MovingSpring

The MovingSpring element simulates a moving spring (a combination of spring and damper) rolling on a line or surface defined by beam elements.

Fig. 4.9-1 MovingSpring Element on a Line Composed of Beams

Fig. 4.9-1. MovingSpring Element on a Line Composed of Beams

Fig. 4.9-2 MovingSpring Element on a 3D Surface

Fig. 4.9-2. MovingSpring Element on a 3D Surface

Fig. 4.9-3 MovingSpring Element on a 2D Surface

Fig. 4.9-3. MovingSpring Element on a 2D Surface

▪ Notes

When performing dynamic analysis, a preliminary static analysis considering self-weight must be conducted first.
To activate the MovingSpring element, the speed must be defined using *State, Type=MovingSpringSpeed.
If damping is considered, the overall stiffness matrix will become an asymmetric matrix.

Example

*ELSET, Name=rail
 Beam

*SECTION, TYPE=MCK, Name=PM
 Mass, 5750

*SECTION, TYPE=MovingSpring, Name=MS
 rail
 Spring, Y, 1595E3
 Damper, Y, 1000E3

*Element, TYPE=PointMass, ELSET=PM
 1000, 1000, S=PM

*Element, TYPE=MovingSpring, ELSET=MS
 1001, 1000, S=MS

*Distribution, TYPE=MovingSpringInitialPosition
 1001, 0.0

*Load, TYPE=Gravity, Name=SelfWeight
 1000,0,-9.81, 0.

*STEP, TYPE=Static Name=S
*Activate, TYPE=Element
 Beam, PM, MS
*Activate, TYPE=Constraint
 BC
*Activate, TYPE=Load
 SelfWeight

*STEP, TYPE=Dynamic Name=Dyn, Prev=S
 , 0.02, 2.
*State, Type=MovingSpringSpeed
 MS, 27.78

*Element, Type=MovingSpring

*Element, Type=MovingSpring, ELSet=elset
 id, n1{, S=section, P=x,y}
 ...

First data line and subsequent data lines

P=x,y: Initial position relative to the reference point. Defined in the ECS. When targeting beam elements, the y value is ignored.

Specifications

No. of nodes: 1
No. of integration points: 1
Fields: SF=[...], SE=[...], DF=[...], DE=[...] at the element center.
Compatible section: MovingSpring
Active DOFs: Can include Y and Z depending on the definition.

Refer to *Element, TYPE=Spring for explanations of SF, SE, DF, and DE.

*Section, Type=MovingSpring

Defines the properties for a MovingSpring.

*Section, Type=MovingSpring, Name=name
  surface, refx, refy, refz, g1x, g1y, g1z, xRigid, yRigid, zRigid
  Spring, oneDof, coef|material
  ...
  Damper, oneDof, coef|material
  ...
  UnitSystem, force-length-time

*Section, Type=MovingSpring, Name=name
  line, xRigid, yRigid, zRigid
  Spring, oneDof, coef|material
  ...
  Damper, oneDof, coef|material
  ...
  UnitSystem, force-length-time

First data line for Line

line: Target beam elset ... The beams should be connected.
xRigid, yRigid, zRigid: Position vector from the reference node (rigid arm vector). x1 is required, others are optional.

First data line for Surface

surface: Target surface (required).
refx, refy, refz: Reference point (optional; default: 0, 0, 0).
g1x, g1y, g1z: Direction of travel (1, 0, 0).
xRigid, yRigid, zRigid: Position vector from the reference node (rigid arm vector) (optional; default: 0, 0, 0).

Second and subsequent data line if necessary

Spring|Damper: Spring or damper
oneDof: Degree of freedom to which the spring/damper is applied; one of X, Y, Z, RX, RY, or RZ
coef: Spring or damping coefficient
material: Reference material model used instead of the spring or damping coefficient. Must support uniaxial material behavior
referenceUnitSysem: Reference unit system of the material model, used when a material is specified. Optional; defaults to the current unit system. Should be specified in the first data line starting with Spring or Damper

Second and subsequent data line starting with Spring

oneDof: Degree of freedom to which the spring is applied; one of Y and Z
coef: Spring coefficient
material: Reference material model used instead of the spring coefficient. Must support uniaxial material behavior

Second and subsequent data line starting with Damper

oneDof: Degree of freedom to which the dmaper is applied; one of Y and Z
coef: Damping coefficient
material: Reference material model used instead of the damping coefficient. Must support uniaxial material behavior

Optional single UnitSystem data line after second data line

force-length-time: The local unit system applied to this section. force must be one of N, kN, kgf, tonf, lbf, or kip; length must be one of m, cm, mm, km, in, ft, yd, or mi; and time must be one of s, min, hr, or day.

Spring, Damper, Mass, and UnitSystem may be defined in any order, and Spring and Damper may be used multiple times depending on the DOF to which they are applied.

Spring or damping coefficients are generally defined as numerical values. However, when nonlinear behavior is to be represented, they may be defined by referencing a material that supports a uniaxial material model. For example, if a uniaxial material model is assigned to a Spring in the X direction, the stress–strain relation of that material is interpreted as a generalized force–displacement relation in the Y direction.

localUnitSystem is optional and is specified in the form of force-length-time, such as kN-mm-s. The force unit shall be one of N, kN, kgf, tonf, lbf, and kip; the length unit shall be one of m, cm, mm, km, in, ft, yd, and mi; and the time unit shall be one of s, min, hr, and day.
If localUnitSystem is specified, the global UnitSystem shall have been defined in advance by *Environment, TYPE=UnitSystem.
If localUnitSystem is not specified, the input for this Section follows the global UnitSystem defined by *Environment, TYPE=UnitSystem.
localUnitSystem defines the unit system for coef or material used in this Section.
If localUnitSystem is identical to the global UnitSystem, the input values are used directly without any additional scaling. If the two unit systems are different, appropriate unit conversion is performed internally. For example, if the global UnitSystem is kN-m-s and the localUnitSystem is kN-mm-s, and a material model is used for a Spring in the X direction, the displacement is converted from the m basis to the mm basis before evaluating the material model, and the generalized force computed by the material model is then converted back to the global UnitSystem and used in the analysis.

Example

*SECTION, TYPE=MovingSpring, Name=MSx
 rail
 Spring, Y, 1595E3
 Damper, Y, 1000E3
*SECTION, TYPE=MovingSpring, Name=MS
 rail
 UnitSystem, kN-mm-s
 Spring, Y, 1595E3
 Damper, Y, 1000E3