topoptlab.voigt module

topoptlab.voigt.from_voigt(A_v: ndarray, eng_conv: bool = False) → ndarray

Convert 2nd rank tensor into from its Voigt representation to the standard matrix represenation.

Parameters:

• A_v (np.ndarray) – 2nd rank tensor in Voigt represenation (so a column vector) shape (…,(ndim**2 + ndim) /2).

• eng_conv (bool) – if True, engineering convention is applied meaning the shear components are scaled by a factor of two in Voigt notation. Usually applies only to strains.

Returns:

A – 2nd rank tensor in matrix notation shape (…,ndim,ndim).

Return type:

np.ndarray

topoptlab.voigt.to_voigt(A: ndarray, eng_conv: bool = False) → ndarray

Convert 2nd rank tensor into from the standard matrix represenation to its Voigt representation.

Parameters:

• A (np.ndarray) – 2nd rank tensor in matrix represenation shape (…,ndim, ndim).

• eng_conv (bool) – if True, engineering convention is applied meaning the shear components are scaled by a factor of two in Voigt notation. Usually applies only to strains.

Returns:

A_v – 2nd rank tensor in Voigt notation shape (…,(ndim**2 + ndim) /2).

Return type:

np.ndarray

topoptlab.voigt.voigt_index(i: ndarray, j: ndarray, ndim: int) → ndarray

Map tensor index pairs (i,j) to Voigt indices for arbitrary dimension.

Parameters:

• i (int or np.ndarray) – first tensor index (1-based).

• j (int or np.ndarray) – second tensor index (1-based).

• ndim (int) – spatial dimension.

Returns:

alpha – Voigt index/indices (0-based).

Return type:

np.ndarray

topoptlab.voigt.voigt_pair(alpha: ndarray, ndim: int) → Tuple[ndarray, ndarray]

Map Voigt indices back to tensor index pairs (i,j),

Parameters:

• alpha (int or np.ndarray) – Voigt index/indices (0-based).

• ndim (int) – spatial dimension.

Returns:

• i (np.ndarray) – first tensor index (0-based).

• j (np.ndarray) – second tensor index (0-based).