```{raw} latex \clearpage ``` # General info for all finite elements ## What the finite elements have in common A finite element is a body with two or more nodes, whose coordinates it interpolates to describe a deformable body - a cable, a beam, a plate. It is a body in every other respect: the general section of the bodies describes its marker interfaces and Jacobians, and each element page gives only its own. | element | nodes | theory | deformation | |---|---|---|---| | `ObjectANCFCable2D` | 2 `NodePoint2DSlope1` | ANCF, Bernoulli-Euler | axial, bending | | `ObjectALEANCFCable2D` | 2 `NodePoint2DSlope1` + `NodeGenericODE2` | the same, with axially moving mass | axial, bending | | `ObjectANCFCable` | 2 `NodePointSlope1` | ANCF, Bernoulli-Euler, 3D | axial, bending; no torsion | | `ObjectANCFBeam` | 2 `NodePointSlope23` | ANCF, shear deformable (under development) | axial, shear, torsion, bending, cross section | | `ObjectBeamGeometricallyExact2D` | 2 or 3 `NodeRigidBody2D` | geometrically exact (Simo-Reissner) | axial, shear, bending | | `ObjectBeamGeometricallyExact` | 2 rigid body nodes | geometrically exact, 3D (under development) | | | `ObjectANCFThinPlate` | 4 `NodePointSlope12` | ANCF, Kirchhoff plate (under construction) | in-plane, bending | ## The page of an element Each element page follows the same order: **nodes and coordinates**, **kinematics and interpolation** - the shape functions and the position of a point -, **strains** and **elastic forces** with their integration rule, the **mass matrix**, **marker interfaces**, and **limitations**. ## Reference configuration and the local coordinates The reference configuration is given by the reference coordinates of the nodes, and the element coordinates are the sum of reference and current coordinates. Whether a curved or stretched reference is stress-free depends on the element: the ANCF cables subtract the reference strains with `strainIsRelativeToReference`, the geometrically exact beam has a reference curvature. The local axial coordinate runs over $[0,\,L]$ for the ANCF cables and over $[-L/2,\,L/2]$ for the other beams; `length` is the length of the element in its reference configuration. ## Meshes The elements share their nodes, and a beam is a chain of elements. `exudyn.beams` creates such chains, e.g. `GenerateBeamElementsAlongLine`, and the markers on a node of the chain connect it to the rest of the model. (sec-drawing-objectsfiniteelement)= ## Drawing A finite element is drawn if `bodies.show` and its own `show` are True, in its `color` or `bodies.defaultColor`; in a contour plot (`contour.outputVariable`, `contour.outputVariableComponent`) colored by the values along it. `bodies.showNumbers` writes its number. The settings: [`bodies.show`](#sec-vsettingsbodies), [`bodies.showNumbers`](#sec-vsettingsbodies), [`bodies.defaultColor`](#sec-vsettingsbodies), [`contour.outputVariable`](#sec-vsettingscontour), [`contour.outputVariableComponent`](#sec-vsettingscontour).