Nodes and Elements


What is a Node?

A node is a coordinate location in space where the degrees of freedom (DOFs) are defined. The DOFs for this point represent the possible movement of this point due to the loading of the structure. The DOFs also represent which forces and moments are transferred from one element to the next. The results of a finite element analysis, (deflections and stresses), are usually given at the nodes.

 

In the real world, a point can move in 6 different directions, translation in X, Y, and Z, and rotation about X, Y, and Z. In FEA, a node may be limited in the calculated motions for a variety of reasons. For example, there is no need to calculate the out of plane translation on a 2-D element; it would not be a 2-D element if its nodes were allowed to move out of the plane. The DOF for the generic element types are given in Table 1.

Table 1: Degrees of Freedom for Element Types

Element Type

Translation

Rotation

X

Y

Z

X

Y

Z

Truss, spring, gap

Yes

Yes

Yes

 

 

 

Beam

Yes

Yes

Yes

Yes

Yes

Yes

2-D

 

Yes

Yes

 

 

 

Membrane

Yes

Yes

Yes

 

 

 

Plate, shell

Yes

Yes

Yes

Yes*

Yes*

*

Brick, tetrahedral

Yes

Yes

Yes

 

 

 

Yes indicates the deflections are calculated. Transmission of forces or moments is supported.

* Rotational DOF for plate elements are based on local direction 1, 2, 3 instead of global direction X, Y, Z. Rotations about the local axes 1 and 2 (axes in the plane of the element) are calculated. Rotation about the local axis 3 (axis perpendicular to the element) is not calculated.

 

The DOF of a node (which is based on the element type) also relates what types of forces and restraints are transmitted through the node to the element. A force (axial or shear) is equivalent to a translation DOF. A moment is equivalent to a rotational DOF. Thus, to transfer a moment about a certain axis, the node must have a rotational DOF about the axis. If a node does not have that rotational DOF, then applying a moment to the node will have no effect on the analysis. This fact may also place requirements on how two parts are connected together. Additional modeling may be required to insure that the connection between the parts does not produce a hinge. See the page "Meshing Overview: Creating Contact Pairs: Examples of Contact" for examples.

 

Likewise, restraining that node with a rotational boundary condition will have no effect if the node does not have the ability to transmit the moment. So, placing a boundary condition of Tx Ty Tz Rx Ry Rz on a node of a brick element is the same as applying a Tx Ty Tz boundary condition; the brick element node does not calculate the rotations.

What is an Element?

An element is the basic building block of finite element analysis. There are several basic types of elements. Which type of element for finite elements analysis that is used depends on the type of object that is to be modeled for finite element analysis and the type of analysis that is going to be performed.

 

An element is a mathematical relation that defines how the degrees of freedom of a node relate to the next. These elements can be lines (trusses or beams), areas (2-D or 3-D plates and membranes) or solids (bricks or tetrahedrals). It also relates how the deflections create stresses.