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196 lines
7.2 KiB
196 lines
7.2 KiB
\documentstyle[12pt]{smemo}
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\def\SLAP{{\sf Slap\-down}}
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\def\slap{{\sf Slap\-down}}
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\def\exo{{\sf EXODUS}}
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\newcommand{\caps}[1]
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{\uppercase{#1}\null}
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\newcommand{\cmd}[1]
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{\mbox{\sf\uppercase{#1}}\null}
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\newcommand{\lcmd}[1]
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{\mbox{\sf#1}\null}
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\newcommand{\param}[1]
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{{\em #1}\null}
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\newcommand{\optparam}[1]
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{[{\em #1\/}]\null}
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\newcommand{\bold}[1]
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{{\bf #1}\null}
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%%\input{setup}
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\begin{document}
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\begin{memo}
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\to{ Distribution}
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\from{G. D. Sjaardema, 1521}
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\subject Modifications to \slap
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\SLAP\ is a computer program written to help analysts determine the
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behavior of a body impacting onto an unyielding surface. The program
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models the body as a three degree-of-freedom system. The deformation of
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the body is approximated by nonlinear springs at each end of the model.
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The program was written to model the impact behavior of both nuclear
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waste transportation casks (subjected to the regulatory 30-foot drops
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onto an unyielding surface) and laydown weapons.
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The code documentation and users' manual are in SAND88-0616, "Numerical
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and Analytical Methods for Approximating the Eccentric Impact Response
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(Slapdown) of Deformable Bodies." However, several modifications and
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improvements have been added to \slap\ since the users' manual was
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written. The modifications and improvements are documented in this
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memo.
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\section*{New Commands}
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A \slap\ analysis normally continues until either both springs have
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unloaded, or the velocities of both the \cmd{NOSE} and \cmd{TAIL} are
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positive. Sometimes a longer or shorter time duration is needed for
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special cases; therefore, a command has been added to let the analyst
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control the length of the analysis. The command syntax is:
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\begin{quote}
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\sf TERMINATION [TIME] \em end\_time
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\end{quote}
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where the keyword \cmd{TIME} is optional, and the parameter
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\param{end\_time} is the time to terminate the analysis.
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If \cmd{TERMINATION~TIME} is not specified, the calculation will
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continue until either both springs have unloaded, or the velocities of
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both the \cmd{NOSE} and \cmd{TAIL} are positive.
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The square end treatment (see Section~3.1, page~19 of the users' manual)
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can now be specified for both the nose and tail of the body; previously
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it could only be specified for the nose. The command syntax is:
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\begin{quote}
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\sf TAIL SQUARE \\
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\end{quote}
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\rm or, if the nose has been specified as \cmd{SQUARE}, the \cmd{TAIL
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SYMMETRIC} command will also result in a square tail.
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\section*{Friction Algorithm Improved}
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The friction algorithm has been extensively modified and improved. The
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algorithm correctly handles both square and round ends and will
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``stick'' at the impact point if the coefficient of friction is high
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enough. The new algorithm also works when both ends are in contact
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simultaneously--the oscillations that occurred with the old algorithm no
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longer occur.
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The algorithm uses an iterative approach to determine the lateral force
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required to completely stick the impacting end. It then compares this
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with the maximum possible lateral force (normal force times the
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coefficient of friction) and returns the minimum of these two values. In
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several test problems and a comparison with an actual test, the new
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algorithm gives much better results.
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\section*{Modifications to \slap\ Output Files}
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\paragraph*{\exo\ Database Changes:} Two new nodes have been added to
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the \exo\ database file. The left end contact point is node~4 and the
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right end contact point is node 5. Figure~\ref{geometry} shows the node
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and element numberings used in \slap. The nodes at the contact points
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were added to provide information about the behavior at these points for
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bodies with square ends. For square ends, the $x$-velocities at the
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contact points are not the same as the $x$-velocities at the ends of the
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body centerline.
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The global variable \cmd{DAMKE} (damaging kinetic energy) has been added
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to the database. This variable is sometimes used in laydown weapon
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analysis to indicate the severity of the impact. The damaging kinetic
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energy is equal to
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\begin{displaymath}
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\cmd{DAMKE} = \sfrac1/2 \left(m v_y^2 + I \omega^2\right)
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\end{displaymath}
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where $m$ is the mass, $I$ is the mass moment of inertia, $v_y$ is the
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vertical velocity at the center of gravity, and $\omega$ is the angular
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velocity about the center of gravity.
