GMTFLEXURE(1gmt) GMT GMTFLEXURE(1gmt)

# NAME¶

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¶

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.

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¶

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.

Change the current value of Poisson's ratio [0.25].
Change the current value of Young's modulus [7.0e10 N/m^2].

Set a constant horizontal in-plane force, in Pa m [0]

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].

Compute the curvature along with the deflections and report them via the third output column [none].

Supply a file with pre-existing deformations [undeformed surface].

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.

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.

Select verbosity level [c].

Select native binary input.

Replace input columns that equal nodata with NaN and do the reverse on output.

Only accept data records that match the given pattern.

Select input columns and transformations (0 is first column).

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
```