# RD-E: 0500 Beam Frame

A beam frame receives an impact from a mass having initial velocity.

A beam frame with clamped extremities receives an impact at its mid-point from a pointed mass
having initial velocity. The material is subjected to the elasto-plastic law of
Johnson-Cook. The model is meshed with beam elements. An infinite rigid wall with
only one secondary node, including the impacted node, is subjected to the initial
velocity. This example is considered a dynamic problem and the explicit solver is
used.

The explicit approach leads to finding a quasi-static equilibrium of the structure after impact.

## Options and Keywords Used

- Beam
- Plasticity and Johnson-Cook material (/MAT/LAW2 (PLAS_JOHNS))
- Boundary conditions (/BCS)
- Initial velocities (/INIVEL)
- Beam element (/PROP/TYPE3 (BEAM))
- Rigid wall (/RWALL)

The impacting mass is simulated using a sliding rigid plane wall
(/RWALL) having an initial velocity of 10 ms^{-1}and
a mass of 3000 g. Only one secondary node exists: the node O to simulate a point
impact.

Points A, F, F', D, E and E' are fully fixed.

## Input Files

Before you begin, copy the file(s) used in this example to
your working directory.

## Model Description

The purpose of this example is to perform a static analysis using beam elements.

A pointed mass (3 kg) makes an impact at point O of a beam frame (see Figure 4 for the geometry) using a speed of 10
ms

^{-1}in the Z direction. The beams are made of steel and each beam section is square-shaped (each side being 6 mm long).Dimensions are: AB = BC = CD = BE = BF = E'C = CF' = 90 mm.

Points A, D, E, F, E', and F' are fixed.

**Beam Properties****Value**- Cross section
- 36 mm
^{2} - Moments of inertia in Y and Z
- 108 mm
^{4} - Moments of inertia in X
- 216 mm
^{4}

The steel material used has the following properties:

**Material Properties****Value**- Density
- 0.0078 $\left[\frac{g}{m{m}^{3}}\right]$
- Young's modulus
- 200 000 $\left[\mathrm{MPa}\right]$
- Poisson's ratio
- 0.3
- Yield stress
- 320 $\left[\mathrm{MPa}\right]$
- Hardening parameter
- 134.65 $\left[\mathrm{MPa}\right]$
- Hardening exponent
- 1.0

All other coefficients are set to default values. Plasticity is taken into account using LAW2 without failure.

### Model Method

The mesh is a regular beam mesh, each beam being 9 mm long (total = 70 beams).

## Results

### Curves and Animations

The main results refer to the time history of points B and O with regard to displacements and
velocities.