Load case | Node \(\varvec{I}\) | Basis \(\varvec{r}\) | Single shape function | 1st shape function | 2nd shape function |
---|---|---|---|---|---|
A | 1 | 1 | \(\alpha ^2\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) |
2 | \(\alpha ^2\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) | ||
2 | 1 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
B | 1 | 1 | \(\alpha ^2\) | \(\alpha ^3\) | \(\alpha ^4-\alpha ^3\) |
2 | \(-3\alpha ^4 + 4\alpha ^3\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
2 | 1 | \(\alpha ^2\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) | |
2\(^\mathrm{a}\) | \(\alpha ^3-\alpha ^2\) | \(\alpha ^5 - \alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
C | 1 | 1 | \(\alpha ^2\) | \(\alpha ^3\) | \(\alpha ^4 - \alpha ^3\) |
2 | \(\alpha ^3\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) | ||
2 | 1 | \(\alpha ^2\) | \(\alpha ^3\) | \(\alpha ^4-\alpha ^3\) | |
2\(^\mathrm{a}\) | \(\alpha ^3 - \alpha ^2\) | \(\alpha ^4 - \alpha ^3\) | \(\frac{1}{2} \alpha ^5 - \alpha ^4 + \frac{1}{2} \alpha ^3\) | ||
D | 1 | 1 | \(\alpha ^2\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
2 | 1 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-3\alpha ^4 + 4\alpha ^3\) | \(\frac{1}{2} \alpha ^5 - \alpha ^4 + \frac{1}{2} \alpha ^3\) | |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
E | 1 | 1 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-3\alpha ^4 - 4\alpha ^3\) | \(\frac{1}{2} \alpha ^5 - \alpha ^4 + \frac{1}{2} \alpha ^3\) |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
2 | 1 | \(\alpha ^2\) | \(\alpha ^4\) | \(\alpha ^5 - \alpha ^4\) | |
2\(^\mathrm{a}\) | \(\alpha ^3 - \alpha ^2\) | \(\alpha ^5 - \alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
F | 1 | 1 | \(\alpha ^2\) | \(\alpha ^3\) | \(\alpha ^4 - \alpha ^3\) |
2\(^\mathrm{a}\) | \(\alpha ^3 - \alpha ^2\) | \(\alpha ^5 - \alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
2 | 1 | \(\alpha ^2\) | \(\alpha ^3\) | \(\alpha ^4 - \alpha ^3\) | |
2\(^\mathrm{a}\) | \(\alpha ^3 - \alpha ^2\) | \(\alpha ^5 - \alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
G | 1 | 1 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | ||
2 | 1 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) | |
2 | \(-2\alpha ^3 + 3\alpha ^2\) | \(-4\alpha ^5 + 5\alpha ^4\) | \(\frac{1}{2} \alpha ^6 - \alpha ^5 + \frac{1}{2} \alpha ^4\) |