Analysis diagnostics : Error norm

Static analysis

In a static analysis the error norm is calculated only when ill-conditioning is suspected. The calculation is as follows:

Calculate the residual and solver for residual displacements

$$\begin{aligned} \left\{f_{R}\right\}&=\{f\}-[\mathrm{K}]\{u\} \\ \left\{u_{R}\right\}&=[K]^{-1}\left\{f_{R}\right\} \end{aligned}$$

and then the error is

$$e=\frac{\left\|u_{R}\right\|}{\|u\|}$$

where

$$\|u\|=\sqrt{\sum u_{i}^{2}}$$

These error norms are reported in the Analysis details output.

Modal analysis

In a modal analysis the error norm is always calculated. The calculation for a dynamic analysis is as follows:

$$e=\frac{\|[K]\{u\}-\lambda[M]\{u\}\|}{\| [K]\{u\} \|}$$

and for a buckling analysis:

$$e=\frac{\| K]\{u\}+\lambda\left[K_{g}\right]\{u\} \|}{\|[K]\{u\}\|}$$

These are reported in the Analysis details output.