# interpolateStrain

Interpolate strain at arbitrary spatial locations

## Syntax

## Description

returns the interpolated strain values at the 2-D points specified in
`intrpStrain`

= interpolateStrain(`structuralresults`

,`xq`

,`yq`

)`xq`

and `yq`

. For transient and
frequency-response structural models, `interpolateStrain`

interpolates strain for all time- or frequency-steps, respectively.

uses the 3-D points specified in `intrpStrain`

= interpolateStrain(`structuralresults`

,`xq`

,`yq`

,`zq`

)`xq`

, `yq`

, and
`zq`

.

uses the points specified in `intrpStrain`

= interpolateStrain(`structuralresults`

,`querypoints`

)`querypoints`

.

## Examples

### Interpolate Strain for Plane-Strain Problem

Create a structural analysis model for a plane-strain problem.

structuralmodel = createpde("structural","static-planestrain");

Include the square geometry in the model. Plot the geometry.

geometryFromEdges(structuralmodel,@squareg); pdegplot(structuralmodel,"EdgeLabels","on") axis equal

Specify Young's modulus and Poisson's ratio.

structuralProperties(structuralmodel,"PoissonsRatio",0.3, ... "YoungsModulus",210E3);

Specify the *x*-component of the enforced displacement for edge 1.

structuralBC(structuralmodel,"XDisplacement",0.001,"Edge",1);

Specify that edge 3 is a fixed boundary.

structuralBC(structuralmodel,"Constraint","fixed","Edge",3);

Generate a mesh and solve the problem.

generateMesh(structuralmodel); structuralresults = solve(structuralmodel);

Create a grid and interpolate the *x*- and *y*-components of the normal strain to the grid.

v = linspace(-1,1,101); [X,Y] = meshgrid(v); intrpStrain = interpolateStrain(structuralresults,X,Y);

Reshape the *x*-component of the normal strain to the shape of the grid and plot it.

```
exx = reshape(intrpStrain.exx,size(X));
px = pcolor(X,Y,exx);
px.EdgeColor="none";
colorbar
```

Reshape the *y*-component of the normal strain to the shape of the grid and plot it.

```
eyy = reshape(intrpStrain.eyy,size(Y));
figure
py = pcolor(X,Y,eyy);
py.EdgeColor="none";
colorbar
```

### Interpolate Strain for 3-D Static Structural Analysis Problem

Solve a static structural model representing a bimetallic cable under tension, and interpolate strain on a cross-section of the cable.

Create a static structural model for solving a solid (3-D) problem.

structuralmodel = createpde("structural","static-solid");

Create the geometry and include it in the model. Plot the geometry.

gm = multicylinder([0.01,0.015],0.05); structuralmodel.Geometry = gm; pdegplot(structuralmodel,"FaceLabels","on", ... "CellLabels","on", ... "FaceAlpha",0.5)

Specify Young's modulus and Poisson's ratio for each metal.

structuralProperties(structuralmodel,"Cell",1,"YoungsModulus",110E9, ... "PoissonsRatio",0.28); structuralProperties(structuralmodel,"Cell",2,"YoungsModulus",210E9, ... "PoissonsRatio",0.3);

Specify that faces 1 and 4 are fixed boundaries.

structuralBC(structuralmodel,"Face",[1,4],"Constraint","fixed");

Specify the surface traction for faces 2 and 5.

structuralBoundaryLoad(structuralmodel,"Face",[2,5], ... "SurfaceTraction",[0;0;100]);

Generate a mesh and solve the problem.

generateMesh(structuralmodel); structuralresults = solve(structuralmodel)

structuralresults = StaticStructuralResults with properties: Displacement: [1x1 FEStruct] Strain: [1x1 FEStruct] Stress: [1x1 FEStruct] VonMisesStress: [22767x1 double] Mesh: [1x1 FEMesh]

Define the coordinates of a midspan cross-section of the cable.

[X,Y] = meshgrid(linspace(-0.015,0.015,50)); Z = ones(size(X))*0.025;

Interpolate the strain and plot the result.

intrpStrain = interpolateStrain(structuralresults,X,Y,Z); surf(X,Y,reshape(intrpStrain.ezz,size(X)))

Alternatively, you can specify the grid by using a matrix of query points.

querypoints = [X(:),Y(:),Z(:)]'; intrpStrain = interpolateStrain(structuralresults,querypoints); surf(X,Y,reshape(intrpStrain.ezz,size(X)))

### Interpolate Strain for 3-D Structural Dynamic Problem

Interpolate the strain at the geometric center of a beam under a harmonic excitation.

