2.8 Triangle, Prism and Tetrahedral Elements

Degenerated elements are often used for modeling transition regions between fine and coarse meshes, for modeling irregular and warped surfaces, etc. Degenerated elements formed from quadrilateral and brick elements without midside nodes are much less accurate than those formed from elements with midside nodes and should not be used in high stress gradient regions. If used elsewhere, they should be used with caution.

An exception where triangular shell elements are preferred is for severely skewed or warped elements. Quadrilateral shaped elements should not be skewed such that the included angle between two adjacent faces is outside the range of 90° 45° for non-midside-node elements or 90° 60° for midside-node elements. Warping occurs when the four nodes of a quadrilateral shell element (or solid element face) are not in the same plane, either at input or during large deflection. Warping is measured by the relative angle between the normals to the face at the nodes. A flat face (no warping) has all normals parallel (zero relative angle). A warning message is output if warping is beyond a small, but tolerable value. If warping is excessive, the problem will abort. See the ANSYS Theory Reference for element warping details and other element checking details. Triangular (or prism) elements should be used in place of a quadrilateral (or brick) element with large warping.

When using triangular elements in a rectangular array of nodes, best results are obtained from an element pattern having alternating diagonal directions. Also, for shell elements, since the element coordinate system is relative to the I-J line, the stress results are most easily interpreted if the I-J lines of the elements are all parallel.

Degenerated triangular 2-D solid and shell elements may be formed from four-node quadrilateral elements by defining duplicate node numbers for the third and fourth (K and L) node locations. The node pattern then becomes I, J, K, K. If the L node is not input, it defaults to node K. If extra shape functions are included in the element, they are automatically suppressed (degenerating the element to a lower order). Element loads specified on a nodal basis should have the same loads specified at the duplicate node locations. When forming a degenerated triangular element by repeating node numbers, the face numbering remains the same. Face 3, however, condenses to a point. The centroid location printed for a degenerated triangular element is usually at the geometric centroid of the element. Elements should be oriented with alternating diagonals, if possible.

Degenerated triangular prism elements may be formed from eight-noded 3-D solid elements by defining duplicate node numbers for the third and fourth (K and L) and the seventh and eighth (O and P) node locations. The node pattern then becomes I,J,K,K,M,N,O,O. When forming a degenerated prism element by repeating node numbers, the face numbering remains the same. Face 4, however, condenses to a line. The centroid location printed for a degenerated element is not at the geometric centroid but is at an average nodal location. The integration points are proportionately rearranged within the element. Elements should be oriented with alternating diagonals, if possible. If extra shape functions are included in the element, they are partially suppressed. Element loads should have the same loads specified at the duplicate node locations.

A degenerated tetrahedral element may be formed from a triangular prism element by a further condensation of face 6 to a point. The input node pattern should be I,J,K,K,M,M,M,M. If extra shape functions are included in the element, they are automatically suppressed. Element nodal loads should have the same loads specified at the duplicate node locations.

Warning: Surface stress (or convection heat flow) printout (see Section 2.2.2.5) should not be requested on a condensed face. Also, pressures (or convection conditions) should not be defined on a condensed face.