interpolateStress

Interpolate stress at arbitrary spatial locations

Syntax

intrpStress = interpolateStress(structuralresults,xq,yq)

intrpStress = interpolateStress(structuralresults,xq,yq,zq)

intrpStress = interpolateStress(structuralresults,querypoints)

Description

intrpStress = interpolateStress(structuralresults,xq,yq) returns the interpolated stress values at the 2-D points specified in xq and yq. For a dynamic structural model, interpolateStress interpolates stress for all time-steps.

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

intrpStress = interpolateStress(structuralresults,querypoints) uses the points specified in querypoints.

Examples

Interpolate Stress 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 the 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 stress to the grid.

v = linspace(-1,1,151);
[X,Y] = meshgrid(v);
intrpStress = interpolateStress(structuralresults,X,Y);

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

sxx = reshape(intrpStress.sxx,size(X));
px = pcolor(X,Y,sxx);
px.EdgeColor='none';
colorbar

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

syy = reshape(intrpStress.syy,size(Y));
figure
py = pcolor(X,Y,syy);
py.EdgeColor='none';
colorbar

Interpolate Stress for 3-D Static Structural Analysis Problem

Solve a static structural model representing a bimetallic cable under tension, and interpolate stress 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 the 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 struct]
            Strain: [1x1 struct]
            Stress: [1x1 struct]
    VonMisesStress: [22281x1 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 stress and plot the result.

intrpStress = interpolateStress(structuralresults,X,Y,Z);
surf(X,Y,reshape(intrpStress.szz,size(X)))

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

querypoints = [X(:),Y(:),Z(:)]';
intrpStress = interpolateStress(structuralresults,querypoints);
surf(X,Y,reshape(intrpStress.szz,size(X)))

Interpolate Stress for 3-D Structural Dynamic Problem

Interpolate the stress 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 the Young's modulus, Poisson's ratio, and 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 stress at the geometric center of the beam.

coordsMidSpan = [0;0;0.005];
intrpStress = interpolateStress(structuralresults,coordsMidSpan);

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

figure
plot(structuralresults.SolutionTimes,intrpStress.sxx)
title('X-Direction Normal Stress at Beam Center')

Input Arguments

structuralresults — Solution of structural analysis problem

StaticStructuralResults object | TransientStructuralResults object

Solution of the structural analysis problem, specified as a StaticStructuralResults or TransientStructuralResults 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. interpolateStress evaluates the stresses 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.

interpolateStress converts the query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns stresses as a structure array with fields 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 intrpStress = reshape(intrpStress.sxx,size(xq)).

Data Types: double

yq — y-coordinate query points

real array

y-coordinate query points, specified as a real array. interpolateStress evaluates the stresses 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, interpolateStress 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. interpolateStress evaluates the stresses 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, interpolateStress 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. interpolateStress evaluates stresses 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

intrpStress — Stresses at query points

structure array

Stresses at the query points, returned as a structure array with fields representing spatial components of stress at the query points. For query points that are outside the geometry, intrpStress returns NaN.