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\paragraph*{Output File Changes:} The text output file has also been
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modified slightly. The event sequence summary (see Figure~A.5 in the
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users' manual) now includes the ratio of the impact velocity to the
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initial velocity which makes it easier to determine the severity of the
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slapdown effect.
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Also, the maximum strain energy in each of the springs during the impact
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event is output in the results summary. These values are important
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in determining the severity of the slapdown effect since for some
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geometries the second impact will occur at a velocity greater than the
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initial velocity; however, due to the bodies angular position and
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velocity, the strain energy in the spring will be less than that caused
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by a flat impact. The opposite effect will also occur (higher strain
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energy at lower impact velocity).
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\section*{Support and Notification of Modifications}
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An \cmd{ICER} facility has been created for \slap. This facility will
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be used to provide a more immediate notification of any future
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modifications or problems. If there are any problems with \slap, contact
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Greg Sjaardema, 1521, at 844--7045.
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\begin{figure}
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%\begin{center}
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\unitlength 1in
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\begin{picture}(6.0,4)
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\thicklines
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\put(0.25, 2.5){\framebox(.75,.3){Nose}}
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\put(5.00, 3.5){\framebox(.75,.3){Tail}}
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\put(3.125,2.0){\framebox(.75,.3){CG}}
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\put(1.25, 1){\line(-1,4){0.25}}
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\put(1.00, 2){\line( 4,1){4.0}}
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\put(5.00, 3){\line(0,-1){1.0}}
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\put(3.50, 2.6250){\circle*{.1}}
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%\put(5.25, 2.4000){\vector(0,-1){.4}}
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\put(0.8, 2.0000){\makebox(0,0){N1}}
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\put(3.50, 2.7750){\makebox(0,0){N2}}
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\put(5.2, 3.0000){\makebox(0,0){N3}}
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\put(1.4, 1.1){\makebox(0,0){N4}}
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\put(5.2, 1.9500){\makebox(0,0){N5}}
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\put(2.25, 2.4625){\makebox(0,0){E1}}
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\put(4.25, 2.9625){\makebox(0,0){E2}}
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%\put(5.25, 2.5000){\makebox(0,0){$R_t$}}
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%\put(5.25, 2.6000){\vector(0, 1){.4}}
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%
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% force vectors
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%
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%\put(3.50, 2.6250){\vector(0, 1){.5}}
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%\put(3.50, 3.1250){\makebox(0,0)[b]{$V_{Y0}$}}
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%\put(3.50, 2.6250){\vector(1, 0){.5}}
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%\put(4.000,2.6250){\makebox(0,0)[l]{$V_{X0}$}}
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%%
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%\put(5.00, 1.5 ){\vector(0, 1){.5}}
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%\put(5.00, 1.5 ){\makebox(0,0)[t]{$F_N^t$}}
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%\put(4.50, 2.0 ){\vector(1, 0){.5}}
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%\put(4.50, 2.0 ){\makebox(0,0)[r]{$F_T^t$}}
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%%
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%\put(1.25, 0.5 ){\vector(0, 1){.5}}
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%\put(1.25, 0.5 ){\makebox(0,0)[t]{$F_N^n$}}
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%\put(0.75, 1.0 ){\vector(1, 0){.5}}
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%\put(0.75, 1.0 ){\makebox(0,0)[r]{$F_T^n$}}
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%%
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%% Dimensions
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%%
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%\put(1.40, 1.4){\vector(1,-4){.10}}
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%\put(1.375,1.5){\makebox(0,0){$R_n$}}
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%\put(1.35, 1.6){\vector(-1,4){.10}}
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%%
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%\put(2.10, 2.5250){\vector(-4,-1){1.10}}
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%\put(2.25, 2.5625){\makebox(0,0){$L_n$}}
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%\put(2.40, 2.6000){\vector( 4, 1){1.10}}
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%%
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%\put(4.10, 3.0250){\vector(-4,-1){0.60}}
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%\put(4.25, 3.0625){\makebox(0,0){$L_t$}}
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%\put(4.40, 3.1000){\vector( 4, 1){0.60}}
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%
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% Rigid surface
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%
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\put(1,1){\line(1,0){4.5}}
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\put(3.5,.8){Rigid Surface}
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%
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\put(1.50,2){\line(1,0){0.5}}
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\put(1.75,2.05){\makebox(0,0)[b]{$\theta$}}
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\thinlines
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%
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\end{picture}
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%\end{center}
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\caption{\SLAP\ Node (N) and Element (E) Numberings ({\sf SQUARE}
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end)}\label{geometry}
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\end{figure}
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\end{memo}
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\end{document}
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