/ALE/SOLVER/FINT

Block Format Keyword This option defines the numerical method for internal force integration. This is relevant only for brick element and ALE legacy solver (momentum equation solved with FEM).

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/ALE/SOLVER/FINT
`Iform`

Definitions

Field	Contents	SI Unit Example
`Iform`	Integration method (internal force for brick elements) flag. = 0 Set to 3. = 1 Volume integration of the stress tensor using a shape function. = 2 Surface integration for the hydrostatic stress tensor only. = 3 (Default) Surface integration for the stress tensor. (Real)

Field

Contents

SI Unit Example

Iform

Integration method (internal force for brick elements) flag.

= 0: Set to 3.
= 1: Volume integration of the stress tensor using a shape function.
= 2: Surface integration for the hydrostatic stress tensor only.
= 3 (Default): Surface integration for the stress tensor.

(Real)

Comments

Momentum equation has local form:
(1)
$\frac{\partial ρ u}{\partial t} + d i v (ρ u u) = d i v (σ) + ρ g$ $\frac{\partial ρ u}{\partial t} + d i v (ρ u u) = d i v (σ) + ρ g$

Iform is a flag defining the numerical method to compute $d i v (σ)$ $d i v (σ)$ when integrated over the cell with legacy solver (nodal velocities).

Iform=1

$F_{int} = \int_{Ω}^{} d i v (σ) d V$ $F_{int} = \int_{Ω}^{} d i v (σ) d V$

Was the default method up to Radioss version 2019.

Iform=2

$F_{int} = - \int_{\partial Ω}^{} p d S + \int_{Ω}^{} d i v (σ) d V$ $F_{int} = - \int_{\partial Ω}^{} p d S + \int_{Ω}^{} d i v (σ) d V$

The integration method used with obsolete card /CAA (Obsolete)

Iform=3

$F_{int} = \int_{\partial Ω}^{} (- p I + σ_{d e v}) d S$ $F_{int} = \int_{\partial Ω}^{} (- p I + σ_{d e v}) d S$

The integration method used as of Radioss version 2020.

For volume integration, shape functions are used to compute at node, N:(2)
$F_{int}^{i N} = σ_{i k} {\frac{\partial Φ_{N}}{\partial x_{k}} |}_{0} | Ω |$ $F_{int}^{i N} = σ_{i k} {\frac{\partial Φ_{N}}{\partial x_{k}} |}_{0} | Ω |$

Where, $i = 1, 3$ $i = 1, 3$

The value ${\frac{\partial Φ_{N}}{\partial x_{k}} |}_{0}$ ${\frac{\partial Φ_{N}}{\partial x_{k}} |}_{0}$ is taken at the integration point. It is assumed that:(3)
$\frac{\partial Φ_{N 1}}{\partial x_{j}} = - \frac{\partial Φ_{N 7}}{\partial x_{j}}; \frac{\partial Φ_{N 2}}{\partial x_{j}} = - \frac{\partial Φ_{N 8}}{\partial x_{j}}; \frac{\partial Φ_{N 3}}{\partial x_{j}} = - \frac{\partial Φ_{N 5}}{\partial x_{j}}; \frac{\partial Φ_{N 4}}{\partial x_{j}} = - \frac{\partial Φ_{N 6}}{\partial x_{j}}$ $\frac{\partial Φ_{N 1}}{\partial x_{j}} = - \frac{\partial Φ_{N 7}}{\partial x_{j}}; \frac{\partial Φ_{N 2}}{\partial x_{j}} = - \frac{\partial Φ_{N 8}}{\partial x_{j}}; \frac{\partial Φ_{N 3}}{\partial x_{j}} = - \frac{\partial Φ_{N 5}}{\partial x_{j}}; \frac{\partial Φ_{N 4}}{\partial x_{j}} = - \frac{\partial Φ_{N 6}}{\partial x_{j}}$

This assumption is exact for parallelepipedic shape only, which is why the new default value method is set to surface integration (Iform=3).