bc

Although called boundary condition, here we only deal with trivial Dirichlet boundary condition.

Syntax

There are currently several commands to define boundary conditions.

fix (1) (2) (3...)
fix2 (1) (2) (3...)
multiplierbc (1) (2) (3...)
penaltybc (1) (2) (3...)
# (1) int, unique tag
# (2) string, dof identifier
# (3...) int, tags of nodes that shall be constrained

To apply BCs to node groups, it is possible to use the following commands.

groupmultiplierbc (1) (2) (3...)
grouppenaltybc (1) (2) (3...)
# (1) int, unique tag
# (2) string, dof identifier
# (3...) int, tags of groups that shall be constrained

Remark

1. Both fix and fix2 serve the same purpose but with different approaches. The fix command modifies the corresponding main diagonal term by multiplying a large number, for example $10^8$. The fix2 command erase the column and row of target DoF and set the main diagonal to unity. In both case, the corresponding right hand side entry is erased.

2. The fix and penaltybc commands is computationally efficient but leads to an ill-conditioned matrix. This may not be a problem for direct solvers but will greatly affect the performance of iterative solvers. The penalty number can be controlled by set command via constraint_multiplier option.

3. The fix2 and multiplierbc commands requires more operations but the final matrix is well conditioned.

4. The performance difference is almost negligible. Either one can be used with direct solvers. The error won't accumulate as there is a special mechanism to prevent it.

5. The DoF identifier (2) takes the following string input: 1, 2, 3, 4, 5, 6, pinned, encastre, xsymm, ysymm, zsymm and the corresponding initials p, e, x, y, z. The names do not actually reflect their meaning, instead, following DoFs would be restrained when string input is given.

   1. pinned: U1 U2 U3

   2. encastre: U1 U2 U3 UR1 UR2 UR3

   3. xsymm: U1 UR2 UR3

   4. ysymm: UR1 U2 UR3

   5. zsymm: UR1 UR2 U3

6. The nontrivial Dirichlet boundary condition is treated as displacement load.