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229 lines
9.7 KiB
229 lines
9.7 KiB
\chapter{Utility Usage Examples}\label{c:examples}
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Examples of the usage of the utilities described in the report will be
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given in this chapter. A two-dimensional finite element model of a
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portion of a transportation container will be used for most of the
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examples. The outline of the model is shown in Figure~\ref{exmodel}.
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\begin{figure}
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\centering
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\includegraphics[scale=0.75]{figures/Model.png}
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\caption{Finite Element Model for \numbers\ Examples}\label{exmodel}
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\end{figure}
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The model is composed of nine materials. Material~1 is the outer shell
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which is a $\sfrac{3}{8}$-inch thick stainless steel wall with four
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elements through the thickness. Material~2 is the inner shell which is
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a $\sfrac{1}{4}$-inch thick stainless steel wall with three elements
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through the thickness. The energy-absorbing foam between the inner and
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outer shells is Material~3. Above the inner shell is another layer of
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energy-absorbing foam which is Material~7; on top of the foam is a thin
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0.120-inch thick steel sheet (Material~9), and the cargo material
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(Material~10). Materials 11 and~22 are the same thickness as Materials
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1 and~2, respectively, except that the density has been increased to
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account for the top half of the container. The 6-inch diameter punch at
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the bottom of the model is Material~8. There are five contact surfaces
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in this model that are defined by ten side sets. The contact surfaces
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and the corresponding side set identifications and locations are defined
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in the following table.
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\begin{center}
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\begin{tabular}{|ccl|}\hline
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Contact & Side Set & Location \\
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Surface & Number & \\ \hline \hline
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1 & 100 & Bottom of outer shell \\
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& 999 & Top and side of punch \\ \hline
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2 & 200 & Top of outer shell \\
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& 300 & Bottom of energy-absorbing foam \\ \hline
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3 & 400 & Top of energy-absorbing foam \\
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& 500 & Bottom of inner shell \\ \hline
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4 & 600 & Top of inner shell \\
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& 700 & Bottom of foam beneath cargo \\ \hline
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5 & 900 & Top of sheet beneath cargo \\
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& 1000 & Bottom of cargo \\ \hline
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\end{tabular}
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\end{center}
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Several of the utilities in \numbers\ were used during the development
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of this model. Examples of the \cmd{mass properties}, \cmd{overlap},
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\cmd{locate}, and \cmd{timestep} utilities will be shown below using the
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above model.
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\section{\cmd{mass properties} Utility Example}
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The \cmd{mass properties} command was used to determine the
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pseudo-densities of Materials 10, 11, and~22. These densities are
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called ``pseudo-densities'' since the density is modified to account for
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the mass of the body that was omitted from the finite element model.
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Material~10 is the cargo material that has a total mass of 22.0~lb-s$^2$/in
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(8,500~pounds), and Materials 11 and~22 are the tops of the inner and
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outer shells which are used to simulate the mass of the top half of the
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container. The \cmd{mass} utility was used to determine the volume of
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each of the materials in the model. The density of the cargo
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(Material~10) was then calculated by dividing the cargo mass by the
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cargo volume. Materials 11 and~22 are intended to simulate the mass of
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the upper half of the container. The density $\rho_{11}$ of Material~11
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is calculated as:
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\begin{equation}
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\rho_{11} = \rho_1 (V_1 + 2V_{11}) / V_{11}
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\end{equation}
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where $\rho_1$ and $V_1$ are the density and volume of Material~1, and
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$V_{11}$ is the volume of Material~11. The input required to calculate
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the mass properties for an axisymmetric body with distinct densities
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using four-point quadrature is:
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\begin{verbatim}
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AXISYMMETRIC
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DENSITY
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7.324E-04 OUTER_SHELL
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3.297E-03 MASS_OUTER_SHELL
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1.035E-05 FOAM
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7.324E-04 INNER_SHELL
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2.901E-03 MASS_INNER_SHELL
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1.603E-05 CARGO_FOAM
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7.324E-04 PUNCH
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7.324E-04 THIN_SHEET
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7.781E-04 CARGO_MASS
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MASS 4
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EXIT
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\end{verbatim}
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Figure~\ref{exmassout} shows the resulting output. Note that the
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material labels cannot contain spaces; the character ``\_'' was used to
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simulate a space. Although only the masses and volumes were needed for
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this example, the output also shows the location of the centroid, the
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mass moments of inertia, and the minimum, maximum, and average element
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volumes for each material block.
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The mass properties utility was also used during the documentation of
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this analysis to estimate the weight savings due to using a thinner
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wall. A separate analysis of this body was performed with a
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\sfrac{3}{8}-inch thick inner wall and a \sfrac{1}{2}-inch thick outer wall.
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\numbers\ was then run to determine the mass of the inner and outer
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shells for both models so that the weight differences could be
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calculated.
