Provided by: gmt-common_5.4.3+dfsg-1_all

**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**

gmtflexurecomputes 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]/rwSets density for mantle, load, infill (optionally, otherwise it is assumed to equal the load density), and water. Ifriis not given then it defaults torl.-ETe[u]|D|fileSets the elastic plate thickness (in meter); appendkfor km. If the elastic thickness exceeds 1e10 it will be interpreted as a flexural rigidityDinstead (by defaultDis computed fromTe, Young’s modulus, and Poisson’s ratio; see-Cto change these values). Alternatively, supply afilewith 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 theleft andright boundary. Thebccan 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 whereargs(if given) sets the deflection value [0] (and its first derivative is set to zero), while 3 selects the free condition whereargsis given asmoment/forcewhich specify the end bending moment and vertical shear force [0/0]. Use SI units for any optional arguments.-CpPoissonChange the current value of Poisson’s ratio [0.25].-CyYoungChange 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:-Qnmeans 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-Ethen you must also appendmin/max/incto initiate the locations used for the calculations. Append+toincto indicate the number of points instead.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-Mfor topography unit used [m].-SCompute the curvature along with the deflections and report them via the third output column [none].-TwfileSupply a file with pre-existing deformations [undeformed surface].-WwdSpecify water depth in m; append k for km. Must be positive [0]. Any subaerial topography will be scaled via the densities set in-Dto compensate for the larger density contrast with air.-ZzmSpecify 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 equalnodatawith 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-Moption controls the units used in all input and output files. However, this option doesnotcontrol values given on the command line to the-E,-W, and-Zoptions. These are assumed to be in meters unless an optionalkfor 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 intopo.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