evaluatePrincipalStress
Evaluate principal stress at nodal locations
Description
evaluates principal stress at nodal locations using stress values from
pStress
= evaluatePrincipalStress(structuralresults
)structuralresults
. For transient and frequency response
structural models, evaluatePrincipalStress
evaluates principal
stress for all time- and frequency-steps, respectively.
Examples
Octahedral Shear Stress for Bimetallic Cable Under Tension
Solve a static structural model representing a bimetallic cable under tension, and compute octahedral shear stress.
Create a structural model.
structuralmodel = createpde("structural","static-solid");
Create a 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 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 FEStruct] Strain: [1x1 FEStruct] Stress: [1x1 FEStruct] VonMisesStress: [22402x1 double] Mesh: [1x1 FEMesh]
Evaluate the principal stress at nodal locations.
pStress = evaluatePrincipalStress(structuralresults);
Use the principal stress to evaluate the first and second invariant of stress.
I1 = pStress.s1 + pStress.s2 + pStress.s3; I2 = pStress.s1.*pStress.s2 + ... pStress.s2.*pStress.s3 + ... pStress.s3.*pStress.s1; tauOct = sqrt(2*(I1.^2 -3*I2))/3; pdeplot3D(structuralmodel,"ColorMapData",tauOct)
Principal Stress for 3-D Structural Dynamic Problem
Evaluate the principal stress and octahedral shear stress in 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 Young's modulus, Poisson's ratio, and the 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);
Evaluate the principal stress in the beam.
pStress = evaluatePrincipalStress(structuralresults);
Use the principal stress to evaluate the first and second invariants.
I1 = pStress.s1 + pStress.s2 + pStress.s3; I2 = pStress.s1.*pStress.s2 + ... pStress.s2.*pStress.s3 + ... pStress.s3.*pStress.s1;
Use the stress invariants to compute the octahedral shear stress.
tauOct = sqrt(2*(I1.^2 -3*I2))/3;
Plot the results.
figure
pdeplot3D(structuralmodel,"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.
Example: structuralresults =
solve(structuralmodel)
Output Arguments
pStress
— Principal stress at nodal locations
structure array
Principal stress at the nodal locations, returned as a structure array.
Version History
Introduced in R2017bR2019b: Support for frequency response structural problems
For frequency response structural models,
evaluatePrincipalStress
evaluates principal stress for all
frequency-steps.
R2018a: Support for transient structural problems
For transient structural models, evaluatePrincipalStress
evaluates principal stress for all time-steps.
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