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View new features for Radioss 2024.1.
Overview
Radioss^® is a leading explicit finite element solver for crash and impact simulation.
Tutorials
Discover Radioss functionality with interactive tutorials.
User Guide
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
Reference Guide
This manual provides a detailed list of all the input keywords and options available in Radioss.
Example Guide
This manual presents examples solved using Radioss with regard to common problem types.
Verification Problems
This manual presents solved verification models.
Frequently Asked Questions
This section provides quick responses to typical and frequently asked questions regarding Radioss.
Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
- Large Displacement Finite Element Analysis Theory Manual
  - Introduction
    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.
  - Basic Equations
  - Finite Element Formulation
  - Dynamic Analysis
    - Direct Integration Method: Explicit Scheme
      - Newarks Method
      - Central Difference Algorithm
      - Numerical Starting Procedure
      - Algorithm Flow Chart
      - Body Drop Example
      - Numerical Stability
        The definition of numerically stability is similar to the stability of mechanical systems. A numerical procedure is stable if small perturbations of initial data result in small changes in the numerical solution.
      - Explicit Scheme Stability
      - Courant Condition Stability
        Radioss uses elements with a lumped mass approach. This reduces computational time considerably as no matrix inversion is necessary to compute accelerations.
      - Time Step Control
      - Time Step Control Limitations
    - Large Scale Eigen Value Computation
    - Combine Modal Reduction
  - Element Library
    Radioss element library contains elements for one, two or three dimensional problems.
  - Kinematic Constraints
    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.
  - Linear Stability
    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.
  - Interfaces
    Interfaces solve the contact and impact conditions between two parts of a model.
  - Material Laws
    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.
  - Monitored Volume
    An airbag is defined as a monitored volume. A monitored volume is defined as having one or more 3 or 4 node shell property sets.
  - Static
    Explicit scheme is generally used for time integration in Radioss, in which velocities and displacements are obtained by direct integration of nodal accelerations.
  - Radioss Parallelization
    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.
- ALE, CFD and SPH Theory Manual
- Appendix A: Basic Relations of Elasticity
User Subroutines
This manual describes the interface between Altair Radioss and user subroutines.

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Central Difference Algorithm

The central difference algorithm corresponds to the Newmark algorithm with $γ = \frac{1}{2}$ and $β = 0$ so that Newarks Method, Equation 7 and Equation 8 become:

{\dot{u}}_{n + 1} = {\dot{u}}_{n} + \frac{1}{2} h_{n + 1} ({\ddot{u}}_{n} + {\ddot{u}}_{n + 1})

u_{n + 1} = u_{n} + h_{n + 1} {\dot{u}}_{n} + \frac{1}{2} h_{n + 1}^{2} {\ddot{u}}_{n}

with $h_{n + 1}$ the time step between $t_{n}$ and $t_{n + 1}$ .

It is easy to show that the central difference algorithm ^¹ can be changed to an equivalent form with 3 time steps, if the time step is constant.

{\ddot{u}}_{n} = \frac{u_{n + 1} - 2 u_{n} + u_{n - 1}}{h^{2}}

From the algorithmic point of view, it is, however, more efficient to use velocities at half of the time step:

{\dot{u}}_{n + \frac{1}{2}} = \dot{u} (t_{n + \frac{1}{2}}) = \frac{1}{h_{n + 1}} (u_{n + 1} - u_{n})

so that:

{\ddot{u}}_{n} = \frac{1}{h_{n + \frac{1}{2}}} ({\dot{u}}_{n + \frac{1}{2}} - {\dot{u}}_{n - \frac{1}{2}})

h_{n + \frac{1}{2}} = (h_{n} + h_{n + 1}) / 2

Time integration is explicit, in that if acceleration

{\ddot{u}}_{n}

is known (Combine Modal Reduction), the future velocities and displacements are calculated from past (known) values in time:

${\dot{u}}_{n + \frac{1}{2}}$ is obtained from Equation 5:
${\dot{u}}_{n + \frac{1}{2}} = {\dot{u}}_{n - \frac{1}{2}} + h_{n + \frac{1}{2}} {\ddot{u}}_{n}$

The same formulation is used for rotational velocities.

$u_{n + 1}$ is obtained from Equation 4:
$u_{n + 1} = u_{n} + h_{n + 1} {\dot{u}}_{n + \frac{1}{2}}$

The accuracy of the scheme is of $h^{2}$ order, that is, if the time step is halved, the amount of error in the calculation is one quarter of the original. The time step $h$ may be variable from one cycle to another. It is recalculated after internal forces have been computed.

¹ Ahmad S., Irons B.M., and Zienkiewicz O.C., Analysis of thick and thin shell structures by curved finite elements, Computer Methods in Applied Mechanics and Engineering, 2:419-451, 1970.