4.27 MATRIX27 Stiffness, Damping, or Mass Matrix

4.27 MATRIX27 Stiffness, Damping, or Mass Matrix (UP19980821 ) MATRIX27 represents an arbitrary element whose geometry is undefined but whose elastic kinematic response can be specified by stiffness, damping, or mass coefficients. The matrix is assumed to relate two nodes, each with six degrees of freedom per node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. See Section 14.27 in the ANSYS Theory Reference for more details about this element. Other similar, but less general, elements are the spring-damper element (COMBIN14), and the mass element (MASS21).

Figure 4.27-1 MATRIX27 Stiffness, Damping or Mass Matrix



4.27.1 Input Data

The node locations and the coordinate system for this element are shown in Figure 4.27-1. The element is defined by two nodes and the matrix coefficients. The stiffness, damping, or mass matrix constants are input as real constants. The units of the stiffness constants are Force/Length or Force*Length/Radian and the damping constants, Force*Time/Length and Force*Length*Time/Radian. The mass constants should have units of Force*Time2/Length or Force*Time2*Length/Radian.

All matrices generated by this element are 12 by 12. The degrees of freedom are ordered as UX, UY, UZ, ROTX, ROTY, ROTZ for node I followed by the same for node J.

The matrix constants should be input according to the matrix diagrams shown on the next page. For example, if a simple spring of stiffness K in the nodal x direction is desired, the input constants would be C1=C58=K and C7=-K for KEYOPT(2)=0 and KEYOPT(3)=4.

A summary of the element input is given in Table 4.27-1. Section 2.1 gives a general description of element input.

Table 4.27-1 MATRIX27 Input Summary

Element Name

MATRIX27

Nodes

I, J

Degrees of Freedom

UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants

Constants C1 through C78 define the upper triangular portion of the matrix
Constants C79 through C144, which are required only if KEYOPT(2)=1, define the lower triangular portion of an unsymmetric matrix.

Material Properties

None

Surface Loads

None

Body Loads

None

Special Features

Birth and death

KEYOPT(2)

0 - Symmetric matrices
1 - Unsymmetric matrices

KEYOPT(3)

2 - Input data defines a 12 x 12 mass matrix
4 - Input data defines a 12 x 12 stiffness matrix
5 - Input data defines a 12 x 12 damping matrix

KEYOPT(4)

0 - Do not print element matrix
1 - Print element matrix at beginning of solution phase

4.27.2 Output Data

The solution output associated with the element consists of node displacements included in the overall nodal solution. There is no element solution output associated with the element. KEYOPT(4)=1 causes the element matrix to be printed (for the first substep of the first load step only). Section 2.2 gives a general description of solution output.

For KEYOPT(2)=0, the symmetric matrix has the form:



For KEYOPT(2)=1, the unsymmetric matrix has the form:



4.27.3 Assumptions and Restrictions

Nodes may be coincident or noncoincident. Since element matrices should normally not be negative definite, a note is printed for those cases where this can be easily detected. With a lumped mass matrix [LUMPM,ON] all off-diagonal terms must be zero.

The matrix terms are associated with the nodal degrees of freedom and are assumed to act in the nodal coordinate directions (see Section 2.3.2).

4.27.4 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

ANSYS/LinearPlus