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Spring Properties

Springs are a general type of element which can be used to model both simple springs and more sophisticated types of behaviour. For springs connected to ground these are specified directly on a node rather than as an element. The two simplest and most robust types of spring are the axial and rotational springs which have only and axial or rotational stiffness respectively. The more general spring types can violate equilibrium conditions so use be used with care. General non linear springs require material curves to define the load deflection characteristics. A completely general linear spring connected to ground uses a material matrix to define the stiffness, but this matrix must be positive definite. Springs follow the same local axis definition as beam, but the exceptions are zero length springs and nodal springs. For zero length springs the local axis is the constraint axis or the first node and for nodal springs it is the constraint axis of the node.

Definition​

Name

The name is only used as a convenient way of identifying a spring property.

Type

The type defines the spring is one of:

  • Axial – single translational degree of freedom
  • Torsional – single rotational degree of freedom
  • General – six degrees of freedom, linear or nonlinear
  • Matrix – six degrees of freedom referring to a full 6 × 6 stiffness matrix
  • Tension only – single translational degree of freedom, only active in tension
  • Compression only – single translational degree of freedom, only active on compression
  • Connector – six degree of freedom coupling different parts
  • Lock-up – single translational degree of freedom, active when the spring reaches the lock up limit
  • Gap – single translational degree of freedom, active when the gap closes
  • Friction – three translational degrees of freedom, active when a gap closes, and generates a transverse friction force

Material Curve and Stiffness

If it is linear spring or tension only or compression only springs, springs stiffness can be defined here directly. Most spring types only require a single stiffness, but the general spring has six degree of freedom and six spring stiffness need to be defined, if type is friction, three friction coefficients need to be defined. If spring is nonlinear, the reference to the nonlinear spring curve (material curve) need to be defined here and no stiffness definitions are needed, the relationships of force-displacement and moment-rotation of the spring are defined by the referred nonlinear spring curve.

Material Matrix

For a spring defined by a matrix the stiffness characteristics are defined in a material matrix. This allows for definition of the 6 × 6 stiffness matrix. This can only be referenced by nodal springs.

Lock-up

Lock up elements have no stiffness until the element locks up at the specified displacements. At this point the element behaves as a spring with the defined stiffness. The lock up for tension and compression are both defined as positive values.

Friction Coefficient

For a friction spring the transverse (shear) forces are limited to the by the friction coefficient × the normal force.

Damping Ratio

The damping ratio is used during a dynamic analysis to calculate an estimate of the modal damping ratio.

Spring Properties​

Spring elements define both conventional 'springs', but also other 1D elements which are not defined as beams or bars. The characteristics of these are described below.

  • Tension only – uniaxial nonlinear spring element. This element have no stiffness under compressive loading and creates penetration without any resistance.
  • Compression only – uniaxial nonlinear spring element. This element have no stiffness when subjected tensile loading/displacements. Under tensile loading this element will create gap.
  • Connector – six degree of freedom linear spring element coupling two different parts. Program automatically calculate the stiffness for this element using total stiffness at connecting nodes.
  • Lock-up – uniaxial nonlinear spring element, active when the spring displacement reaches the lock up limit. Similar to the Connector element, program automatically calculate the stiffness for this element using total stiffness at connecting nodes. This stiffness can be overridden by providing stiffness greater than zero in the element property definition.
  • Gap – special type of compression only spring element with initial gap. Initial gap is calculated from the element nodal positions. This element will have zero stiffness in the analysis while the displacements are within the initial gap or element is subjected to tensile loading. Program automatically calculate the stiffness for this element using total stiffness at connecting nodes. By default program assigns very high stiffness. This stiffness can be overridden by providing stiffness greater than zero in the element property definition.
  • Friction – Gap element with two additional translational degrees of freedom. When axial stiffness is active, this element will generate frictional resistance in transverse directions. This element will have zero stiffness in the analysis while the axial displacements are within the initial gap or element is subjected to tensile loading. Program automatically calculate the stiffness for this element using total stiffness at connecting nodes. By default program assigns very high stiffness. This stiffness can be overridden by providing stiffness greater than zero in the element property definition.

Tips for Convergence​

Compression only and Gap elements

  • Usually Compression only elements subjected to tensile loading requires large number of iteration to converge, if the stiffness is high.
  • To identify the elements, which creates the convergence issue, start the analysis using very low axial stiffness and check for the convergence.
  • Verify the results and check if the elements are subjected to tensile loading or creates gap then leave the stiffness of those elements as it is or reduce even further to increase the convergence.
  • If the results of the spring elements indicates large penetration beyond acceptable limit, then slowly increase the axial stiffness for those elements until acceptable results obtained.
  • In case, the non-convergence is due to rigid body motion between the two bodies replace the elements with friction elements.

Tension only elements

  • Similar to Compression only elements, use very low stiffness and check for the convergence by running the analysis.
  • If the results creates large gap beyond acceptable limit, increase the axial stiffness of the elements.

Friction Element

  • This type of elements have the convergence issues either when they are subjected tensile loading or when these elements are subjected lateral movement.
  • To avoid convergence issues due to tensile loading on the element follow similar steps defined for Compression only elements.
  • To avoid non-convergence due to lateral movement, start providing transverse stiffness equal to 1/10th stiffness in normal direction or less. Increase the stiffness gradually for the elements subjected to compressive loadings.

Note about the property axis​

If the property is used by 1D elements and the element length is not zero, the axis definition is the same as beam elements, if the element length is zero, i.e. the two nodes of the element are coincide, the nodal constraint axis of the first topology node of the element is used as the spring property axis.  

If the property is used by a node, the nodal constraint axis of the node will be used as the spring property axis.