# Curved beam

## 1 Model

For this test, a curved beam fixed onto the ground on one end is considered, as shown in the figure below:

The structure corresponds to a quarter of a circle with radius
$$r = 4.22\text{ m}$$
. The cross section has a height and a width of
$$h=0.2\text{ m}$$
and
$$w=0.1\text{ m}$$
, respectively. The elastic modulus of the material is
$$E = 10\cdot10^6\text{ Pa}$$
and the Poisson ratio is
$$\nu = 0.25$$
. The structure is divided into 6 elements. more details can be found in Macneal et al. (1985)

## 2 Benchmarks

### 2.1 In plane shear

For this benchmark, a force
$$F_z = -1\text{ N}$$
is applied in the z-direction, as shown in the figure below:

According to Macneal et al. (1985), the expected displacement of the tip in the z-direction is
$$d_z = 0.08734\text{ m}$$
.

### 2.2 Out-of-plane shear

For this benchmark, a force
$$F_x = 1\text{ N}$$
is applied in the x-direction, as shown in the figure below:

According to Macneal et al. (1985), the expected displacement of the tip in the y-direction is
$$d_y = 0.5022\text{ m}$$

## 3 Results

The tests are considered passed when the last 20% of the time series from Ashes is within 2% of the results from Macneal et al. (1985)

The report for this test can be found on the following link: