pihnn.bc.symmetry_bc

class pihnn.bc.symmetry_bc

Bases: linear_elasticity_bc

Symmetry boundary condition:

\[(\sigma \cdot n) \times n = u \cdot n = 0,\]

where \(\sigma\) is the stress tensor, \(u\) is the displacement vector and \(n\) is the outward normal vector.

To be used for the linear elasticity problem.

__call__(z, sxx, syy, sxy, ux, uy, normal, rhs=0)

Calculate residual of the boundary condition.

Parameters:

• z (torch.tensor) – Coordinates of the points where the BC is evaluated.

• sxx (torch.tensor) – \(\sigma_{xx}\) evaluated at the ‘z’ coordinates.

• syy (torch.tensor) – \(\sigma_{yy}\) evaluated at the ‘z’ coordinates.

• sxy (torch.tensor) – \(\sigma_{xy}\) evaluated at the ‘z’ coordinates.

• ux (torch.tensor) – \(u_{x}\) evaluated at the ‘z’ coordinates.

• uy (torch.tensor) – \(u_{y}\) evaluated at the ‘z’ coordinates.

• normal (torch.tensor) – Boundary outward normal vectors at the ‘z’ coordinates.

• rhs (torch.tensor) – Boundary condition RHS assigned value at the ‘z’ coordinates.

Returns:

• error (torch.tensor) - Residual of the boundary condition at the ‘z’ coordinates.