Element Types

This section lists the elements that can be used in FEA and MPM calculations

FEA Element Types

Solid Elements

The following solid elements are currently available in NairnFEA:

• 1 or "3 Node Triangle": 3-node constant-strain triangular elements (linear)
• 2 or "4 Node Quadrilateral": 4-node isoparametric rectangular elements (linear)
• 3 or "8 Node Quadrilateral": 8-node isoparametric rectangular elements (quadratic)
• 4 or "6 Node Triangle": 6-node isoparametric triangular elements (quadratic)
• 8 or "9 Node Lagrange": 9-node Langrangian rectangular element (quadratic) (9 point Gaussian quadrature)

These FEA element types are illustrated in the following figure.

Interface Elements

The following interface elements are used to model imperfect interface:

• 5 or "4 Node Interface": 4-node imperfect interface elements (linear)
• 6 or "6 Node Interface": 6-node imperfect interface elements (quadratic)

These FEA interface element types are illustrated in the following figure. Note that imperfect interface elements are comprised of two separate paths with identical nodal coordinates and thus twice as many actual nodes as appear in the figure.

Scripted Input Files

In scripted input files, the element type is set using the Element command:

Element (elem)

where (elem) is a number or name from the above lists (by name or number). Once an element is selected, it remains the element used for all subsequent Area commands. If no Element command has been used, FEA calculations will default to "8 Node Quadrilateral" elements. Solid (or quadrilateral) areas can only use solid elements while interface areas can use only interface elements.

When using triangular elements (type 1 and 4), quadrilateral areas meshed using the Area Command first meshes the area into quadrilaterals and then creates triangular elements by dividing each quadrilaterals along its diagonal. To determine which diagonal in used, you can use the FlipTriangles command: into triangular elements. The command to flip triangles is

FlipTriangles <(option)>

where (option) is yes or no to flip or not flip the triangles. This argument is optional. If it is omitted, the command will toggle the previous setting for triangle flipping. The initial value is always no. Any new setting by a FlipTriangles command remains in effect until it is changed by another FlipTriangles command.

XML Input Files

In XML input files, the first <Area> block must define an element type in an attribute and refer to it by number from the above list. Subsequent <Area> blocks can omit the type attribute unless the element type is changed to have an analysis with mixed elements. Solid (or quadrilateral) areas can only use solid elements while interface areas can use only interface elements. For triangular elements, the diagonals are flipped using a flip attribute on the <Area> command instead of using a separate FlipTriangles command.

MPM Element Types

In theory, MPM could use any element type int he background. In practice, all MPM codes use linear elements and unpublished attempts to try other element types have not been successful. Furthemore, many MPM features required a regular orthogonal grid, although there is no particular need for grid spacings to be the same in all directions. As a result, MPM in 2D and 3D uses the following two types of elements

• 2 or "4 Node Quadrilateral": 4-node rectangular (usually) elements (linear)
• 7 or "8 Node Brick": 8-node rectangular box (usually) elements (linear)

These MPM element types, in there usual shape, are illustrated in the following figure.

Notes

1. When mixed elements are used, they must be compatible elements. In other words, you can mix linear elements (types 1, 2, and 5) with each other or quadratic elements (types 3, 4, 6, and 8) with each other, but cannot mix linear elements with quadratic elements in the same mesh.