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

       -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 …)
              Skip or produce header record(s).

       -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

REFERENCES

SEE ALSO

       gmt, gravfft, grdflexure, grdmath

COPYRIGHT

       2018, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe