In the standard text output of a Nastran analysis (the .f06 file), two entries are found under USER INFORMATION MESSAGE 5293. The output under this message looks something like this:
LOADSEQ.NO. EPSILON EXTERNAL WORK
1 -3.5565372E-14 2.8650830E+06
Epsilon is a measure of numerical accuracy and round off error provided in the .f06 results file of linear static analysis runs. This round off error is based on a strain energy error ratio, i.e. a ratio of work done by residual forces to the work done by the applied forces. A small value of epsilon, approximately less than 10e-9, indicates a numerically stable problem. On other hand a large value of epsilon is evidence of numerical ill-conditioning. A system of linear equations is said to be ill-conditioned if small perturbations in the system lead to large changes in the solution. Nastran checks for evidence of ill-conditioning in the system of equations representing the structural model. A high value of epsilon indicates a potential ill-conditioning problem. Ill-conditioning does not necessarily result in a fatal error but can result in inaccurate answers.
Possible causes of ill-conditioning include:
a high difference in stiffness between adjacent elements in the model
unconnected degrees of freedom (poorly defined constraint equations)
rigid body motion
or the presence of mechanisms
One epsilon value is generated for each load case. An acceptable value may also be machine dependent. Epsilon should be one of the first items you examine when reviewing your output file. It does not matter whether epsilon is positive or negative, as long as it is small.
External Work as the term implies is the work done by the applied loads. The external work is calculated as ½{P}T{U} and constitutes the denominator to calculate Epsilon.
It is always advised to check the Epsilon values and External Work values of a Nastran analysis to ensure the numerical stability of the structural model. The more complexity in the model, the more crucial it becomes to check and verify these.
LOADSEQ.NO. EPSILON EXTERNAL WORK
1 -3.5565372E-14 2.8650830E+06
Epsilon is a measure of numerical accuracy and round off error provided in the .f06 results file of linear static analysis runs. This round off error is based on a strain energy error ratio, i.e. a ratio of work done by residual forces to the work done by the applied forces. A small value of epsilon, approximately less than 10e-9, indicates a numerically stable problem. On other hand a large value of epsilon is evidence of numerical ill-conditioning. A system of linear equations is said to be ill-conditioned if small perturbations in the system lead to large changes in the solution. Nastran checks for evidence of ill-conditioning in the system of equations representing the structural model. A high value of epsilon indicates a potential ill-conditioning problem. Ill-conditioning does not necessarily result in a fatal error but can result in inaccurate answers.
Possible causes of ill-conditioning include:
a high difference in stiffness between adjacent elements in the model
unconnected degrees of freedom (poorly defined constraint equations)
rigid body motion
or the presence of mechanisms
One epsilon value is generated for each load case. An acceptable value may also be machine dependent. Epsilon should be one of the first items you examine when reviewing your output file. It does not matter whether epsilon is positive or negative, as long as it is small.
External Work as the term implies is the work done by the applied loads. The external work is calculated as ½{P}T{U} and constitutes the denominator to calculate Epsilon.
It is always advised to check the Epsilon values and External Work values of a Nastran analysis to ensure the numerical stability of the structural model. The more complexity in the model, the more crucial it becomes to check and verify these.
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