$
*SECTION_SHELL
\$      sid    elform      shrf       nip     propt   qr/irid     icomp
1         6   0.83333       2.0       3.0
\$
\$       t1        t2        t3        t4      nloc
2.0       2.0       2.0       2.0
\$
\$
*END```