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FEM problem

  1. Oct 1, 2007 #1
    1. The problem statement, all variables and given/known data
    An element mesh is based on the following 3-node and 4-node elements (0,0) (0.5,0.5) (0,1) (1.5,0) (1.5,0.5). The approximation for the 4-node elements is T = a1 +a2x +a3y +a4xy, while the approximation for the 3-node element is T = b1 +b2x +b3y. Is the converegence criterion fulfilled?

    3. The attempt at a solution

    I looked in the book and found that for the convergence criterion both completeness and compatibility or conforming requirement be satisfied.

    *the approximation of the displacement vector u must be able to represent an arbitrary constant rigid-body motion

    *the approximation of the displacement vector u must be able to represent an arbitrary constant strain state

    compatibility or conforming requirement.:
    *The approximation of the displacement vector u must vary in a continuous manne over element boundaries.

    The solution says
    The completeness requirement is fulfilled for both elements. To fulfill the compatibility requirement the approximated field must be continues i.e the approximation must be uniquely determined by the nodal values on the boundaries. This is not satisfied for the current configuration, i.e compatibility is not satisfied.

    So, here I have both the question and the solution, the problem is that I dont understand it. Can anyone help? I dont really understand how to check for the criterias and what they really mean.
  2. jcsd
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