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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

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# Force Matrix for Transient Thermal Analysis

Can you offer guidance or do you also need help?

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