How to find the position of spring stiffness in Maltab PDE toolbox

Hello, everyone! I'm wondering how can I get the position of spring stiffness in PDE toolbox. In the PDE toolbox, there is a function "structuralBoundaryLoad" that could be used for adding spring stiffness on the model. For example:

structuralBoundaryLoad(model,"edge",3,'TranslationalStiffness',[1;0])

However, the translational stiffness here is described as a distributed spring stiffness, how can I find out the actual or visualize the spring position in the model. In other words, normally in a problem, a spring will be acted on one point, but here in PDE it is defined as a distributed spring stiffness, what does a distributed spring stiffness mean? for example, I got a edge with length=1meter, then i add the distributed spring in PDE on this edge, will the spring only act on the two endpoints of the edge or the spring will be acted on the whole edge? It really confused me cause I haven't search some useful information on this kind of distributed spring sitffness, I could only find something about the distrubuted load and how to transfer that distributed load into a point load.

If any one knows this distributed spring stiffness and knows how to visulize them in PDE toolbox, PLZ give me some suggestions.

Kind regards,

Jay

[Dolon Mandal]

You can try the following code:

% Create a PDE model
model = createpde();

% Define your geometry and specify the boundary conditions

% Add the distributed spring stiffness
structuralBoundaryLoad(model, 'edge', 3, 'TranslationalStiffness', [1; 0]);

% Generate the finite element mesh
generateMesh(model);

% Assemble the finite element matrices
assembleFEMatrices(model);

% Solve the model
results = solvepde(model);

% Visualize the displacement and deformation
pdeplot(model, 'XYData', results.Displacement, 'Deformation', 'on');

Answer 1

[Avni Agrawal]

Hi @jiye zhou,

When you're dealing with distributed spring stiffness in the PDE Toolbox, it's essential to understand how this concept is applied within the framework of finite element analysis (FEA).

Distributed Spring Stiffness

1. Definition: Distributed spring stiffness refers to the stiffness applied continuously along an edge or surface rather than at discrete points. In your example, the `structuralBoundaryLoad` function applies a translational stiffness along the specified edge, meaning the stiffness is uniformly distributed across the entire length of that edge.

2. Effect: For an edge of length 1 meter with a distributed spring stiffness, the spring effect is not concentrated at the endpoints but rather spread across the whole edge. This means every infinitesimal segment of the edge experiences the same stiffness.

3. Visualization: In terms of visualization, the PDE Toolbox itself may not provide a direct visualization of the spring stiffness. However, you can visualize the effects of the stiffness by observing the deformation or stress distribution in the model once you solve the PDE. This can be done using the `pdeplot` function or similar visualization tools to show how the structure behaves under load with the applied stiffness.

4. Comparison with Point Springs: Contrast this with a point spring, which would apply stiffness at a specific node or point in the model. The distributed spring is more akin to having an infinite number of very small springs along the edge.

How to Proceed

- Model Verification: To verify the effect of the distributed spring, you can run simulations with and without the spring and compare the results. Look at the deformation patterns or reaction forces to understand how the spring affects the model.

- Documentation and Examples: Refer to the MATLAB documentation for `structuralBoundaryLoad` and related functions. MATLAB's documentation often includes examples that can help you understand the application of distributed stiffness.

- Custom Visualization: If you need a more explicit visualization of where the spring stiffness is applied, consider creating a custom plot that overlays the edge with markers or annotations indicating the presence of the distributed stiffness.

If you are still unsure about the implementation in your specific case, consider reaching out to MATLAB support or community forums where you can get insights from other users who might have tackled similar problems.

I hope this helps!