1. Introduction

The LIAISON_SOLIDE keyword in AFFE_CHAR_MECA commands makes it possible to model an undeformable part of a structure. The principle adopted is to write relationships between the degrees of freedom of the « solid » part; these relationships express the fact that the distances between the nodes are invariable. The relationships expressing the undeformability of a solid are not linear.

To be convinced of this, let’s take the example of a segment \(\mathit{AB}\) in 2D:

The undeformability of \(\mathit{AB}\) is written as:

(1.1)\[\begin{split} \ begin {array} {c} {\ left [\ left ({x}} _ {A} _ {A} + {\ text {xx}}} _ {A}\ right) -\ left ({x} _ {B}} + {\ text {xx}}}}} _ {xx}}} _ {A}\ right) -\ left ({y} _ {B} _ {B} + {\ text {dy}}} _ {B}\ right)\ right]} ^ {2} = {\ left ({x} _ {A} - {A} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} - {x} _ {x} _ {x} _ {x} _ {x} _ {x} _ {x} _ {x} _ {x} _ {}\\\ iff {\ left ({\ text {sx}}} _ {X}}} _ {X}} _ {A}\ right)} ^ {2} +2\ left ({x} _ {B} - {B} - {B} - {X} - {x} - {x} - {x} - {X} - {X} - {X} - {X} - {B} - {B} - {B} - {B} - {B} - {B} - {B} - {B} - {B} - {B} - {B} - {A} - {X} - {B} - {X} - {B} - {B} - {A} - {X} - {X} - {X} - {X} - {X} - {X} - {X left ({\ text {dy}}} _ {B} - {\ text {dy}} - {\ text {dy}}}} _ {A}\ right)} ^ {2} +2\ left ({y} _ {A}\ right)\ left ({\ text {dy}}\ right)\ left ({\ text {dy}}\ right)\ left ({\ text {dy}} - {B} - {y} _ {A}\ right) _ {A}\ right)\ left ({A}\ right)\ left ({\ text {dy}\ right)\ left ({\ text {dy}}\ right) =0\ end {array})\end{split}\]

Noting \(\left\{{x}_{A},{y}_{A},{x}_{B},{y}_{B}\right\}\) the coordinates and \(\left\{{\mathit{dx}}_{A},{\mathit{dy}}_{A},{\mathit{dx}}_{B},{\mathit{dy}}_{B}\right\}\) the movements of \(A\) and \(B\). We can see that the expression is quadratic in \({\text{dx}}_{A},{\text{dx}}_{B},{\text{dy}}_{A}\) and \({\text{dy}}_{B}\) .

When the displacements are small, the quadratic terms are negligible and the linearization of these relationships can be justified. They no longer depend on the displacement and they can be calculated (on the initial geometry) as soon as command AFFE_CHAR_MECA is executed.

On the other hand, when the rotations are finite, the linearization of these relationships depends on the displacement and must therefore be recalculated at each iteration of the Newton algorithm. If the user thinks that the rotations will not remain infinitesimal, they should report it in the STAT_NON_LINE command (keyword EXCIT/TYPE_CHARGE =” SUIV “). The code will then recalculate the linearization of relationships during the calculation.

Taking into account the « follower » type of these relationships is subject to certain restrictions that are detailed in the user documentation (U4.44.01). To « rigidify » a solid part, if the program does not allow the use of LIAISON_SOLIDE, you must use a « hard » material (compared to the rest of the structure).