interpolateVelocity

Interpolate velocity at arbitrary spatial locations for all time steps for transient structural model

Syntax

intrpVel = interpolateVelocity(structuralresults,xq,yq)

intrpVel = interpolateVelocity(structuralresults,xq,yq,zq)

intrpVel = interpolateVelocity(structuralresults,querypoints)

Description

intrpVel = interpolateVelocity(structuralresults,xq,yq) returns the interpolated velocity values at the 2-D points specified in xq and yq for all time-steps.

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

intrpVel = interpolateVelocity(structuralresults,querypoints) uses the points specified in querypoints.

Examples

Interpolate Velocity for 3-D Structural Dynamic Problem

Interpolate velocity 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 velocity at the geometric center of the beam.

coordsMidSpan = [0;0;0.005];
intrpVel = interpolateVelocity(structuralresults,coordsMidSpan);

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

figure
plot(structuralresults.SolutionTimes,intrpVel.vy)
title('Y-Velocity of the Geometric Center of the Beam')

Input Arguments

structuralresults — Solution of dynamic structural analysis problem

TransientStructuralResults object

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

Example: structuralresults = solve(structuralmodel,tlist)

xq — x-coordinate query points

real array

x-coordinate query points, specified as a real array. interpolateVelocity evaluates velocities 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.

interpolateVelocity converts query points to column vectors xq(:), yq(:), and (if present) zq(:). It returns velocities 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 intrpVel = reshape(intrpVel.ux,size(xq)).

Data Types: double

yq — y-coordinate query points

real array

y-coordinate query points, specified as a real array. interpolateVelocity evaluates velocities 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, interpolateVelocity 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. interpolateVelocity evaluates velocities 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, interpolateVelocity 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. interpolateVelocity evaluates velocities 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

intrpVel — Velocities at query points

structure array

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