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.

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, bodies.showNumbers, bodies.defaultColor, contour.outputVariable, contour.outputVariableComponent.