Boundary

*Boundary, [amplitude=<amplitude name>, <option>]
<node set name>, <dof>, <...>

• Theory Manual

  ---

  The theory behind the implementations

This command is used to prescribe boundary conditions on nodes or node sets. It is possible to define more than one *Boundary command per step. However, the defined boundary conditions are only active in the step for which they are defined.

The *Boundary command has the following keywords:

• amplitude=<amplitude name>

  The optional amplitude parameter allows for the specification of an amplitude by which the boundary values are scaled (mainly used for non-linear static and dynamic calculations). This only makes sense for non-zero boundary values. Thus, in that case, the values entered on the sub-lines of the *Boundary command are interpreted as reference values to be multiplied with the (time dependent) amplitude value to obtain the actual value.

• <type>

  The second optional keyword <type> can be used to prescribe more "advanced" boundary conditions.

  Type	Description	Section
  none	prescribe degree of freedom (dof)	Section 1
  type=velocity	first time derivative of the prescribed dof	Section 2
  type=acceleration	second time derivative of the prescribed dof	Section 3
  type=increment	increment (i.e. the change) of a dof	Section 4
  type=hydrostatic	hydrostatic (linear increase with depth) distribution	Section 5
  type=moving-hydrostatic	hydrostatic distribution with a "moving" zero-level	Section 6

The following degrees of freedom (dof) can be prescribed:

Degrees of freedom	Description
u1	Displacement in x1-direction
u2	Displacement in x2-direction
u3	Displacement in x3-direction
pw	Pore-water pressure
pa	Pore-air pressure
w1	Water displacement in x1-direction
w2	Water displacement in x2-direction
w3	Water displacement in x3-direction

1. Default

For the default case (no type prescribed), the subsequent lines take the flowing form:

<node set name>, <dof>, <value>.

They can be repeated as often as needed.

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <value> = set this parameter equal to the value to be prescribed to the boundary condition. Notice that this value is interpreted as a reference value, which is multiplied with the amplitude value (in case an amplitude is assigned to the boundary condition).

2. Velocity

For type=velocity, the subsequent lines take the flowing form:

<node set name>, <dof>, <value>.

They can be repeated as often as needed.

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <value> = set this parameter equal to the value to be prescribed to the boundary condition. Notice that this value is interpreted as a reference value, which is multiplied with the amplitude value (in case an amplitude is assigned to the boundary condition).

3. Acceleration

For type=acceleration, the subsequent lines take the flowing form:

<node set name>, <dof>, <value>.

They can be repeated as often as needed.

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <value> = set this parameter equal to the value to be prescribed to the boundary condition. Notice that this value is interpreted as a reference value, which is multiplied with the amplitude value (in case an amplitude is assigned to the boundary condition).

4. Increment

For type=increment, the increment (i.e. the change) of a variable relative to its original value at the start of the step. The subsequent lines take the flowing form:

<node set name>, <dof>, <value>.

They can be repeated as often as needed.

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <value> = set this parameter equal to the value to be prescribed to the boundary condition. Notice that this value is interpreted as a reference value, which is multiplied with the amplitude value (in case an amplitude is assigned to the boundary condition).

5. Hydrostatic

If type=hydrostatic is used to define the boundary condition, the subsequent line differs from the one above and takes the form:

<node set name>, <dof>, <slope>, <zero level>

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <slope> = slope of hydrostatic distribution, e.g. unit weight of water in case of a hydrostatic distribution pore water pressure.
• <zero level> = coordinate (y-coordinate in 2-D and z-coordinate in 3-D) where the distribution is zero, e.g. location of the water table in case of a hydrostatic distribution of pore water pressure

An example for the hydrostatic boundary condition is depicted in Figure1 for two different geometrical settings (scenario 1 and scenario 2).

Figure 1: Example for boundary conditions of type `hydrostatic`

Although the term 'hydrostatic' implies that this boundary condition is intended for the pore water pressure degree of freedom (DOF), it can also be applied to other degrees of freedom. For instance, it can be used to describe the horizontal movement of a hinged sheet pile wall.

6. Moving Hydrostatic

If type=moving-hydrostatic is used to define a more general form of the type=hydrostatic boundary condition, the subsequent lines take the form:

<node set name>, <dof>, <dir>, <slope>, <zero-level 0>, <t0>, <zero-level 1>, <t1>

• <node set name> = name of the node set to which the boundary condition is applied
• <dof> = the degree of freedom to be constrained.
• <dir> = Direction of action in global coordinates (x=1, y=2, z=3)
• <slope> = slope of hydrostatic distribution, e.g. unit weight of water in case of a hydrostatic distribution pore water pressure.
• <zero-level 0> = coordinate of the initial zero-level for the hydrostatic distribution at time t0
• <t0> = initial time t0
• <zero-level 1> = coordinate of the final zero-level for the hydrostatic distribution at time t1

Figure 2: Example for boundary conditions of type `moving-hydrostatic`

For times smaller than t0 the zero-level for the hydrostatic distribution is <zero-level 0> and for times larger than t1 the zero-level corresponds to <zero-level 1>