interpolateDisplacement

Interpolate displacement at arbitrary spatial locations

Syntax

intrpDisp = interpolateDisplacement(structuralresults,xq,yq)

intrpDisp = interpolateDisplacement(structuralresults,xq,yq,zq)

intrpDisp = interpolateDisplacement(structuralresults,querypoints)

Description

intrpDisp = interpolateDisplacement(structuralresults,xq,yq) returns the interpolated displacement values at the 2-D points specified in xq and yq. For transient and frequency response structural problems, interpolateDisplacement returns the interpolated displacement values for all time or frequency steps, respectively.

intrpDisp = interpolateDisplacement(structuralresults,xq,yq,zq) uses 3-D points specified in xq, yq, and zq.

intrpDisp = interpolateDisplacement(structuralresults,querypoints) uses points specified in querypoints.

Examples

Interpolate Displacement for Plane-Strain Problem

Create an femodel object for static structural analysis and include a unit square geometry.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry=@squareg);

Switch the type of the model to plane-strain.

model.PlanarType = "planeStrain";

Plot the geometry.

pdegplot(model.Geometry,EdgeLabels="on")
xlim([-1.1 1.1])
ylim([-1.1 1.1])

Specify Young's modulus and Poisson's ratio.

model.MaterialProperties = ...
    materialProperties(PoissonsRatio=0.3, ...
                       YoungsModulus=210E3);

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

model.EdgeBC(1) = edgeBC(XDisplacement=0.001);

Specify that edge 3 is a fixed boundary.

model.EdgeBC(3) = edgeBC(Constraint="fixed");

Generate a mesh and solve the problem.

model = generateMesh(model);
R = solve(model);

Create a grid and interpolate the x- and y-components of the displacement to the grid.

v = linspace(-1,1,21);
[X,Y] = meshgrid(v);
intrpDisp = interpolateDisplacement(R,X,Y);

Reshape the displacement components to the shape of the grid. Plot the displacement.

ux = reshape(intrpDisp.ux,size(X));
uy = reshape(intrpDisp.uy,size(Y));
quiver(X,Y,ux,uy)

Interpolate Displacement for 3-D Static Structural Analysis Problem

Analyze a bimetallic cable under tension, and interpolate the displacement on a cross-section of the cable.

Create and plot a geometry representing a bimetallic cable.

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

Create an femodel object for static structural analysis and include the geometry into the model.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry=gm);

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

model.MaterialProperties(1) = ...
    materialProperties(YoungsModulus=110E9, ...
                       PoissonsRatio=0.28);
model.MaterialProperties(2) = ...
    materialProperties(YoungsModulus=210E9, ...
                       PoissonsRatio=0.3);

Specify that faces 1 and 4 are fixed boundaries.

model.FaceBC([1 4]) = faceBC(Constraint="fixed");

Specify the surface traction for faces 2 and 5.

model.FaceLoad([2 5]) = faceLoad(SurfaceTraction=[0;0;100]);

Generate a mesh and solve the problem.

model = generateMesh(model);
R = solve(model)

R = 
  StaticStructuralResults with properties:

      Displacement: [1x1 FEStruct]
            Strain: [1x1 FEStruct]
            Stress: [1x1 FEStruct]
    VonMisesStress: [23098x1 double]
              Mesh: [1x1 FEMesh]

Define 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 displacement and plot the result.

intrpDisp = interpolateDisplacement(R,X,Y,Z);
surf(X,Y,reshape(intrpDisp.uz,size(X)))

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

querypoints = [X(:),Y(:),Z(:)]';
intrpDisp = interpolateDisplacement(R,querypoints);
surf(X,Y,reshape(intrpDisp.uz,size(X)))

Interpolate Displacement for Transient Structural Analysis Problem

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

Create and plot a beam geometry.

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

Create an femodel object for transient structural analysis and include the geometry into the model.

model = femodel(AnalysisType="structuralTransient", ...
                Geometry=gm);

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

model.MaterialProperties = ...
    materialProperties(YoungsModulus=210E9, ...
                       PoissonsRatio=0.3, ...
                       MassDensity=7800);

Fix one end of the beam.

model.FaceBC(5) = faceBC(Constraint="fixed");

Apply a sinusoidal displacement along the y-direction on the end opposite the fixed end of the beam.

yDisplacementFunc = ...
@(location,state) ones(size(location.y))*1E-4*sin(50*state.time);
model.FaceBC(3) = faceBC(YDisplacement=yDisplacementFunc);

Generate a mesh.

model = generateMesh(model,Hmax=0.01);

Specify the zero initial displacement and velocity.

model.CellIC = cellIC(Displacement=[0;0;0],Velocity=[0;0;0]);

Solve the problem.

tlist = 0:0.002:0.2;
R = solve(model,tlist);

Interpolate the displacement at the geometric center of the beam.

coordsMidSpan = [0;0;0.005];
intrpDisp = interpolateDisplacement(R,coordsMidSpan);

Plot the y-component of displacement of the geometric center of the beam.

figure
plot(R.SolutionTimes,intrpDisp.uy)
title("y-Displacement of the Geometric Center of the Beam")

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. For TransientStructuralResults and FrequencyStructuralResults objects, interpolateDisplacement returns the interpolated displacement values for all time and frequency steps, respectively.

xq — x-coordinate query points

real array

x-coordinate query points, specified as a real array. interpolateDisplacement evaluates the displacements 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.

interpolateDisplacement converts query points to column vectors xq(:), yq(:), and (if present) zq(:). The function returns displacements 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 intrpDisp = reshape(intrpDisp.ux,size(xq)).

Data Types: double

yq — y-coordinate query points

real array

y-coordinate query points, specified as a real array. interpolateDisplacement evaluates the displacements 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, interpolateDisplacement converts 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. interpolateDisplacement evaluates the displacements 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, interpolateDisplacement converts 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. interpolateDisplacement evaluates the displacements 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

intrpDisp — Displacements at query points

FEStruct object

Displacements at the query points, returned as an FEStruct object with the properties representing spatial components of displacement at the query points. For query points that are outside the geometry, intrpDisp 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 problems, interpolateDisplacement interpolates displacement for all frequency steps.

R2018a: Support for transient structural problems

For transient structural problems, interpolateDisplacement interpolates displacement for all time steps.