What does deflection mean in Structural Mechanics PDE Toolbox?

Let us consider a rectangular structure of length L under strain (x-direction) is elongated by ∆L.

a) Is deflection in this case ∆L, ∆L per L or its bending?

b) If left and right edges of the rectangle are stretched outward, should I use Dirichlet Boundary condition on top and bottom edges or

Neumann Boundary condition on the botton edge.

c) I could export the mesh and solve PDE. How do I plot deflection in horizontal and vertical cuts of the structure?

Thanks in advance.

Answer 1

[Ravi Kumar]

a) Results output from PDE Toolbox contains Displacements wstruct array ith ux, uy, and uz as fields, these values are displacement from the reference state. These values are sort to (in 1-D) in each direction at each node.

b) You need to decide what BCs represents the physical problem. If you are modelling streaching by pulling of the rectangle with lateral edges free to deflect the just don't assign any BCs on them. In addition you can fix left end and then apply the Dirchlet BC on the right end to simulation pulling, otherwise your model is not fully constrained for rigid motion.

c) Refer to interpolateDisplacement function to get the displacement at you desired locations.

[Briggs]

Thanks Ravi Kumar, 1st and 2nd part of the answer I got.

2nd part: I am still confused with the BC. Left and right edges of the rectangle are pulled by a load say 100 N/m. Did you mean to apply Neumann BC at the left and right edges? Also, what values of the coefficients g1, g2 (surface tractions) should be used in this case. If load is applied at the edges, volume forces Kx=0, right?

Thanks you.

[Ravi Kumar]

To simulate pulling of the bar, you can fix one end (Dirichlet BC) and apply traction on the other end (Neumann BC). Leave the lateral edges unspecified BCs, those will default to zero Neumann BC.

I suggest you use the structural workflow, then you don't have to think in terms of Dirichlet and Neumann type of BC, instead you can specify BC a 'fixed' and 'SurfaceTraction'. Here is an example for you:

gm = multicuboid(0.5,0.05,0.05);
smodel = createpde('structural');
smodel.Geometry = gm;
pdegplot(smodel,'FaceLabels','on')

generateMesh(smodel);
structuralProperties(smodel,'YoungsModulus',227E9,'PoissonsRatio',0.27,'CTE',12.7E-6);
structuralBC(smodel,'Face',5,'Constraint','fixed');
structuralBoundaryLoad(smodel,'Face',3,'SurfaceTraction',[100;0;0])
Rs = solve(smodel)
pdeplot3D(smodel,'ColorMapData',Rs.VonMisesStress,'Deformation',Rs.Displacement)

[Briggs]

Thanks for your reply. U mentioned "To simulate pulling of the bar, you can fix one end (Dirichlet BC) and apply traction on the other end (Neumann BC)". I agree. My confusion was "If both the left and right edges are pulled simultaneously should one use Neumann BCs on both the edges".

[Ravi Kumar]

You can use Neumann BCs for both ends. However, your problem will be illconditioned. You might get rigid body motion warning and resutls won't be reliable. You need to specify enough constraints to prevent all six body motions for 3-D space.

[Briggs]

I follow. Thanks

[Briggs]

Do you have example file on strain. I saw for stress, clamping etc

[Ravi Kumar]

Not sure what you are asking for. You will get strain tensor as an output. You can impose Displacements as BCs to produce required strain.

Answer 2

[Briggs]

How to export ux, uy etc.?