How to model non linear governing equation in FEA?

In summary: In a linear spring model for materials, the governing matrix equation is K * U = Fwhere K is the material stiffness AE/l , u is the displacement at each nodes and F is the force in the discretized elements.But this is only true for a linear spring. If you have a nonlinear spring, you need to generate a matrix that includes the nonlinear governing equation. You can do this by adding a term to the governing equation that represents the nonlinearity.
  • #1
hihiip201
170
0
Hi:in a linear spring model for materials, the governing matrix equation is K * U = F

where K is the material stiffness AE/l , u is the displacement at each nodes and F is the force in the discretized elements.but this is only true for a linear spring, what if I have some non linear spring? I know there's no such thing but what if I now have some other physics that I would like to model that involves a non linear governing equation? how would I model my matrix?
thank you hihiip201
 
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  • #2
hihiip201 said:
but this is only true for a linear spring, what if I have some non linear spring? I know there's no such thing

You have that backwards. In real life there is not such thing as a linear spring, but linear is a good enough approximation for a many purposes.

For an elastic nonlinear material, you can make E a function of the strain in the material. You need to do an iteration until the solution converges with consistent values of E and the strain.

If the material behavior is plastic (i.e. when you remove the loads, the displacements do not return to zero), that is too complicated to explain how to model it here - get a textbook on nonlinear FE analysis!
 
  • #3
AlephZero said:
You have that backwards. In real life there is not such thing as a linear spring, but linear is a good enough approximation for a many purposes.

For an elastic nonlinear material, you can make E a function of the strain in the material. You need to do an iteration until the solution converges with consistent values of E and the strain.

If the material behavior is plastic (i.e. when you remove the loads, the displacements do not return to zero), that is too complicated to explain how to model it here - get a textbook on nonlinear FE analysis!


But with E as a function of strain (so I guess i will have something like: K u^n = F.)

can I call u^n at some node constant and then solve the system like it was still linear?


or do I have to do :

logK + n logn = log F to generate a matrix?



thanks
 
  • #4
In a progressive rate spring, k increases as the spring is compressed.
 

Related to How to model non linear governing equation in FEA?

1. How do I determine the non-linear governing equation for my FEA model?

The non-linear governing equation for an FEA model is typically determined through a combination of theoretical analysis and experimental data. This involves identifying the relevant physical principles and parameters that describe the behavior of the system, and then using these to construct the governing equation. It is important to carefully consider the non-linear effects that may be present, such as material non-linearity or geometric non-linearity.

2. What is the difference between linear and non-linear governing equations in FEA?

The main difference between linear and non-linear governing equations in FEA is that a linear equation assumes a linear relationship between the input and output variables, while a non-linear equation allows for a more complex relationship. In FEA, this typically means that a linear equation assumes small displacements and/or strains, while a non-linear equation allows for large displacements and/or strains.

3. Can I use the same approach to model non-linear governing equations in FEA as I would for linear equations?

No, the approach for modeling non-linear governing equations in FEA is different from that of linear equations. Non-linear equations require more sophisticated numerical techniques, such as iteration or time-stepping, to solve. Additionally, the parameters and assumptions used in linear equations may not be valid for non-linear equations, so it is important to carefully consider the specific behavior of the system when modeling non-linear equations.

4. How do I validate the results of a non-linear FEA model?

Validating the results of a non-linear FEA model is a critical step in the analysis process. This typically involves comparing the results to experimental data or analytical solutions, and assessing the accuracy and reliability of the model. It is important to carefully consider the assumptions and limitations of the model, as well as the quality of the data used for validation.

5. Are there any common pitfalls to avoid when modeling non-linear governing equations in FEA?

Yes, there are several common pitfalls to avoid when modeling non-linear governing equations in FEA. These include neglecting important non-linear effects, using inappropriate assumptions or parameters, and not properly validating the results. It is also important to carefully consider the convergence and stability of the solution, as non-linear equations can be more prone to numerical errors. It is recommended to consult with experienced FEA analysts or refer to established guidelines and best practices to avoid these pitfalls.

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