evaluatePrincipalStrain

Evaluate principal strain at nodal locations

Syntax

pStrain = evaluatePrincipalStrain(structuralresults)

Description

pStrain = evaluatePrincipalStrain(structuralresults) evaluates principal strain at nodal locations using strain values from structuralresults. For transient and frequency response structural analysis, evaluatePrincipalStrain evaluates principal strain for all time- or frequency-steps, respectively.

Examples

Octahedral Shear Strain for Bimetallic Cable Under Tension

Analyze a bimetallic cable under tension, and compute octahedral shear strain.

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]

Evaluate the principal strain at nodal locations.

pStrain = evaluatePrincipalStrain(R);

Use the principal strain to evaluate the first and second invariant of strain.

I1 = pStrain.e1 + pStrain.e2 + pStrain.e3;
I2 = pStrain.e1.*pStrain.e2 + ...
     pStrain.e2.*pStrain.e3 + ...
     pStrain.e3.*pStrain.e1;
tauOct = sqrt(2*(I1.^2 -3*I2))/3;
pdeplot3D(R.Mesh,ColorMapData=tauOct)

Principal Strain for 3-D Structural Dynamic Problem

Evaluate the principal strain and octahedral shear strain in 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.

yDisplacemenmtFunc = ...
@(location, state) ones(size(location.y))*1E-4*sin(50*state.time);
model.FaceBC(3) = faceBC(YDisplacement=yDisplacemenmtFunc);

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);

Evaluate the principal strain in the beam.

pStrain = evaluatePrincipalStrain(R);

Use the principal strain to evaluate the first and second invariants.

I1 = pStrain.e1 + pStrain.e2 + pStrain.e3;
I2 = pStrain.e1.*pStrain.e2 + ...
     pStrain.e2.*pStrain.e3 + ...
     pStrain.e3.*pStrain.e1;

Use the stress invariants to compute the octahedral shear strain.

tauOct = sqrt(2*(I1.^2 -3*I2))/3;

Plot the results.

figure
pdeplot3D(R.Mesh,ColorMapData=tauOct(:,end))

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.

Output Arguments

pStrain — Principal strain at nodal locations

structure array

Principal strain at the nodal locations, returned as a structure array.

Version History

Introduced in R2017b

R2019b: Support for frequency response structural problems

For frequency response structural problems, evaluatePrincipalStrain evaluates principal strain for all frequency-steps.

R2018a: Support for transient structural problems

For transient structural problems, evaluatePrincipalStrain evaluates principal strain for all time-steps.