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.TH "GMTFLEXURE" "1gmt" "May 21, 2019" "5.4.5" "GMT"
.SH NAME
gmtflexure \- Compute flexural deformation of 2-D loads, forces, bending and moments
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.SH SYNOPSIS
.sp
\fBgmtflexure\fP  \fB\-D\fP\fIrm\fP/\fIrl\fP[/\fIri\fP]/\fIrw\fP \fB\-E\fP\fITe\fP[\fBu\fP]|\fID\fP|\fIfile\fP
[  \fB\-A\fP[\fBl\fP|\fBr\fP][/\fIargs\fP] ]
[  \fB\-C\fP\fBp\fP\fIPoisson\fP ] [  \fB\-C\fP\fBy\fP\fIYoung\fP ]
[  \fB\-F\fP\fIforce\fP ]
[  \fB\-Q\fP\fIargs\fP] [  \fB\-S\fP ] [  \fB\-T\fP\fIwfile\fP]
[  \fB\-V\fP[\fIlevel\fP] ]
[  \fB\-W\fP\fIwd\fP]
[  \fB\-Z\fP\fIzm\fP]
[ \fB\-bi\fPbinary ]
[ \fB\-d\fPnodata ]
[ \fB\-e\fPregexp ]
[ \fB\-h\fPheaders ]
[ \fB\-i\fPflags ]
[ \fB\-o\fPflags ]
.sp
\fBNote:\fP No space is allowed between the option flag and the associated arguments.
.SH DESCRIPTION
.sp
\fBgmtflexure\fP 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.
.SH REQUIRED ARGUMENTS
.INDENT 0.0
.TP
\fB\-D\fP\fIrm\fP/\fIrl\fP[/\fIri\fP]/\fIrw\fP
Sets density for mantle, load, infill (optionally, otherwise it is
assumed to equal the load density), and water.  If \fIri\fP is not given
then it defaults to \fIrl\fP\&.
.UNINDENT
.INDENT 0.0
.TP
\fB\-E\fP\fITe\fP[\fBu\fP]|\fID\fP|\fIfile\fP
Sets the elastic plate thickness (in meter); append \fBk\fP for km.
If the elastic thickness exceeds 1e10 it will be interpreted as
a flexural rigidity \fBD\fP instead (by default \fBD\fP is computed from \fITe\fP, Young\(aqs
modulus, and Poisson\(aqs ratio; see \fB\-C\fP to change these values).
Alternatively, supply a \fIfile\fP with variable plate thicknesses or rigidities.
The file must be co\-registered with any file given via \fB\-Q\fP\&.
.UNINDENT
.SH OPTIONAL ARGUMENTS
.INDENT 0.0
.TP
\fB\-A\fP[\fBl\fP|\fBr\fP]\fIbc\fP[/\fIargs\fP]
Sets the boundary conditions at the \fBl\fPeft and \fBr\fPight boundary.
The \fIbc\fP 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 \fIargs\fP (if given) sets the deflection
value [0] (and its first derivative is set to zero), while 3 selects the free condition
where \fIargs\fP is given as \fImoment\fP/\fIforce\fP which specify the end bending
moment and vertical shear force [0/0].  Use SI units for any optional arguments.
.UNINDENT
.INDENT 0.0
.TP
\fB\-Cp\fP\fIPoisson\fP
Change the current value of Poisson\(aqs ratio [0.25].
.TP
\fB\-Cy\fP\fIYoung\fP
Change the current value of Young\(aqs modulus [7.0e10 N/m^2].
.UNINDENT
.INDENT 0.0
.TP
\fB\-F\fP\fIforce\fP]
Set a constant horizontal in\-plane force, in Pa m [0]
.UNINDENT
.INDENT 0.0
.TP
\fB\-Qn\fP|\fBq\fP|\fBt\fP[\fIargs\fP]
Sets the vertical load specification. Choose among these three options:
\fB\-Qn\fP means there is no input load file and that any deformation is
simply driven by the boundary conditions set via \fB\-A\fP\&.  If no rigidity or
elastic thickness file is given via \fB\-E\fP then you must also append \fImin\fP/\fImax\fP/\fIinc\fP
to initiate the locations used for the calculations.  Append \fB+\fP to \fIinc\fP
to indicate the number of points instead.
