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Force Matrix for Transient Thermal Analysis

  1. Oct 21, 2009 #1
    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
     
  2. jcsd
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