3.1.7.1: Mesh to Shell

The “MeshToShell” component converts a triangle or quad mesh into a group of shell or membrane elements (see Fig. 3.1.9.1). Quads are automatically decomposed into triangles. Shell patches are rigidly connected when some of their nodes have the same index.

Colors can be attached to shells via the “Color” input. To enable the display of shell element colors, activate “Elements” in the “Colors” submenu of the “ModelView” component. Additionally, ensure “Cross section” is selected in the “Render Settings” submenu of the “ShellView” component.

Each patch of shells can be given an identifier via the “Id” input for later reference when attaching custom material or cross-section properties. By default, shells have a thickness of 1 cm and steel as their material. Use the “CroSec” input to change these properties. Clicking on the “Options” submenu header reveals additional inputs: “Pts” and “LDist” serve the same purpose as in the “LineToBeam” component (see section 3.1.6). Additionally, mesh faces with an area smaller than $LDist^2 \cdot 0.1$ are automatically removed.

Fig. 3.1.9.1: The “MeshToShell”-component turns meshes into shells.

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MeshToShell.gh

The shell elements used in Karamba3D resemble the TRIC-element devised by Argyris and coworkers (see [1], [2] for details). They are faceted (i.e. flat) elements. Karamba3D neglects transverse shear deformation in case of shell elements.

Shells and Membranes

For very thin shells, the bending stiffness can be neglected relative to the in-plane stiffness, resulting in membrane elements with three translational degrees of freedom (DOFs) per node. If t stands for the shell thickness, its bending stiffness is proportional to t³ while the in-plane stiffness varies with t. This discrepancy leads to significantly different magnitudes of entries in the element stiffness matrices, causing numerical problems in the solution procedure.

Membrane elements result from the “MeshToShell” component when the “Bending” input is set to “False”. Flat assemblies of membrane elements have kinematic modes in the transverse direction unless stabilized via positive$N^{II}$-values.

Drilling Degrees of Freedom

In Karamba3D shell elements do not have bending stiffness with respect to nodal rotations about the shell normal. In the case of curved surfaces, drilling degrees of freedom are blocked since the elements connecting to a node do not lie in a plane.

For flat surfaces this is not the case. therefore the "Analysis" component will report a rigid body mode. You can either ignore this warning or add a rotational support perpendicular to the plane at an arbitrary node of the slab.