\fB\-Qq\fP[\fIloadfile\fP] is a file (or stdin if not given) with (x,load in Pa)
for all equidistant data locations.  Finally, \fB\-Qt\fP[\fItopofile\fP] is a file
(or stdin if not given) with (x,load in m or km, positive up); see \fB\-M\fP for
topography unit used [m].
.UNINDENT
.INDENT 0.0
.TP
\fB\-S\fP
Compute the curvature along with the deflections and report them via the
third output column [none].
.UNINDENT
.INDENT 0.0
.TP
\fB\-T\fP\fIwfile\fP
Supply a file with pre\-existing deformations [undeformed surface].
.UNINDENT
.INDENT 0.0
.TP
\fB\-W\fP\fIwd\fP
Specify water depth in m; append k for km.  Must be positive [0].
Any subaerial topography will be scaled via the densities set in \fB\-D\fP
to compensate for the larger density contrast with air.
.UNINDENT
.INDENT 0.0
.TP
\fB\-Z\fP\fIzm\fP
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.
.UNINDENT
.INDENT 0.0
.TP
\fB\-V\fP[\fIlevel\fP] (more ...)
Select verbosity level [c].  
.UNINDENT
.INDENT 0.0
.TP
\fB\-bi\fP[\fIncols\fP][\fBt\fP] (more ...)
Select native binary input.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-d\fP[\fBi\fP|\fBo\fP]\fInodata\fP (more ...)
Replace input columns that equal \fInodata\fP with NaN and do the reverse on output.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-e\fP[\fB~\fP]\fI"pattern"\fP \fB|\fP \fB\-e\fP[\fB~\fP]/\fIregexp\fP/[\fBi\fP] (more ...)
Only accept data records that match the given pattern.  
.UNINDENT
.INDENT 0.0
.TP
\fB\-h\fP[\fBi\fP|\fBo\fP][\fIn\fP][\fB+c\fP][\fB+d\fP][\fB+r\fP\fIremark\fP][\fB+r\fP\fItitle\fP] (more ...)
Skip or produce header record(s).  
.UNINDENT
.INDENT 0.0
.TP
\fB\-i\fP\fIcols\fP[\fB+l\fP][\fB+s\fP\fIscale\fP][\fB+o\fP\fIoffset\fP][,\fI\&...\fP] (more ...)
Select input columns and transformations (0 is first column).
.UNINDENT
.INDENT 0.0
.TP
\fB\-o\fP\fIcols\fP[,...] (more ...)
Select output columns (0 is first column).
.UNINDENT
.INDENT 0.0
.TP
\fB\-^\fP or just \fB\-\fP
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use \fB\-\fP).
.TP
\fB\-+\fP or just \fB+\fP
Print an extensive usage (help) message, including the explanation of
any module\-specific option (but not the GMT common options), then exits.
.TP
\fB\-?\fP or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
.UNINDENT
.SH NOTE ON UNITS
.sp
The \fB\-M\fP option controls the units used in all input and output files.
However, this option does \fInot\fP control values given on the command line
to the \fB\-E\fP, \fB\-W\fP, and \fB\-Z\fP options.  These are assumed to be in
meters unless an optional \fBk\fP for km is appended.
.SH PLATE FLEXURE NOTES
.sp
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.
.SH EXAMPLES
.sp
To compute elastic plate flexure from the topography load in \fItopo.txt\fP,
for a 10 km thick plate with typical densities, try
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.sp
.nf
.ft C
gmt flexure \-Qttopo.txt \-E10k \-D2700/3300/1035 > flex.txt
.ft P
.fi
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.SH REFERENCES
.SH SEE ALSO
.sp
gmt, gravfft,
grdflexure, grdmath
.SH COPYRIGHT
2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
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