# gmtflexure¶

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

## Synopsis¶

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

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

## Description¶

gmtflexure 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]
-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 min/max/inc to initiate the locations used for the calculations. Append + to inc to indicate the number of points instead. -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 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 …)
-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.

## 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