interpolateDisplacement

Interpolate displacement at arbitrary spatial locations

Syntax

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

Description

example

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

example

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

example

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

Examples

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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 displacement to the grid.

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

Solve a static structural model representing a bimetallic cable under tension, and interpolate the displacement 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 displacement and plot the result.

intrpDisp = interpolateDisplacement(structuralresults,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(structuralresults,querypoints);
surf(X,Y,reshape(intrpDisp.uz,size(X)))

Interpolate the displacement 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 the 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 displacement at the geometric center of the beam.

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

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

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

Input Arguments

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Solution of the structural analysis problem, specified as a StaticStructuralResults or TransientStructuralResults object. Create structuralresults by using the solve function. For a TransientStructuralResults object, interpolateDisplacement returns the interpolated displacement values for all time-steps.

Example: structuralresults = solve(structuralmodel)

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 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 intrpDisp = reshape(intrpDisp.ux,size(xq)).

Data Types: double

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

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

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

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

Introduced in R2017b