Scalar Spring Element for Stress Analysis

1. Introduction

The scalar spring element connects two nodal degrees-of-freedom and, in dynamic analysis, their velocities:

F = K ( u 1 - u 2 ) + D ( v 1 - v 2 )

The element is linear and works with the branch-global coordinate system, i.e., it ignores any node-local coordinate systems. If only one degree-of-freedom is specified, this will be connected to the ground:

F = K u 1 + D v 1

2. MDL Syntax

The syntax is as follows:

elements
  ...
  type SPRING element-id "[" K K [D D] node node1-id dof dof1 [system branch|local] [node node2-id dof dof2i [system branch|local]] "]"
  ...
end

The element stiffness K has to be specified always, however, the damping coefficient D is optional and has a default value of 0.

If a translation degree-of-freedom (UX, UY, or UZ) is specified, that node will have 3 degrees-of-freedom. If a rotation degree-of-freedom (RX, RY, or RZ) is specified, that node will have 6 degrees-of-freedom. In this case it may be necessary to lock the degrees-of-freedom that are not connected.

If a node-local coordinate system is defined on the node, and system local is specified, the spring translation or rotation is in that node-local coordinate system.

3. Example

Two spring elements connect degrees-of-freedom UX (translation in X-direction) and RY (rotation around the Y-axis) of node 1 to the ground. No damping coefficients are specified, thus, the default value of zero will be used. There is also a point-mass element defined at that node. The node could be connected by an RBE element to other parts of a FE model. This is not the case here, therefore, the not-connected degrees-of-freedom are locked.

nodes
  1  0. 0. 0.
end

elements
  type SPRING
  1 [k 20000.    node 1 dof UZ]
  2 [k 17391.125 node 1 dof RY]

  type PMASS6.S
  matrix [
  0.   0.   0.   0.   0.     0.
       0.   0.   0.   0.     0.
            2.   0.   -1.8   0.
                 0.   0.     0.
                      1.7391 0.
                             0.
  ]
  3  1
end

ebc 1
  dof [UX UY RX RZ] value 0. node 1
end