appendices:a15
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appendices:a15 [2019/06/21 17:18] helene |
appendices:a15 [2020/08/25 15:46] (current) |
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| The computation is performed as shown in the table below: | The computation is performed as shown in the table below: | ||
| ^ NTNOR ^ COMPA(i) ≤ 0 ^ COMPA(i) > 0 ^ | ^ NTNOR ^ COMPA(i) ≤ 0 ^ COMPA(i) > 0 ^ | ||
| - | | 0 |\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{UNOR(i)}{\max(DNOR(i),COMPA(i)²)}} \]|\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{UNOR(i)}{COMPA(i)²}} \]| | + | | 0 |\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{\frac{FNOR(i)}{NFO(i)}}{\max\left(\frac{RNOR(i)}{NRE(i)},\frac{COMPA(i)²}{NRE(i)}\right)}} \]|\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{\frac{FNOR(i)}{NFO(i)}}{COMPA(i)²}} \]| |
| - | | 1 or 2 |\[\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{UNOR(i)}{\max(DNOR(i),-COMPA(i))} \]|\[\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{UNOR(i)}{COMPA(i)} \]| | + | | 1 or 2 |\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{\frac{FNOR(i)}{NFO(i)}}{\max\left(\frac{RNOR(i)}{NRE(i)},\frac{-COMPA(i)}{NRE(i)}\right)}} \]|\[\sqrt{\frac{1}{NDIM} \displaystyle\sum_{i=1}^{NDIM} \frac{\frac{FNOR(i)}{NFO(i)}}{COMPA(i)}} \]| |
| - | Remark: the norm can be absolute for some dimensions and relative for others, in which case the formula need to be adapted. This will be clearer with some examples… \\ | + | Remark: the norm can be absolute for some dimensions and relative for others, in which case the formula needs to be adapted. This will be clearer with some examples… \\ |
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| For 3D analysis (NTANA = ±2) with NTNOR=0 and COMPA(1)=0: | For 3D analysis (NTANA = ±2) with NTNOR=0 and COMPA(1)=0: | ||
| - | \[CONVE=\sqrt{\frac{UNOR(1)}{DNOR(1)}}\] | + | \[CONVE=\sqrt{\frac{\frac{FNOR(i)}{NFO(i)}}{\frac{RNOR(i)}{NRE(i)}}}\] |
| For 3D shell analysis (NTANA = ±8) with NTNOR=0, COMPA(1)<0 and COMPA(3)>0: | For 3D shell analysis (NTANA = ±8) with NTNOR=0, COMPA(1)<0 and COMPA(3)>0: | ||
| - | \[\sqrt{\frac{1}{2} \left(\frac{UNOR(1)}{\max(DNOR(1),COMPA(1)²)} +\frac{UNOR(3)}{COMPA(3)²}\right)} \] | + | \[ CONVE=\sqrt{\frac{1}{2} \left( \frac{\frac{FNOR(1)}{NFO(1)}}{\max\left(\frac{RNOR(1)}{NRE(1)},\frac{COMPA(1)²}{NRE(1)}\right)} +\frac{\frac{FNOR(3)}{NFO(3)}}{COMPA(3)²}\right)} \] |
| ==== Step 4: Check the convergence of the step ==== | ==== Step 4: Check the convergence of the step ==== | ||
| - | The step is converged for the displacements if $CONVE \leq PRECD$ \\ | + | The step is converged for the displacements if $CONVE \leq PRECF$ \\ |
| - | For example, for 3D analysis (NTANA = ±2) with NTNOR=0 and COMPA(1)=-10<sup>-1</sup> and PRECD=10<sup>-2</sup>, the step is converged if: | + | For example, for 3D analysis (NTANA = ±2) with NTNOR=0 and COMPA(1)=-10<sup>-1</sup> and PRECF=10<sup>-2</sup>, the step is converged if: |
| - | \[\sqrt{\frac{UNOR(1)}{\max(DNOR(1),COMPA(1)²)}} \leq PRECD \\ <=> \sqrt{\frac{UNOR(1)}{\max(DNOR(1),10^{-2})}} \leq 10^{-2} \\ <=> UNOR(1) \leq 10^{-4}*\max(DNOR(1),10^{-2})\] | + | \[\sqrt{\frac{\frac{FNOR(1)}{NFO(1)}}{\frac{\max(RNOR(1),COMPA(1)²)}{NRE(1)}}} \leq PRECF \\ <=> \sqrt{\frac{\frac{FNOR(1)}{NFO(1)}}{\frac{\max(RNOR(1),10^{-2})}{NRE(1)}}} \leq 10^{-2} \\ <=> \frac{FNOR(1)}{NFO(1)} \leq 10^{-4}*\frac{\max(RNOR(1),10^{-2})}{NRE(1)}\] |
| - | If $DNOR(1)=10^{-8}$, the step is converged if $UNOR(1) \leq 10^{-4}*10^{-2}=10^{-6}$ \\ | + | If $RNOR(1)=10^{-8}$, the step is converged if $\frac{FNOR(1)}{NFO(1)} \leq 10^{-4}*\frac{10^{-2}}{NRE(1)}=\frac{10^{-6}}{NRE(1)}$ \\ |
| - | If $DNOR(1)=10^{-1}$, the step is converged if $UNOR(1) \leq 10^{-4}*DNOR(1)=10^{-5}$ \\ | + | If $RNOR(1)=10^{-1}$, the step is converged if $\frac{FNOR(1)}{NFO(1)} \leq 10^{-4}*\frac{RNOR(1)}{NRE(1)}=\frac{10^{-5}}{NRE(1)}$ \\ |
appendices/a15.1561130337.txt.gz · Last modified: 2020/08/25 15:33 (external edit)
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