Spring Foundation

The and Thin Elastic 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 http://www.comsol.com/products/specifications/).

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

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

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

Select the and its associated spring constant or force using Table 4-5 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 4-6. 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 4-5: 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, and 2D axisymmetric
Total spring constant	ktot	N/m	domains, edges	3D, 2D, and 2D axisymmetric
Spring constant per unit area	kA	N/(m⋅m)2	boundaries	3D, 2D
Spring constant per unit length	kL	N/(m⋅m)	edges, boundaries (2D)	3D, 2D
Spring constant	kP	N/m	points	3D, 2D, and 2D axisymmetric
Force per volume as function of extension	FV	N/m3	domains	3D, 2D, and 2D axisymmetric
Total force as function of extension	Ftot	N	domains, boundaries, edges	3D, 2D, and 2D 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
Force as function of extension	FP	N	points	3D, 2D, and 2D axisymmetric
Use material data	N/A	N/A	boundaries	3D, 2D, and 2D axisymmetric

Table 4-5: Spring Types for the Spring Foundation Feature

Spring Type

variable

SI units

Geometric Entity Level

Space Dimension

Spring constant per unit volume

N/(m⋅m3)

domains

3D, 2D, and 2D axisymmetric

Total spring constant

ktot

N/m

domains, edges

3D, 2D, and 2D axisymmetric

Spring constant per unit area

N/(m⋅m)2

boundaries

3D, 2D

Spring constant per unit length

N/(m⋅m)

edges, boundaries (2D)

3D, 2D, and 2D axisymmetric

Force per volume as function of extension

N/m3

domains

3D, 2D, and 2D axisymmetric

Total force as function of extension

Ftot

domains, boundaries, edges

3D, 2D, and 2D axisymmetric

Force per area as function of extension

N/m2

domains, boundaries

3D, 2D

Force per length as function of extension

N/m

edges

Force as function of extension

points

3D, 2D, and 2D axisymmetric

Use material data

N/A

boundaries

3D, 2D, and 2D axisymmetric

Table 4-6: 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

Table 4-6: Expressions for the Elastic Moduli.

Description

Variable

D(E,ν)

D(E,G)

D(K,G)

E =

ν =

K =

G =

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

From the list, select or .

•

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

•

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.

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

Select the using Table 4-7 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 4-7: 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
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, and 2D axisymmetric
Damping constant per unit length	dL	N⋅s/(m⋅m)	edges	3D

Table 4-7: Damping Types for the Spring Foundation Feature

Damping Type

variable

SI units

Geometric Entity Level

Space Dimension

Damping constant per unit volume

N⋅s/(m⋅m3)

domains, boundaries (2D)

3D, 2D

Damping constant per unit area

N⋅s/(m⋅m2)

domains, boundaries

3D, 2D, and 2D axisymmetric

Total damping constant

dtot

N⋅s/m

domains, boundaries, edges, points

3D, 2D, and 2D axisymmetric

Damping constant per unit length

N⋅s/(m⋅m)

edges

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