Mathematical relative calculation errors

Table of Contents

Relative errors #

The error values are displayed in the status window after the analysis finishes.

E(U): relative error of the displacement convergence (nonlinear analysis)
E(P): relative error of the force convergence
E(W): relative error of the work convergence
E(ER): condition of the system of equations

The relative error values can not be used to make conclusions about the possible result deviation from the “exact” values, since the “exact” values are unknown. It is merely a measure of the mathematical accuracy of the methods used to solve the equations system.

If the relative error exceeds the value of E>=10^(-5), the corresponding value is shown in red. A large relative error indicates an unstable system of equations. The calculated results are not reliable in this case, and should not be used for further project planning.

Improve accuracy #

Unstable model #

Unstable models (individual components can deform without resistance – The model contains singularities, unstable mode ) typically have large error values. In addition, “singularities in the equation system” is reported in these cases. The relative error of the calculation can be reduced by stabilizing the static system (changing the model).

Model simplification #

Especially with iterative calculations (e.g.: nonlinear static analysis, vibration), the relative error may be reduced by model simplifications in many cases.

Mesh size #

The calculation of relative errors are only minimally affected by the selected mesh size. In order to improve the accuracy of the mathematical solution, model adjustment is needed in almost every case.

A sufficient mesh fineness is evaluated by a result plausibility check (singularities, intensity variation).

Using results in case of large error values #

Results of a calculation with large error values (E>=10^(-5)) should be considered “not reliable” and should not be simply used for the design of structural components. Large error values may be accepted, if the cause is known, and it can be assumed that it has no significant effect on the calculation.

  • Vibration with a low modal mass fraction
  • Error is caused by non-relevant components
    It should be checked whether the affected components can be neglected in the calculation

Related article

  • Page:

The model contains singularities, unstable mode (Knowledge Base)

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