# flexure¶

flexure - Compute flexural deformation of 2-D loads, forces, bending and moments

## Synopsis¶

gmt flexure -Drm/rl[/ri]/rw -ETe[u]|D|file [ -A[l|r][/args] ] [ -CpPoisson ] [ -CyYoung ] [ -Fforce ] [ -L ] [ -Qargs] [ -S ] [ -Twfile] [ -V[level] ] [ -Wwd] [ -Zzm] [ -bibinary ] [ -dnodata ] [ -eregexp ] [ -hheaders ] [ -iflags ] [ -oflags ] [ –PAR=value ]

Note: No space is allowed between the option flag and the associated arguments.

## Description¶

flexure computes the flexural response to 2-D loads using a range of user-selectable options, such as boundary conditions, pre-existing deformations, variable rigidity and restoring force, and more. The solutions are obtained using finite difference approximations to the differential equations.

## Required Arguments¶

-Drm/rl[/ri]/rw
Sets density for mantle, load, infill (optionally, otherwise it is assumed to equal the load density), and water. If ri is not given then it defaults to rl.
-ETe[u]|D|file
Sets the elastic plate thickness (in meter); append k for km. If the elastic thickness exceeds 1e10 it will be interpreted as a flexural rigidity D instead (by default D is computed from Te, Young’s modulus, and Poisson’s ratio; see -C to change these values). Alternatively, supply a file with variable plate thicknesses or rigidities. The file must be co-registered with any file given via -Q.

## Optional Arguments¶

-A[l|r]bc[/args]
Sets the boundary conditions at the left and right boundary. The bc can be one of four codes: 0 selects the infinity condition, were both the deflection and its slope are set to zero. 1 selects the periodic condition where both the first and third derivatives of the deflection are set to zero. 2 selects the clamped condition where args (if given) sets the deflection value [0] (and its first derivative is set to zero), while 3 selects the free condition where args is given as moment/force which specify the end bending moment and vertical shear force [0/0]. Use SI units for any optional arguments.
-CpPoisson
Change the current value of Poisson’s ratio [0.25].
-CyYoung
Change the current value of Young’s modulus [7.0e10 N/m^2].
-Fforce]
Set a constant horizontal in-plane force, in Pa m [0]
-L
Use a variable restoring force that depends on sign of the flexure [constant].
-Qn|q|t[args]
Sets the vertical load specification. Choose among these three options: -Qn means there is no input load file and that any deformation is simply driven by the boundary conditions set via -A. If no rigidity or elastic thickness file is given via -E then you must also append arguments to create the locations used for the calculations; for details on array creation, see Generate 1D Array. -Qq[loadfile] is a file (or stdin if not given) with (x,load in Pa) for all equidistant data locations. Finally, -Qt[topofile] is a file (or stdin if not given) with (x,load in m or km, positive up); see -M for topography unit used [m].
-S
Compute the curvature along with the deflections and report them via the third output column [none].
-Twfile
Supply a file with pre-existing deformations [undeformed surface].
-Wwd
Specify water depth in m; append k for km. Must be positive [0]. Any subaerial topography will be scaled via the densities set in -D to compensate for the larger density contrast with air.
-Zzm
Specify reference depth to flexed surface in m; append k for km. Must be positive [0]. We add this value to the flexed surface before output.
-V[level] (more ...)
Select verbosity level [c].
-bi[ncols][t] (more ...)
Select native binary format for primary input.
-d[i|o]nodata (more ...)
Replace input columns that equal nodata with NaN and do the reverse on output.
-e[~]“pattern” | -e[~]/regexp/[i] (more ...)
Only accept data records that match the given pattern.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more ...)
Skip or produce header record(s).
-icols[+l][+sscale][+ooffset][,...] (more ...)
Select input columns and transformations (0 is first column).
-ocols[,...] (more ...)
Select output columns (0 is first column).
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
–PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.

## Generate 1D Array¶

Make an evenly spaced coordinate array from min to max in steps of inc. Append +b if we should take log2 of min and max and build an equidistant log2-array using inc integer increments in log2. Append +l if we should take log10 of min and max and build an array where inc can be 1 (every magnitude), 2, (1, 2, 5 times magnitude) or 3 (1-9 times magnitude). For less than every magnitude, use a negative integer inc. Append +n if inc is meant to indicate the number of equidistant coordinates instead. Alternatively, give a file with output coordinates in the first column, or provide a comma-separated list of coordinates.

If the module allows you to set up an absolute time series, append a valid time unit from the list year, month, week, day, hour, minute, and second to the given increment; add +t to ensure time column (or use -f) Note: The internal time unit is still controlled independently by TIME_UNIT.

Likewise, if the module allows you to set up a spatial distance series (with distance computed from the first two data columns), specify the increment as [±][unit]inc, where - means fast (Flat Earth) and + means slow (ellipsoidal) distance calculations [great circle], and append a geospatial distance unit from the list degree (arc), minute (arc), second (arc), meter, foot, kilometer, Miles (statute), nautical miles, or survey foot. For Cartesian distances, you must use the special unit c.

## Note on Units¶

The -M option controls the units used in all input and output files. However, this option does not control values given on the command line to the -E, -W, and -Z options. These are assumed to be in meters unless an optional k for km is appended.

## Plate Flexure Notes¶

We solve for plate flexure using a finite difference approach. This method can accommodate situations such as variable rigidity, restoring force that depends on the deflection being positive or negative, pre-existing deformation, and different boundary conditions.

## Examples¶

To compute elastic plate flexure from the topography load in topo.txt, for a 10 km thick plate with typical densities, try

```gmt flexure -Qttopo.txt -E10k -D2700/3300/1035 > flex.txt
```