Nonlinear finite element analyses confront users with many choices. An understanding of the fundamental concepts of
nonlinear finite element analysis is necessary if you do not want to use the finite element program as a black box.
The purpose of this manual is to describe the numerical methods included in Radioss.

Kinematic constraints are boundary conditions that are placed on nodal velocities. They are mutually exclusive for each degree
of freedom (DOF), and there can only be one constraint per DOF.

The stability of solution concerns the evolution of a process subjected to small perturbations. A process is considered
to be stable if small perturbations of initial data result in small changes in the solution. The theory of stability
can be applied to a variety of computational problems.

A large variety of materials is used in the structural components and must be modeled in stress analysis problems.
For any kind of these materials a range of constitutive laws is available to describe by a mathematical approach the
behavior of the material.

The airbag simulation used by Radioss uses a special uniform pressure airbag. Hence, regardless of state of inflation or shape, the pressure remains uniform.

This option can be used to inflate an airbag instead of simulating the real unfolding which is difficult numerically.
A jetting effect can be added in order to set a preferential direction for the unfolding.

Explicit scheme is generally used for time integration in Radioss, in which velocities and displacements are obtained by direct integration of nodal accelerations.

The performance criterion in the computation was always an essential point in the architectural conception of Radioss. At first, the program has been largely optimized for the vectored super-calculators like CRAY. Then, a first parallel
version SMP made possible the exploration of shared memory on processors.

The airbag simulation used by Radioss uses a special uniform pressure airbag. Hence, regardless of state of inflation or shape, the pressure remains uniform.

Being the normalized vector between the projection of the center of the element upon
segment (${N}_{1}$, ${N}_{3}$) and the center of element as shown in Figure 1.

$\theta $

The angle between the vector ${\overrightarrow{MN}}_{2}$ and the vector ${\overrightarrow{n}}_{1}$.

$\delta $

The distance between the center of the element and its projection of a point upon
segment (${N}_{1}$, ${N}_{3}$).

The projection upon the segment (${N}_{1}$, ${N}_{3}$) is defined as the projection of the point in direction ${\overrightarrow{MN}}_{2}$ upon the line (${N}_{1}$, ${N}_{3}$) if it lies inside the segment (${N}_{1}$, ${N}_{3}$). If this is not the case, the projection of the point upon
segment (${N}_{1}$, ${N}_{3}$) is defined as the closest node ${N}_{1}$ or ${N}_{3}$. If ${N}_{3}$ coincides to ${N}_{1}$, the dihedral shape of the jet is reduced to a conical
shape.