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Force Matrix for Transient Thermal Analysis

  1. Oct 21, 2009 #1

    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

    Research Assistant
    Structural and Multidisciplinary Optimization Lab.
    University of Florida
  2. jcsd
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