Modelling shell behavior with femodel

I apologize if this question is banal but is there a way to model bending plates with femodel?

Playing around with the object definition I managed to make a 2D rectangular model with uniform surface pressure and fixed edges, I assigned material properties, generated a mesh and solved the model. When I inspect the results, there are only null fields that correspond to membrane behavior and no bending.

Answer 1

[Karan Singh]

Hi Daniel,

As I don’t have access to your code, I can’t pinpoint the exact problem you're facing, but we can proceed with an example.

• You create a rectangular geometry with length \(L = 1\) meter and width \(W = 0.5\) meter.

    L = 1; % Length of the rectangle
    W = 0.5; % Width of the rectangle
    gdm = [3, 4, 0, L, L, 0, 0, 0, W, W]';
    g = decsg(gdm, 'R1', ('R1')');

• You create a structural model for static plane stress analysis.

    model = createpde('structural', 'static-planestress');

• The geometry is included in the structural model.

    geometryFromEdges(model, g);

• This step visualizes the geometry with edge labels for reference.

    figure;
    pdegplot(model, 'EdgeLabels', 'on');
    title('Geometry with Edge Labels');
    axis equal;

• You specify the material properties (Young's modulus and Poisson's ratio) for the rectangular plate.

    E = 210e9; % Young's modulus in Pascals
    nu = 0.3; % Poisson's ratio
    structuralProperties(model, 'YoungsModulus', E, 'PoissonsRatio', nu);

• The edges are fixed to prevent rigid body motion and to ensure the model is properly constrained.

Edge 1 (Bottom Edge): Fully fixed (both x and y displacements are zero).

Edge 4 (Left Edge): Fixed in the x direction to prevent horizontal movement.

    % Fix the bottom edge completely
    structuralBC(model, 'Edge', 1, 'Constraint', 'fixed');
    
    % Fix the left edge in the x direction to prevent horizontal movement
    structuralBC(model, 'Edge', 4, 'XDisplacement', 0);

• You apply a uniform pressure load to the top and right edges.

    pressure = 1e5; % Uniform pressure in Pascals
    structuralBoundaryLoad(model, 'Edge', [2, 3], 'SurfaceTraction', [0; -pressure]);

• A mesh with a specified maximum element size is generated.

    generateMesh(model, 'Hmax', 0.05);

• This step visualizes the generated mesh.

    figure;
    pdeplot(model);
    title('Mesh');
    axis equal;

• The structural model is solved.

    result = solve(model);

• The displacement magnitude and Von Mises stress are plotted to visualize the results, including deformation.

    figure;
    pdeplot(model, 'XYData', result.Displacement.Magnitude, 'Deformation', result.Displacement, 'DeformationScaleFactor', 1);
    title('Displacement Magnitude with Deformation');
    colorbar;

    figure;
    pdeplot(model, 'XYData', result.VonMisesStress, 'Deformation', result.Displacement, 'DeformationScaleFactor', 1);
    title('Von Mises Stress with Deformation');
    colorbar;

I hope this helps you get a clearer picture!

Thanks,

Karan