# gmtflexure man page

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

## Synopsis

**gmtflexure** **-D***rm*/*rl*[/*ri*]/*rw* **-E***Te*[**u**]|*D*|*file* [ **-A**[**l**|**r**][/*args*] ] [ **-Cp***Poisson* ] [ **-Cy***Young* ] [ **-F***force* ] [ **-Q***args*] [ **-S** ] [ **-T***wfile*] [ **-V**[*level*] ] [ **-W***wd*] [ **-Z***zm*] [ **-bi***binary* ] [ **-h***headers* ] [ **-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

**-D***rm*/*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*.

**-E***Te*[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
**l**eft and**r**ight 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.

**-Cp***Poisson*- Change the current value of Poisson's ratio [0.25].
**-Cy***Young*- Change the current value of Young's modulus [7.0e10 N/m^2].

**-F***force*]- 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].

**-T***wfile*- Supply a file with pre-existing deformations [undeformed surface].

**-W***wd*- 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.

**-Z***zm*- 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.

**-h[i|o][***n*][+c][+d][+r*remark*][+r*title*]*(more ...)*- Skip or produce header record(s).

**-i***cols*[l][s*scale*][o*offset*][,*...*]*(more ...)*- Select input columns (0 is first column).

**-o***cols*[,...]*(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.

## 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`

## See Also

**gmt**, **gravfft grdflexuregrdmath**

## Copyright

2016, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe