Deformation due to thermal expansion/contraction

[Hassan2]

Dear all,

I have a 3D cube with a nonuniform distribution of temperature. In order to calculate the deformation of the cube using the finite element method, we need nodal forces. How we calculate the nodal force from the temperature distribution?

I am aware of a the method based on the element thermal strain and element stiffness matrix, but I use a method which is a modification of what we use in the calculation of magnetic nodal force. This method, in context of thermal expansion, calculates the force as the divergence of a tensor called thermal stress tensor. The results, are exactly the same as the other method but easier to implement. I would like to know if the method already exists in this field. I need the answer for writing my paper.

If equations are required, I will write them down.

Your help is highly appreciated.

Thanks.

Hassan

 

[Achy47]

Dear Hassan,

Thank you for your question. The method you are describing is known as the thermal stress method and is commonly used in the field of computational mechanics for calculating nodal forces in thermal analysis. This method involves calculating the thermal stress tensor, which is a measure of the stress induced in a material due to temperature changes.

To calculate the thermal stress tensor, you will need to use the thermal strain and stiffness matrices, as you mentioned. The thermal stress tensor is then calculated as the product of the thermal strain matrix and the stiffness matrix. This tensor can then be used to calculate the nodal forces, as you have described.

The thermal stress method is a well-established and widely used method in the field of thermal analysis, so you can be confident in using it for your research. However, if you would like to explore other methods, there are also other approaches for calculating nodal forces from temperature distributions, such as the element thermal force method and the average nodal temperature method.

I hope this helps and good luck with your research.