Spring Foundation

Use the node to apply elastic and damping boundary conditions for domains, boundaries, edges, and points.

By adding the Predeformation subnode, you can prescribe that the spring force is zero at a nonzero spring extension.

The and Thin Layer nodes are similar, with the difference that a connects the structural part on which it is acting to a fixed “ground”, while a acts between two parts, either on an interior boundary or between two boundaries forming a pair.

The node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).

Shell Properties


	This section is only present in the Layered Shell interface, where it is described in the documentation for the Spring Foundation node.

Interface Selection


	This section is only present in the Layered Shell interface, where it is described in the documentation for the Spring Foundation, Interface node.

Pair Selection

If this node is selected from the menu, choose the pair on which to apply this condition. An identity pair has to be created first.

Coordinate System Selection

The spring and damping constants are given with respect to the selected coordinate system.

Spring

Select the and its associated spring constant or force using Table 4-9 as a guide. The default option is the spring type for the type of geometric entity and space dimension, and there are different combinations available based on this.

When the option is of the type ‘force as function of extension’, then the built-in variables describing the spring extension must be used in the expression as described in Springs and Dampers. The spring matrix can be entered as , , , or . For the same spring constant is used in all the diagonal elements of the spring matrix.

When is selected as , the spring stiffness values are computed from the given material data and a layer thickness. From the list, select a pair of elastic properties — , , or . Each of these pairs define the elastic properties and it is possible to convert from one set of properties to another according to Table 4-10. For the chosen properties, select from the applicable list to use the value or enter a value or expression. In order to use , you must have assigned a material to the selected boundaries.

Enter a , ds, to specify the physical thickness of the elastic layer.

Table 4-9: Spring Types for the Spring Foundation Feature.
Spring Type	variable	SI units	Geometric Entity Level	Space Dimension
Spring constant per unit volume	kV	N/(m⋅m3)	domains	3D, 2D, 1D, and 2D/1D axisymmetric
Total spring constant	ktot	N/m	domains, edges	3D, 2D, 1D, and 2D/1D axisymmetric
Spring constant per unit area	kA	N/(m⋅m2)	boundaries	3D, 2D
Spring constant per unit length	kL	N/(m⋅m)	edges, boundaries (2D)	3D, 2D, 1D
Spring constant	kP	N/m	points	3D, 2D, 1D, and 2D axisymmetric
Force per volume as function of extension	FV	N/m3	domains	3D, 2D, 1D, and 2D/1D axisymmetric
Total force as function of extension	Ftot	N	domains, boundaries, edges	3D, 2D, 1D, and 2D/1D axisymmetric
Force per area as function of extension	FA	N/m2	domains, boundaries	3D, 2D
Force per length as function of extension	FL	N/m	edges	3D/1D
Force as function of extension	FP	N	points	3D, 2D, 1D, and 2D/1D axisymmetric
Use material data	N/A	N/A	boundaries	3D, 2D, and 2D axisymmetric

Table 4-10: Expressions for the Elastic Moduli.
Description	Variable	D(E,ν)	D(E,G)	D(K,G)
Young’s modulus	E =	E	E
Poisson’s ratio	ν =	ν
Bulk modulus	K =			K
Shear modulus	G =		G	G

Rotational Spring


	This section is available for the Beam and Pipe Mechanics interfaces. All settings are analogous to the corresponding settings in the Spring section, but with forces replaced by moments and displacements replaced by rotations.

Loss Factor Damping

From the list, select or . The latter option is not available for 1D or 1D axisymmetry.

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For enter a single ηs, which is used to multiply all values of the spring matrix or spring force vector.

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For select , , , or , then enter values or expressions in the table for the ηk or ηf based on space dimension. The loss factors act on the corresponding components of the spring matrix or spring force vector. If you select , the effect is the same as when you select and enter the same value for all diagonal elements.

Rotational Loss Factor Damping


	This section is available for the Beam and Pipe Mechanics interfaces. All settings are analogous to the corresponding settings in the Loss Factor Damping section.

Viscous Damping

Select the using Table 4-11 as a guide. The default option is the default damping type for the type of geometric entity and space dimension, and there are different combinations available based on this. The damping matrix can be entered as , , , or . For the same viscous constant is used in all the diagonal elements of the damping matrix

Table 4-11: Damping Types for the Spring Foundation Feature.
Damping Type	variable	SI units	Geometric Entity Level	Space Dimension
Damping constant per unit volume	dV	N⋅s/(m⋅m3)	domains, boundaries (2D)	3D, 2D, 1D
Damping constant per unit area	dA	N⋅s/(m⋅m2)	domains, boundaries	3D, 2D, and 2D axisymmetric
Total damping constant	dtot	N⋅s/m	domains, boundaries, edges, points	3D, 2D, 1D, and 2D/1D axisymmetric
Damping constant per unit length	dL	N⋅s/(m⋅m)	edges	3D, 1D

Rotational Viscous Damping


	This section is available for the Beam and Pipe Mechanics interfaces. All settings in this section are analogous to the corresponding settings in the Viscous Damping section, but with forces replaced by moments and velocities replaced by angular velocities.