# 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

The impacting mass is simulated using a sliding rigid plane wall (/RWALL) having an initial velocity of 10 ms-1and 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-1in 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
Cross section
36 mm2
Moments of inertia in Y and Z
108 mm4
Moments of inertia in X
216 mm4
The steel material used has the following properties:
Material Properties
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.