Create a transient dynamic model for a 3-D problem.

structuralmodel = createpde("structural","transient-solid");

Create a geometry and include it in the model. Plot the geometry.

gm = multicuboid(0.06,0.005,0.01); structuralmodel.Geometry = gm; pdegplot(structuralmodel,"FaceLabels","on","FaceAlpha",0.5) view(50,20)

Specify Young's modulus, Poisson's ratio, and the mass density of the material.

structuralProperties(structuralmodel,"YoungsModulus",210E9, ... "PoissonsRatio",0.3, ... "MassDensity",7800);

Fix one end of the beam.

structuralBC(structuralmodel,"Face",5,"Constraint","fixed");

Apply a sinusoidal displacement along the `y`

-direction on the end opposite the fixed end of the beam.

structuralBC(structuralmodel,"Face",3, ... "YDisplacement",1E-4, ... "Frequency",50);

Generate a mesh.

`generateMesh(structuralmodel,"Hmax",0.01);`

Specify the zero initial displacement and velocity.

structuralIC(structuralmodel,"Displacement",[0;0;0], ... "Velocity",[0;0;0]);

Solve the model.

tlist = 0:0.002:0.2; structuralresults = solve(structuralmodel,tlist);

Interpolate the strain at the geometric center of the beam.

coordsMidSpan = [0;0;0.005]; intrpStrain = interpolateStrain(structuralresults,coordsMidSpan);

Plot the normal strain at the geometric center of the beam.

```
figure
plot(structuralresults.SolutionTimes,intrpStrain.exx)
title("X-Direction Normal Strain at Beam Center")
```

## Input Arguments

`structuralresults`

— Solution of structural analysis problem

`StaticStructuralResults`

object | `TransientStructuralResults`

object | `FrequencyStructuralResults`

object

Solution of the structural analysis problem, specified as a `StaticStructuralResults`

, `TransientStructuralResults`

, or `FrequencyStructuralResults`

object. Create
`structuralresults`

by using the `solve`

function.

**Example: **```
structuralresults =
solve(structuralmodel)
```

`xq`

— *x*-coordinate query points

real array

*x*-coordinate query points, specified as a real array.
`interpolateStrain`

evaluates the strains at the 2-D
coordinate points `[xq(i),yq(i)]`

or at the 3-D coordinate
points `[xq(i),yq(i),zq(i)]`

. Therefore,
`xq`

, `yq`

, and (if present)
`zq`

must have the same number of entries.

`interpolateStrain`

converts query points to column
vectors `xq(:)`

, `yq(:)`

, and (if present)
`zq(:)`

. The function returns strains as an
`FEStruct`

object with the properties containing
vectors of the same size as these column vectors. To ensure that the
dimensions of the returned solution are consistent with the dimensions of
the original query points, use the `reshape`

function. For
example, use ```
intrpStrain =
reshape(intrpStrain.exx,size(xq))
```

.

**Data Types: **`double`

`yq`

— *y*-coordinate query points

real array

*y*-coordinate query points, specified as a real array.
`interpolateStrain`

evaluates the strains at the 2-D
coordinate points `[xq(i),yq(i)]`

or at the 3-D coordinate
points `[xq(i),yq(i),zq(i)]`

. Therefore,
`xq`

, `yq`

, and (if present)
`zq`

must have the same number of entries.
Internally, `interpolateStrain`

converts the query points
to the column vector `yq(:)`

.

**Data Types: **`double`

`zq`

— *z*-coordinate query points

real array

*z*-coordinate query points, specified as a real array.
`interpolateStrain`

evaluates the strains at the 3-D
coordinate points `[xq(i),yq(i),zq(i)]`

. Therefore,
`xq`

, `yq`

, and
`zq`

must have the same number of entries. Internally,
`interpolateStrain`

converts the query points to the
column vector `zq(:)`

.

**Data Types: **`double`

`querypoints`

— Query points

real matrix

Query points, specified as a real matrix with either two rows for 2-D
geometry or three rows for 3-D geometry. `interpolateStrain`

evaluates the strains at the coordinate
points `querypoints(:,i)`

, so each column of
`querypoints`

contains exactly one 2-D or 3-D query
point.

**Example: **For 2-D geometry, ```
querypoints = [0.5,0.5,0.75,0.75;
1,2,0,0.5]
```

**Data Types: **`double`

## Output Arguments

`intrpStrain`

— Strains at query points

`FEStruct`

object

Strains at the query points, returned as an `FEStruct`

object with the properties representing spatial components of strain at the
query points. For query points that are outside the geometry,
`intrpStrain`

returns `NaN`

.
Properties of an `FEStruct`

object are read-only.

## Version History

**Introduced in R2017b**

### R2019b: Support for frequency response structural problems

For frequency response structural models, `interpolateStrain`

interpolates strain for all frequency-steps.

### R2018a: Support for transient structural problems

For transient structural models, `interpolateStrain`

interpolates
strain for all time-steps.

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