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Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
Large Displacement Finite Element Analysis Theory Manual
Element Library
Radioss element library contains elements for one, two or three dimensional problems.
Solid Hexahedron Elements
Shock Waves

ヘルプトップ
新機能
Radioss 2024の新機能を確認できます。
概要
Radioss^®は、衝突と衝撃ソリューションのための優れた陽解法有限要素ソルバーです。
Tutorials
Discover Radioss functionality with interactive tutorials.
ユーザーガイド
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
リファレンスガイド
本マニュアルは、Radiossで使用することのできるすべての入力キーワードとオプションを詳細なリストで提供しています。
例題集
このマニュアルは一般的な問題のタイプに関して、Radiossを用いて解かれた例題を示します。
検証問題
このマニュアルでは、解析済みの検証モデルを紹介します。
よくある質問
このセクションでは、Radiossに関するよくある質問へのクィックレスポンスを提供しています。
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
  - Element Library
    Radioss element library contains elements for one, two or three dimensional problems.
    - Solid Hexahedron Elements
      - Linear Brick Shape Functions
      - Strain Rate
      - Assumed Strain Rate
      - Internal Force Calculation
      - Hourglass Modes
      - Stability
      - Shock Waves
      - Element Degeneration
        Element degeneration is the collapsing of an element by one or more edges. For example: making an eight node element into a seven node element by giving nodes 7 and 8 the same node number.
      - Internal Stress Calculation
      - Deviatoric Stress Calculation
    - Solid Tetrahedron Elements
    - Shell Elements
    - Solid-Shell Elements
    - Truss Elements (TYPE2)
    - Beam Elements (TYPE3)
    - One Degree of Freedom Spring Elements (TYPE4)
    - General Spring Elements (TYPE8)
    - Pulley Type Spring Elements (TYPE12)
    - Beam Type Spring Elements (TYPE13)
    - Integrated Beam Elements (TYPE 18)
      Beam type /PROP/TYPE18 uses a shear beam theory or Timoshenko formulation like /PROP/TYPE3, but the section inputs (area, inertia) can be default values and can also be discretized by sub-sections; numerical integrations are used to calculate internal forces.
    - Multistrand Elements (TYPE28)
      Multistrand elements are n-node springs where matter is assumed to slide through the nodes.
    - Spring Type Pretensioners (TYPE32)
  - 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.

Shock Waves

Shocks are non-isentropic phenomena, that is, entropy is not conserved, and necessitates a special formulation.

The missing energy is generated by an artificial bulk viscosity

q

as derived by von Neumann and Richtmeyer. ^¹ This value is added to the pressure and is computed by:

図 1.

q = q_{a}^{2} ρ l^{2} {(\frac{\partial ε_{k k}}{\partial t})}^{2} - q_{b} ρ l c \frac{\partial ε_{k k}}{\partial t}

Where,

l: Is equal to $\sqrt[3]{Ω}$ or to the characteristic length
$Ω$: Volume
$\frac{\partial ε_{k k}}{\partial t}$: Volumetric compression strain rate tensor
$c$: Speed of sound in the medium

The values of

q_{a}

and

q_{b}

are adimensional scalar factors defined as:

$q_{a}$ is a scalar factor on the quadratic viscosity to be adjusted so that the Hugoniot equations are verified. This value is defined by the user. The default value is 1.10.
$q_{b}$ is a scalar factor on the linear viscosity that damps out the oscillations behind the shock. This is user specified. The default value is 0.05.

Default values are adapted for velocities lower than Mach 2. However, for viscoelastic materials (LAW34, LAW35, LAW38) or honeycomb (LAW28), very small values are recommended, that is, 10^-20.

¹ Von Neumann J. and Richtmeyer R., A method for the numerical calculation of hydrodynamical shocks, Journal of applied physics, 1950.