The total energy error (TEE) is reported in the output file (*.out) and captures the discontinuity of the stress contour from one element to another, or else the discretization error due to insufficient mesh density.
For each element, the stress error εσ at each node between the element stress and the averaged nodal stress is approximated by:
εσ = {σ} - {σave} , where
{σ} : is the element stress vector at a node. If there are N elements that share a common node, that node has N element stress vectors.
{σave}: is the average stress vector at a node. If there are N elements that share a common node, the stress values from all N elements are summed and divided by N to give the average stress vector at that node.
The program integrates the stress error over the entire volume of the model and reports the total energy error (TEE):
If the mesh is fine enough such that two neighboring elements have perfectly continuous stress contours, the stress error at each node would be zero.
To reduce the total energy error (TEE), refine the mesh in areas of high stress concentration.
The average percentage error (APE) normalizes the stress energy error over the total strain energy (TSE) given by:
, where {ε} is the element strain vector, and D is the material stiffness matrix.
The average percentage error (APE) is calculated as:
