evaluatePrincipalStrain
Evaluate principal strain at nodal locations
Description
evaluates principal strain at nodal locations using strain values from
pStrain
= evaluatePrincipalStrain(structuralresults
)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 R2017bR2019b: 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.
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