interpolateDisplacement
Interpolate displacement at arbitrary spatial locations
Syntax
Description
returns the interpolated displacement values at the 2-D points specified in
intrpDisp
= interpolateDisplacement(structuralresults
,xq
,yq
)xq
and yq
. For transient and frequency
response structural problems, interpolateDisplacement
returns the
interpolated displacement values for all time or frequency steps,
respectively.
uses 3-D points specified in intrpDisp
= interpolateDisplacement(structuralresults
,xq
,yq
,zq
)xq
, yq
, and
zq
.
uses points specified in intrpDisp
= interpolateDisplacement(structuralresults
,querypoints
)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 R2017bR2019b: 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.
See Also
Objects
Functions
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