5. Implementation in Code_Aster

5.1. Use

The treatment of large displacements for multifibre beams POU_D_TGM is accessed by selecting the deformation “GROT_GDEP” under COMPORTEMENT.

All 1D nonlinear behaviors are available.

5.2. Development

5.2.1. Correction matrix

The expression for the correction matrix due to taking into account moderate rotations is given in (). It comes at the end of the calculation of the tangent stiffness, since it comes in the form of a fully integrated term. The only obstacle concerns the bending moments that constitute this all-integrated term, in fact, they are the bending moments at the nodes of the element, while they are only known at Gauss points (following the integration of the law of behavior).

It is therefore either possible to use the calculation of \({W}_{\text{int}}^{1}\) to extract the moments or else to interpolate the values at the nodes using a polynomial of order 2. It is this last solution that was chosen, because at the beginning of each time step, it is not possible to extract these values from the work, because the latter is not calculated (at the beginning of each time step, only a speed tangent stiffness matrix is assembled for the prediction phase).

Once the values are interpolated, we therefore content ourselves with correcting the geometric rigidity matrix. This is done just after the end of the loop on the Gauss points.

5.2.2. Improved deformation calculation

As noted, this calculation is only relevant when the geometry of the structure is updated at each iteration.

To be able to perform this new calculation, it is necessary to be able to store the deformation increment at each Gauss point and after each iteration (it is a 7-dimensional vector). This information is stored in the field specific to structural elements STRX_ELGA.

This field is also used to store generalized forces because the data from the fiber stress field alone cannot be sufficient to go back to the shear forces, the torsional moment and the bi-moment.