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.

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.

Beam type spring elements are best defined using three nodes (Figure 1). Nodes 1 and 2 are the two ends of the element and define
the local X axis. Node 3 allows the local Y and Z axes to be defined. However, this node
does not need to be supplied.

If all three nodes are defined, the local reference frame is calculated by:(1)

If node 3 is not defined, the local skew frame that can be specified for the element is
used to define the Z axis. The X and Y axes are defined in the same manner as
before.(4)

If no skew frame and no third node are defined, the global Y axis is used to replace the Y
skew axis. If the Y skew axis is collinear with the local X axis, the local Y and Z axes are
placed in a totally arbitrary position. The local Y axis is defined at time zero, and is
corrected at each cycle, taking into account the mean X axis rotation.