interpolateVonMisesStress

Interpolate von Mises stress at arbitrary spatial locations

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Syntax

intrpVMStress = interpolateVonMisesStress(structuralresults,xq,yq)
intrpVMStress = interpolateVonMisesStress(structuralresults,xq,yq,zq)
intrpVMStress = interpolateVonMisesStress(structuralresults,querypoints)

Description

intrpVMStress = interpolateVonMisesStress(structuralresults,xq,yq) returns the interpolated von Mises stress values at the 2-D points specified in xq and yq. For transient and frequency response structural problems, interpolateVonMisesStress interpolates von Mises stress for all time or frequency steps, respectively.

example

intrpVMStress = interpolateVonMisesStress(structuralresults,xq,yq,zq) uses the 3-D points specified in xq, yq, and zq.

example

intrpVMStress = interpolateVonMisesStress(structuralresults,querypoints) uses the points specified in querypoints.

example

Examples

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Open Live Script

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

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

Switch the model type to plane-strain.

model.PlanarType = "planeStrain";

Plot the geometry.

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

Figure contains an axes object. The axes object contains 5 objects of type line, text.

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 von Mises stress to the grid.

v = linspace(-1,1,151);
[X,Y] = meshgrid(v);
intrpVMStress = interpolateVonMisesStress(R,X,Y);

Reshape the von Mises stress to the shape of the grid and plot it.

VMStress = reshape(intrpVMStress,size(X));
p = pcolor(X,Y,VMStress);
p.EdgeColor="none";
colorbar
axis equal

Figure contains an axes object. The axes object contains an object of type surface.

Open Live Script

Analyze a bimetallic cable under tension, and interpolate the von Mises stress 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)

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

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: [1×1 FEStruct]
            Strain: [1×1 FEStruct]
            Stress: [1×1 FEStruct]
    VonMisesStress: [23098×1 double]
              Mesh: [1×1 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 von Mises stress and plot the result.

IntrpVMStress = interpolateVonMisesStress(R,X,Y,Z);
surf(X,Y,reshape(IntrpVMStress,size(X)))

Figure contains an axes object. The axes object contains an object of type surface.

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

querypoints = [X(:),Y(:),Z(:)]';
IntrpVMStress = ...
    interpolateVonMisesStress(R,querypoints);
surf(X,Y,reshape(IntrpVMStress,size(X)))

Figure contains an axes object. The axes object contains an object of type surface.

Open Live Script

Interpolate the von Mises stress 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)

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

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 von Mises stress at the geometric center of the beam.

coordsMidSpan = [0;0;0.005];
VMStress = interpolateVonMisesStress(R,coordsMidSpan);

Plot the von Mises stress at the geometric center of the beam.

plot(R.SolutionTimes,VMStress)
title("von Mises Stress at Beam Center")

Figure contains an axes object. The axes object with title von Mises Stress at Beam Center contains an object of type line.

Input Arguments

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Solution of the structural analysis problem, specified as a StaticStructuralResults, TransientStructuralResults, or FrequencyStructuralResults object. Create structuralresults by using the solve function.

x-coordinate query points, specified as a real array. interpolateVonMisesStress evaluates the von Mises stress 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.

interpolateVonMisesStress converts query points to column vectors xq(:), yq(:), and (if present) zq(:). The function returns von Mises stress as a column vector of the same size as the query point 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 intrpVMStress = reshape(intrpVMStress,size(xq)).

Data Types: double

y-coordinate query points, specified as a real array. interpolateVonMisesStress evaluates the von Mises stress 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, interpolateVonMisesStress converts the query points to the column vector yq(:).

Data Types: double

z-coordinate query points, specified as a real array. interpolateVonMisesStress evaluates the von Mises stress 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, interpolateVonMisesStress converts the query points to the column vector zq(:).

Data Types: double

Query points, specified as a real matrix with either two rows for 2-D geometry or three rows for 3-D geometry. interpolateVonMisesStress evaluates the von Mises stress 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

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von Mises stress at the query points, returned as a column vector.

For query points that are outside the geometry, intrpVMStress = NaN.

Version History

Introduced in R2017b

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See Also

Objects

Functions