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.

Mesh recommendations in crash worthiness and in Implicit Analysis are
covered.

Number of Elements Recommended

It is recommended to set a minimum of five to 10 elements in a structural working length. For
buckling situation, five to 10 elements along one buckle wave length is also
recommended (Figure 1).

On the other hand, due to the direct relation between the size of the smallest element in the
mesh and the time step, it is valuable to suppress geometry details, if they are
smaller than the average size of elements (Figure 2). A uniform mesh allows you to optimize time step and to ensure the
consistency of the momentum transmission during shock wave propagation to avoid
parasite reflections. A minimum of three elements along the width is required for
better elasto-plastic behavior.

Observe the minimum number of elements, taking into account the mechanical behavior. The minimum
number of elements in the width is:

1 for the parts working with quasi-uniform stress distribution as
pressure and shear loading without bending

2 for elastic behavior, including bending

3 for low accuracy elastoplastic behavior

5 for good accuracy elastoplastic behavior

10 for good accuracy elastoplastic behavior, including local
loading or local discontinuities

Mesh Transition

It is not recommended to use different kinds of element formulation in a given physical part. Fully-integrated and under-integrated elements do not have the same stiffness matrices; but they do have the same mass matrix. The transition of momentum between these two kinds of elements may be a problem.

To reduce the number of triangles and to improve the consistency of the mesh, the transition
patterns illustrated in Figure 4 can be used.

Mesh Patterns

With one integration point, there are no element shapes for which the element formulation becomes
completely wrong (elements with angles larger than 180 degrees are still working
with bad accuracy, but without numerical problems). It is recommended to use
elements as regular as possible with an angle typically between 45 and 120 degrees.
The ratio between the largest and smallest edge is not critical for explicit
formulation. A uniform mesh is recommended to distribute mass uniformly over the
structure. It is possible to avoid triangle creation, even for a triangular geometry
or a circle (Figure 5).

In Radioss what kind of mesh quality given often depends on the
robustness of the elements. Often, an explicit run has different exigencies than an
implicit one, for example, homogeneous mesh is more important for explicit (due to
time step), than implicit and positive Jacobi warpage, skewness and aspect ratio are
more important for implicit (due to convergence), than explicit. Initially, getting
a good mesh quality condition is necessary for a good simulation result.