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PROGRAM:

NAME


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

SYNOPSIS


gmtflexure rm/rl[/ri]/rw -ETe[u]|D|file [ [l|r][/args] ] [ pPoisson ] [ yYoung ] [ force ]
[ args] [ ] [ wfile] [ [level] ] [ wd] [ zm] [ -bi<binary> ] [ -i<flags> ] [ -o<flags> ]

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.

-icols[l][sscale][ooffset][,...] (more ...)
Select input columns (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
use just -).

-+ 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 options, then
exits.

--version
Print GMT version and exit.

--show-datadir
Print full path to GMT share directory and exit.

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

REFERENCES


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