#### 2.1.1.7. Element- vs. Node-based Thicknesses

By default, ACP stores the thicknesses per ply and element, in other words, the ply's thickness is constant per element. This representation is consistent with the solver capabilities of layered shells, since they do not support varying ply thickness within one element. Therefore, geometry features (for example thickness by geometry or taper edge) calculate the ply thickness at the element centers (element-based thicknesses). ACP also supports node-based thicknesses. When node-based thickness evaluation is enabled, thicknesses are evaluated supplementary to the element-based thicknesses. This involves some performance losses but gives benefits when working with tapered plies (see Thickness and Cut-off Selection Rules).

Shell Layup

The differences between element- and node-based thicknesses are best explained with a tapered ply. The nominal ply covers the entire plate and a cut-off geometry defines the tapering as shown in the figure below. The figure on the left shows the element-based piercing where the computed ply thickness at the element centers is negative for the upper two elements (red arrows). The right image shoes the node-based piercing that brings a more precise resolution. In that specific case, all elements have at least one node with a positive (valid) thickness.

Figure : Element-based vs. Node-based Piercing

The final result for both optiomns is shown in the following figure. The ply is cropped if the thicknesses are only evaluated at the element corners since two elements have a negative thickness. In contrast, the ply covers the entire plate if the thicknesses are evaluated for each node because at least one node of each element has a valid ply thickness. If the node-based piercing determines that only some nodes of an element have a valid piercing but not the element center, then the thickness at the element center becomes the average node-based thickness.

Figure : Ply Extension and Element-wise Thicknesses of a Tapered Ply with Element-based (left) and Node-based (right) Thicknesses

In summary, node-based thicknesses bring some benefit for shell models but also bring certain restrictions. Node-based thicknesses cannot be evaluated if a ply covers more than two components, as shown in the figure below. In other words, a ply is not allowed to cover three elements that share one edge.

Figure : Restriction for Node-based Thicknesses

Solid Extrusion

The usage of node-based thicknesses brings more benefits if you perform a solid model analysis when compared to a shell analysis because the extrusion of the solid model is performed on a per-node basis. Additionally, layered solid elements support plies with variable thickness. The figure below shows the solid model from an example discussed in a previous section. As for the shell model, the solid model with element-based thicknesses does not cover the entire reference surface. In contrast, the node-based extrusion represents the ply extension more precisely. Additionally, it also captures the variable ply thickness over one element and therefore reproduces the taper much better.

Figure : Extrusion of a Tapered Ply without and with Node-based Thicknesses on the Left and Right, Respectively

There are two additional examples where you can benefit from node-based thicknesses:

- Tapered edge: Only nodal thicknesses can represent tapers with 0 thickness correctly.

  Figure : Solid Model Extrusion of a Tapered Ply without and with Node-based Thicknesses

- Cut-off selection rules with ply tapering: By default, tapering evaluated at the element centers can cause ripples in the extrusion. Node-based thicknesses result in a smoother shape and more accurate ply representation. In this specific case, it even allows you to proceed without a snap-to operation, since the surface is of good quality.

  Figure : Cut-off Selection Rule with Ply Tapering Based on Element-based and Node-based Thicknesses

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