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).

This spring is a simplification of spring TYPE13; in which the properties of the spring cross-section are considered
to be invariable with respect to Y and Z.

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.

Spring TYPE13 functions like a beam element with several independent modes of deformation:

Traction / Compression

Torsion

Bending (2 modes)

Shear (2 modes)

Contrary to a beam element, relations between displacements (resp. rotations) and forces (resp.
moments) are not deducted from the geometry (area, length, and moment of inertia) and
the material properties (Young modulus, shear modulus). Instead, they are user-defined
through different stiffness formulations (see Stiffness Formulation for more details).

Spring TYPE13 works only if the length is not equal to zero. Nodes 1 and 2 are always used to
define the local X-axis. Local Y direction is defined at time t=0 and its position is
updated at each cycle, taking into account the mean X rotation. Initially, the Y-axis
can be defined in different ways. A third node can be used for beam elements. It is also
possible to use the local Y-axis of a skew frame. If a skew frame and third node are not
defined, global Y-axis replaces the Y skew axis. If the Y skew axis is co-linear with
the local X-axis, the local Y-axis and Z-axis are put in an arbitrary position. The
Z-axis is finally computed as the cross product of X-axis and Y-axis.

An illustration of a beam type spring is shown below (Figure 2).

A bending deformation is illustrated in Figure 3. This
deformation only takes into account the difference of the two nodes rotations. Beam
double bending does generate bending deformation; but shear deformation is shown
below.

The beam type spring behaves as a physical beam, in which the variation of bending moment in
length generates the increase in shear. The shear force in the spring implies the change
of bending moment.

Note: When defining the spring properties, it is strongly
recommended to introduce values with physical meanings. A spring with high shear
stiffness and a zero bending stiffness is not recommended and may lead to incorrect
results.

Contrary to spring TYPE8, rigid body rotation is possible without any artificial force and moment
generation for spring TYPE13. Behaviors of spring TYPE8 and TYPE13 under a rigid body
rotation are compared in Figure 5.

To compute the critical time step, the same formula as spring TYPE4 is applied; the minimum
overall degree of freedom is finally kept. Therefore to take into account the coupling
between bending and shear, and the stiffness' in bending are modified:(1)

$${K}_{yy}\approx {K}_{yy}+{l}^{2}{K}_{z}$$

(2)

$${K}_{zz}\approx {K}_{zz}+{l}^{2}{K}_{y}$$

Between spring TYPE8 and TYPE13, the sign conventions is not the same, therefore results may be
rather confusing when trying to compare both spring. For spring TYPE13, the deformation
sign is based on the variation of initial length.

For a spring subjected to axial tension, the deformation will always be positive (Figure 6). This
is not true any longer for spring TYPE8, since this spring can have a zero length for
one (or all) direction, positive and negative spring deformations cannot be defined with
the variation of initial length. The sign convention chosen for all degrees of freedom
is that a deformation is positive (resp. negative), if displacement (or rotation) of
node 2 minus displacement (or rotation) of node 1 is positive (resp. negative).

Figure 7
illustrates the difference between spring TYPE8 and TYPE13, resulting from the sign
conventions in Radioss.