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]
[ -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