Point-mass Elements for Stress Analysis

1. Introduction

The point-mass elements are designed for linear and geometric nonlinear analysis, and for static and dynamic analysis. A point-mass element defines masses and mass moments of inertia at a mesh node, with respect to the node-local coordinate system, see transformations and nodes commands.

2. Element Types

The following element types are available:

Table 18. Point-Mass Elements for Stress Analysis

Element type Remarks
PMASS3.S For the 3 translation DOFs of a node
PMASS6.S For the 3 translation and the 3 rotation DOFs of a node

3. Required element attributes

mass m

For PMASS3.S and PMASS6.S. Specifies the 'lumped' nodal mass of PMASS elements. mass remains defined until a new mass option is specified or until a new eltype option is specified.

matrix m11 m12 m22 m13 m23 m33 m14 m24 m34 m44 m15 m25 m35 m45 m55 m16 m26 m36 m46 m56 m66

For PMASS6.S. Specifies the coefficients of the symmetric nodal mass coefficient matrix, i.e the 21 terms stored column-wise (upper triangle of matrix) of PMASS6.S elements. If matrix is specified, mass, inertia_moments, and offsets may not be specified, and vice versa.

inertia_moments Ixx Iyy Izz Ixy Iyz Ixz

For PMASS6.S. Specifies the components of the inertia moment tensor, expressed in the branch-global coordinate system. The inertia moments are 0 by default.

offsets ox oy oz

For PMASS6.S. Specifies the offset, in each direction, of the mass point with respect to the node. The default offset in each direction is 0.

The mass matrix is computed as follows for a PMASS6.S element:

Equation 1. PMASS6.S mass matrix

M = m 0 0 0 m o z m o y m 0 m o z 0 m o x m m o y m o x 0 I xx + m o z 2 + m o y 2 I xy m o x o y I xz m o x o z I yy + m o z 2 + m o x 2 I yz m o y o z symm I zz + m o y 2 + m o x 2

4. Optional element attributes

group gid

Defines the element group number gid (a non-negative integer number). The default group number is 0. The same definition will be used for all elements defined hereafter, until a new group option is encountered or until the eltype command is specified.

5. Examples

Example 1. Define translation masses

Define masses of 10000 in each of the three translation directions for node 45 and 230 and masses of 50000 each of the three translation directions for node 457 (note the PMASS3.S 'element numbers' are 1, 2, and 3):

  eltype pmass3.s
  mass 10000
  1 45
  2 230
  mass 50000
  3 457