pihnn.bc.stress_bc#

class pihnn.bc.stress_bc#

Bases: linear_elasticity_bc

Stress boundary condition:

$$\sigma \cdot n=t_0,$$

where $\sigma$ is the stress tensor, $n$ is the outward normal vector and $t_0$ is the assigned RHS value (applied traction).

To be used for the linear elasticity problem.

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

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.