StaticStructuralResults

Static structural solution and its derived quantities

Description

A StaticStructuralResults object contains the displacement, stress, strain, and von Mises stress in a form convenient for plotting and postprocessing.

Displacements, stresses, and strains are reported for the nodes of the triangular or tetrahedral mesh generated by generateMesh. Displacement values at the nodes appear as an FEStruct object in the Displacement property. The properties of this object contain components of displacement at nodal locations.

Stress and strain values at the nodes appear as FEStruct objects in the Stress and Strain properties, respectively.

von Mises stress at the nodes appears as a vector in the VonMisesStress property.

To interpolate the displacement, stress, strain, and von Mises stress to a custom grid, such as the one specified by meshgrid, use interpolateDisplacement, interpolateStress, interpolateStrain, and interpolateVonMisesStress, respectively.

To evaluate reaction forces on a specified boundary, use evaluateReaction. To evaluate principal stress and principal strain at nodal locations, use evaluatePrincipalStress and evaluatePrincipalStrain, respectively.

Creation

Solve a static linear elasticity problem by using the solve function. This function returns a static structural solution as a StaticStructuralResults object.

Properties

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Properties of an FEStruct object are read-only.

Displacement values at the nodes, returned as an FEStruct object. The properties of this object contain components of displacement at nodal locations.

Stress values at the nodes, returned as an FEStruct object. The properties of this object contain components of stress at nodal locations.

Strain values at the nodes, returned as an FEStruct object. The properties of this object contain components of strain at nodal locations.

Von Mises stress values at the nodes, returned as a vector.

Data Types: double

Finite element mesh, returned as a FEMesh object. For details, see FEMesh Properties.

Object Functions

interpolateDisplacementInterpolate displacement at arbitrary spatial locations
interpolateStressInterpolate stress at arbitrary spatial locations
interpolateStrainInterpolate strain at arbitrary spatial locations
interpolateVonMisesStressInterpolate von Mises stress at arbitrary spatial locations
evaluateReactionEvaluate reaction forces on boundary
evaluatePrincipalStressEvaluate principal stress at nodal locations
evaluatePrincipalStrainEvaluate principal strain at nodal locations

Examples

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Solve a static structural model representing a bimetallic cable under tension.

Create a static structural model for solving a solid (3-D) problem.

structuralmodel = createpde('structural','static-solid');

Create the 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 the 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: [22281x1 double]
              Mesh: [1x1 FEMesh]

The solver finds the values of displacement, stress, strain, and von Mises stress at the nodal locations. To access these values, use structuralresults.Displacement, structuralresults.Stress, and so on. The displacement, stress, and strain values at the nodal locations are returned as FEStruct objects with the properties representing their components. Note that properties of an FEStruct object are read-only.

structuralresults.Displacement
ans = 
  FEStruct with properties:

           ux: [22281x1 double]
           uy: [22281x1 double]
           uz: [22281x1 double]
    Magnitude: [22281x1 double]

structuralresults.Stress
ans = 
  FEStruct with properties:

    sxx: [22281x1 double]
    syy: [22281x1 double]
    szz: [22281x1 double]
    syz: [22281x1 double]
    sxz: [22281x1 double]
    sxy: [22281x1 double]

structuralresults.Strain
ans = 
  FEStruct with properties:

    exx: [22281x1 double]
    eyy: [22281x1 double]
    ezz: [22281x1 double]
    eyz: [22281x1 double]
    exz: [22281x1 double]
    exy: [22281x1 double]

Plot the deformed shape with the z-component of normal stress.

pdeplot3D(structuralmodel,'ColorMapData',structuralresults.Stress.szz, ...
                          'Deformation',structuralresults.Displacement)

Introduced in R2017b