An explicit is solved by calculating results in small time increments or time steps. The size of the time step depends
on many factors but is automatically calculated by Radioss.

The two beam elements available in Radioss are used on one-dimensional structures and frames. It carries axial loads, shear forces, bending and torsion
moments (contrary to the truss that supports only axial loads).

Under-integrated elements are very familiar in crash worthiness. In these elements, a reduced number of integration
points are used to decrease the computation time. This simplification generates zero energy deformation modes, called
hourglass modes.

Composite materials consist of two or more materials combined each other. Most composites consist
of two materials, binder (matrix) and reinforcement. Reinforcements come in three forms, particulate,
discontinuous fiber, and continuous fiber.

Optimization in Radioss was introduced in version 13.0. It is implemented by invoking the optimization capabilities of
OptiStruct and simultaneously using the Radioss solver for analysis.

The two beam elements available in Radioss are used on one-dimensional structures and frames. It carries axial loads, shear forces, bending and torsion
moments (contrary to the truss that supports only axial loads).

The two beam elements available in Radioss are used on
one-dimensional structures and frames. It carries axial loads, shear forces, bending and
torsion moments (contrary to the truss that supports only axial loads).

Classical Beam (/PROP/BEAM)

The default formulation is based on the Timoshenko formulation; therefore, transverse
shear strain is taken into account. This formulation can degenerate into the
standard Euler-Bernoulli formulation, where transverse shear energy is
neglected.

Nodes 1 and 2 are used to define the local x-axis. Local y-axis is normal to the
x-axis and is in the plane defined by node 1, 2 and 3 at time t=0. Then its position
is corrected at each cycle, taking into account the mean x-rotation. Local z-axis is
obtained using the right-hand rule.

In Radioss, the beam geometry is defined by its
cross-section area and by its three cross-section area moments of inertia. The area
moments of inertia around local Y-axis and Z-axis are for bending and they can be
calculated using:(1)

The area moment of inertia regarding the local X-axis is for torsion. It can simply
be obtained by the summation of ${I}_{y}$ and ${I}_{z}$. The torsion model is only valid for full
cross-section where the warping is neglected.

The minimum time step for a beam element is determined using:(3)

User input parameters to define beam cross-section are the three area moments of
inertia and the area. For accuracy and stability, it is recommended to respect the
following limitations:(4)

Only material LAW1 and LAW2 are available for this beam element. A global plasticity
model in function of internal forces is used in LAW2. The main assumption is that
the beam cross-section is full and rectangular. Optimal interaction between section
and section inertia are:

$12{I}_{y}{I}_{z}={A}^{4}$

${I}_{x}={I}_{y}+{I}_{z}$

This model also provides good results for circular or ellipsoidal cross-section. For
thin-walled cross-sections, the global plasticity model may provide incorrect
results. It is not recommended to use a single beam element per line of frame
structure. The mass is lumped onto the nodes; therefore, to get a correct mass
distribution, a fine mesh is required. This is especially true when dynamic effects
are important.

Moreover, in Radioss beam element, the moment does not
vary along the beam length. The moment is supposed constant and is evaluated at the
beam center, as is the stress.

Consequently, a beam will yield at a slightly higher force in the case of a clamped
cantilever beam, since the moment is calculated at the center, instead of at the
root of the beam.

Note: Output for beam elements are expressed in the
local system. Some results may be confusing, due to the fact, that the local
system is updated taking into account the mean X rotation.
For instance, a beam with one node completely blocked, if an axial rotational
velocity V is imposed to the other node, then the beam will
rotate at a speed of V, but the local system will rotate at a
speed of V/2. This may lead to a bad
interpretation of results, especially the shear forces and bending
moments.

New Beam (/PROP/INT_BEAM)

The cross-section of the element is defined using up to 100 integration points (Figure 2). The element
properties of the cross-section, that is area moments of inertia and area, are
computed by Radioss as:(5)

Beam model is based on the Timoshenko theory and takes into account transverse shear strain
without warping in torsion. It can be used for deep beam cases (short beams). The
use of several integration points in the section allows to get an elasto-plastic
model, in which von Mises criteria is written on each integration point and the
section can be partially plastified contrary to the classical beam element (TYPE3).
Material LAW36 is also available, as well as LAW1 and LAW2. However, as the element
has only one integration point in its length, it is not recommended to use a single
beam element per line of frame structure in order to take into account the
plasticity progress in length, as well as in depth.