---
name: "gmtflexure"
section: "1gmt"
platform: "linux"
package: "gmt-common"
version: "5.4.5+dfsg-2"
release: "Debian 10 (Buster)"
platforms: ["linux"]
url: "https://new.carta.tech/gmtflexure"
---

# gmtflexure(1gmt)

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

## NAME

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**\[*level*\] \] \[  **-W***wd*\] \[  **-Z***zm*\] \[ **-bi**binary \] \[ **-d**nodata \] \[ **-e**regexp \] \[ **-h**headers \] \[ **-i**flags \] \[ **-o**flags \]

**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.

- **-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**\[**i**\|**o**\]\[*n*\]\[**+c**\]\[**+d**\]\[**+r***remark*\]\[**+r***title*\] (more ...)

  Skip or produce header record(s).

- **-i***cols*\[**+l**\]\[**+s***scale*\]\[**+o***offset*\]\[,*...*\] (more ...)

  Select input columns and transformations (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 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

2019, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe