# Outer edge fixed, inner edge free

## Values for calculation

$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$r_o$ $\mathrm{mm}$
$w$ $\mathrm{N/m}$
$E$ $\mathrm{MPa}$
$ν$
$r$ $\mathrm{mm}$

## Calculation

### Plate constant $C_1$

$$C_1=\cfrac{1+ν}{2}\cdot\cfrac{b}{a}\cdot\ln\left(\cfrac{a}{b}\right)+\cfrac{1-ν}{4}\cdot\left(\cfrac{a}{b}-\cfrac{b}{a}\right)$$

### Plate constant $C_4$

$$C_4=\cfrac{1}{2}\cdot\left[\left(1+ν\right)\cdot\cfrac{b}{a}+\left(1-ν\right)\cdot\cfrac{a}{b}\right]$$

### Plate constant $C_7$

$$C_7=\cfrac{1}{2}\cdot\left(1-ν^2\right)\cdot\left(\cfrac{a}{b}-\cfrac{b}{a}\right)$$

### Function of the radial location $F_1$

$$F_1=\cfrac{1+ν}{2}\cdot\cfrac{b}{r}\cdot\ln\left(\cfrac{r}{b}\right)+\cfrac{1-ν}{4}\cdot\left(\cfrac{r}{b}-\cfrac{b}{r}\right)$$

### Function of the radial location $F_2$

$$F_2=\cfrac{1}{4}\cdot\left[1-\left(\cfrac{b}{r}\right)^2\cdot\left(1+2\cdot\ln\left(\cfrac{r}{b}\right)\right)\right]$$

### Function of the radial location $F_3$

$$F_3=\cfrac{b}{4\cdot r}\cdot\left\{\left[\left(\cfrac{b}{r}\right)^2+1\right]\cdot\ln\left(\cfrac{r}{b}\right)+\left(\cfrac{b}{r}\right)^2-1\right\}$$

### Function of the radial location $F_4$

$$F_4=\cfrac{1}{2}\cdot\left[\left(1+ν\right)\cdot\cfrac{b}{r}+\left(1-ν\right)\cdot\cfrac{r}{b}\right]$$

### Function of the radial location $F_5$

$$F_5=\cfrac{1}{2}\cdot\left[1-\left(\cfrac{b}{r}\right)^2\right]$$

### Function of the radial location $F_6$

$$F_6=\cfrac{b}{4\cdot r}\cdot\left[\left(\cfrac{b}{r}\right)^2-1+2\cdot\ln\left(\cfrac{r}{b}\right)\right]$$

### Function of the radial location $F_7$

$$F_7=\cfrac{1}{2}\cdot\left(1-ν^2\right)\cdot\left(\cfrac{r}{b}-\cfrac{b}{r}\right)$$

### Function of the radial location $F_8$

$$F_8=\cfrac{1}{2}\cdot\left[1+ν+\left(1-ν\right)\cdot\left(\cfrac{b}{r}\right)^2\right]$$

### Function of the radial location $F_9$

$$F_9=\cfrac{b}{r}\cdot\left\{\cfrac{1+ν}{2}\cdot\ln\left(\cfrac{r}{b}\right)+\cfrac{1-ν}{4}\cdot\left[1-\left(\cfrac{b}{r}\right)^2\right]\right\}$$