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.

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.

A rigid body is defined by a main node and its associated secondary nodes. Mass and inertia may
be added to the initial main node location. The main node is then moved to the center of mass,
taking into account the main node and all secondary node masses. Figure 1 shows an idealized rigid body.

The boundary conditions given to secondary nodes are ignored. The rigid body has the boundary
conditions given to the main node only.

A kinematic condition is applied on each secondary node, for all directions. A secondary node is
not allowed to have any other kinematic conditions.

No kinematic condition is applied on the main node. However, the rotational velocities are
computed in a local reference frame. This reference frame is not compatible with all options
imposing rotation such as imposed velocity, rotational, rigid link.

The only exception concerns the rotational boundary conditions for which a special treatment is
carried out. Connecting shell, beam or spring with rotation stiffness to the main node, is not
yet allowed either.