# IV. Description of the Elements

## A. Introduction

This chapter describes the finite elements available in the ATILA code. For each element, the name, definition, list ofthe degrees-of-freedom associated with the nodes (translations, rotations, electricalpotential, magnetic potential, pressure), and entry parameters (topology,material properties, geometrical properties) are provided.

Most of the elements in the ATILA library are isoparametric. Thus, complex structures withcurved sides or faces can be modeled using a reduced number of elements. Nevertheless, the best results are obtained when these elements have a reasonable aspect ratio. Wild distortions lead to inaccuracies because the assumptions made within thecode for strains become unrealistic. Extreme distortion may even cause programfailure (negative Jacobian determinant). The user should guard againstexcessive distortion by adhering to the following guidelines for sides of 2-D elements or for faces of 3-D elements:

- The angles between adjacent sides of quadrilaterals should bebetween 45 and 135 degrees
- The angles between adjacent sides of triangles should be between30 and 100 degrees
- In elements with curved sides, the radius of curvature of eachside should exceed the length of the longest side
- For one element, the ratio between the smallest and largestdimensions must be less than or equal to 3 in single precision and 5 in doubleprecision
- Mid-side nodes must be at equal distance from their respectivecorner nodes.

Element node numbering generally follows simple rules:

- Corner nodes first, then mid-side nodes (the only exception isthe SHEL03E element).
- The first node gives the axis center, local to the element.
- The second node gives the direction of local Ox axis.
- The third node, when available, gives the direction of local Oyaxis.

WARNING

All data (except the angles) must be givenusing MKS units or any coherent unit system deduced from the MKS system. Angles are always in degrees.