# Meshing plate structures with solid elements

When analyzing thin-walled structures with solid elements (e.g. tetrahedron elements) the quality of element mesh have a big effect on results accuracy. The behaviour of solid elements in bending is remarkably stiffer than analytical solution would predict because of shear locking effect. The more solid element dimensions are varying inside individual elements, the more shear locking effect have impact. For example in very thin elements where two dimensions are remarkable bigger than third one the impact of shear locking effect is big.

Define the element edge length for plate structures so that the thinnest part of plate have at least two solid elements through the thickness of the plate.

Example: for 5 mm thick plate the maximum edge length of solid element should be 2,5 mm (in the direction of plate thickness).

The following figures illustrates the shear locking effect for plate structures. The plate has fixed supports on both ends and it has uniformly distributed load on it.

- Results with beam element. The shear locking effect does not exist.
- Results with coarse 10 node tetrahedron element mesh. There is only one solid element through the plate thickness and the dimensions of elements are remarkably unequal. The maximum displacement is 47% smaller than in results with beam element.
- Results with a bit more dense 10 node tetrahedron element mesh. There is only one solid element through the plate thickness. The maximum displacement is 6,5% smaller than in results with beam element.
Results with dense 10 node tetrahedron element mesh. There is two solid element through the plate thickness. The maximum displacement is 2,7% smaller than in results with beam element.