Force Matrix for Transient Thermal Analysis

[Shriram]

Hi,

I have developed a 2D transient thermal analysis FE code which doesn't
seem to be correct. I am sure there is a conceptual problem in the
formulation itself which I have not been able to understand and could
not find concrete information in books.

I am putting up the question in a very simplified form so as to address the correctness of the formulation.

Let's say we have a square of unit length with 4 nodes at each corner
(Q4 element). Initial temperatures are specified as 100 for all nodes
(at t=0). The temperature of the nodes 1 and 2 are specified as 200
and 300 at the first time step and we investigate the temperature distribution on other 2
nodes with time say 0 to 100 seconds (with the specified temperatures
maintained). No other thermal load is applied.

-- Now, while solving the FE discreet equation, during the first time step would there be any force matrix on the R.H.S?

-- If no, then would the R.H.S be simply (1/dt)*C*tn (using time integration parameter'theta=1'). 'C' being the specific heat matrix, 'tn' is vector of initial dofs and
'dt' is time-step. (Reference: Ansys theory manual, transient thermal
analysis, eq 17-33)

I have tried to keep the problem as simple as possible without much
theory. Hope it is clear. Any suggestion or comment is deeply
appreciated.

Thanks,
Shriram
------------------------
Research Assistant
Structural and Multidisciplinary Optimization Lab.
University of Florida

 

[Achy47]

Dear Shriram,

Thank you for reaching out with your question about your 2D transient thermal analysis FE code. Based on the information provided, it seems that you may be experiencing a conceptual problem in your formulation. In order to address the correctness of your formulation, it would be helpful to have more information about your specific code and equations. However, I will do my best to provide some general guidance and suggestions.

Firstly, to answer your first question, during the first time step, there may or may not be a force matrix on the R.H.S, depending on the specific equations and boundary conditions used in your formulation. Without further details, it is difficult to determine for certain.

As for your second question, the R.H.S would typically include both the specific heat matrix and the temperature vector at the previous time step (tn). However, again, this may vary depending on the specific equations and time integration method used.

In general, when developing a FE code, it is important to thoroughly understand the underlying theory and equations being used. It may be helpful to consult with experts in the field or refer to textbooks and other resources for a better understanding of the concepts involved.

I hope this helps in addressing your concerns and I wish you the best of luck in your research.