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\begin{figure}
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\verbatiminput{mass_example_out}
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\caption{Output for Mass Properties Example}\label{exmassout}
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\end{figure}
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\section{\cmd{overlap} Utility Example}
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This example will show the input and output for the \cmd{overlap}
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utility. Each of the contact surfaces in the model will be checked to
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see if they are penetrated. Since this is a model that has already been
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tested, none of the contact surfaces overlap.
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The input for the command is:
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\begin{verbatim}
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OVERLAP 100 999
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OVERLAP 200 300
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OVERLAP 400 500
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OVERLAP 600 700
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OVERLAP 900 1000
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EXIT
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\end{verbatim}
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where the first flag is the master surface and the second flag is the
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slave surface. Figure~\ref{exoverlapout} shows the resulting output.
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Normally, the contact surfaces should be checked in both directions,
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that is, check first with one flag as the master and then check again
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with that flag as the slave. Figure~\ref{exoverlap2} shows the output
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from the overlap utility when the contact surfaces do overlap. The
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output shows the number of the penetrating node, the number of the
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penetrated element, and the connectivity of the element.
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\begin{figure}
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\verbatiminput{overlap_example_out}
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\caption{Output for Overlap Utility Example--No
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Penetration}\label{exoverlapout}
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\end{figure}
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\begin{figure}
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\verbatiminput{overlap2_out}
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\caption{Output for Overlap Utility
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Example--Penetration}\label{exoverlap2}
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\end{figure}
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\section{\cmd{locate} Utility Example}
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The analysis performed on the example finite element model was concerned
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with the response of the outer steel shell due to the impact with the
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punch. The relatively thin outer shell of this model makes it very
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difficult to examine the results of the finite element analysis since it
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is not possible to plot contours of the stresses or strains in the steel
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shell. However, the \code{SPLOT} module in the postprocessing code
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\code{BLOT}~\cite{BLOT} can be used to plot the stresses and strains as
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a function of the element number. Although it is possible to determine
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the element numbers of the elements in the outer shell by looking at
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plots of the model, an easier and more efficient method is to use the
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\cmd{locate} command. The outer shell has a inner radius of
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95.75~inches and a thickness of \sfrac{3}{8}~inch. Since there are four
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elements through the thickness, each element is \sfrac{3}{32}~inch thick.
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Using the \cmd{locate point} command with the center point at the center
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of curvature (0.0, 24.2) and a distance of 95.75 + \sfrac{3}{64}\ will
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locate all elements in the innermost element row; a distance of 95.75 +
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\sfrac{21}{64} will locate all elements in the outermost element row.
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The input used to locate all elements in the outermost element row is:
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\begin{verbatim}
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SORT THETA
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LOCATE ELEMENTS POINT 0 24.2 96.078125 .001
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EXIT
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\end{verbatim}
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Figure~\ref{exlocateout} is the resulting output. The output is sorted
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on the \cmd{theta} field so that the elements are ordered from the
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centerline outward.
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\begin{figure}
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\verbatiminput{locate_example_out}
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\caption{Output for Locate Utility Example--No Penetration}\label{exlocateout}
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\end{figure}
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\section{\cmd{limits} Utility Example}
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The \cmd{limits} utility is executed simply by entering the command {\tt
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LIMITS}. The resulting output is shown in Figure~\ref{exlimitsout}.
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\begin{figure}
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\verbatiminput{limits_example_out}
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\caption{Output for Limits Utility Example}\label{exlimitsout}
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\end{figure}
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\section{\cmd{timestep} Estimation Example}
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The final example using this model will be the estimation of the
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timestep using the \cmd{timestep} command. The input is:
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\begin{verbatim}
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WAVESPEED
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2.273e+05 OUTER_SHELL
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1.071e+05 MASS_OUTER_SHELL
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2.003e+04 FOAM
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2.273e+05 INNER_SHELL
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1.142e+05 MASS_INNER_SHELL
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2.731e+04 CARGO_FOAM
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2.273e+05 PUNCH
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2.273e+05 THIN_SHEET
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1.525e+05 CARGO_MASS
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TIMESTEP
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EXIT
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\end{verbatim}
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The resulting output is shown in Figure~\ref{extimestepout}.
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\begin{figure}
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\verbatiminput{timestep_example_out}
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\caption{Output for Timestep Estimation Utility
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Example}\label{extimestepout}
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\end{figure}
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The minimum timestep is 2.273$\times 10^{-7}$ seconds for Material~2 (the inner
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shell). This is exactly equal to the timestep that was used in
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the \code{PRONTO2D} analysis. For this problem, the average CPU time
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per element per timestep in \code{PRONTO2D} was 13.3~$\mu s$. Since
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there are 6,825 elements and 4,399 timesteps per millisecond of analysis
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time, the estimated CPU time per millisecond is 400~seconds. The actual
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CPU time per millisecond was 395~seconds. This example shows that it is
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possible to get a very accurate estimate of the time required to perform
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an analysis prior to running the analysis. The timestep estimation is
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also useful in determining which material has the smallest or
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controlling timestep; if the material with the controlling timestep is
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not in the area of interest, reducing the refinement in that material
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will give a larger timestep and less analysis time.
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