fenics_shells.naghdi package¶
Submodules¶
fenics_shells.naghdi.kinematics module¶
-
fenics_shells.naghdi.kinematics.G(F)¶ Returns the stretching tensor (1st non-linear Naghdi strain measure).
\[G = \frac{1}{2}(F^{T}F - I)\]Parameters: F – Deformation gradient. Returns: UFL expression of stretching tensor.
-
fenics_shells.naghdi.kinematics.K(F, d)¶ Returns the curvature tensor (2nd non-linear Naghdi strain measure).
\[K = \frac{1}{2}(F^{T}\nabla d + (\nabla d)^T F^{T})\]Parameters: - F – Deformation gradient.
- d – Director vector.
Returns: UFL expression of curvature tensor.
-
fenics_shells.naghdi.kinematics.d(theta)¶ Director vector.
\[d = \left\lbrace \sin(\theta_2)\cos(\theta_1), -\sin(\theta_1), \cos(\theta_2)\cos(\theta_1) \right\rbrace^T\]Parameters: vector (Rotation) – Returns: UFL expression of director vector.
-
fenics_shells.naghdi.kinematics.g(F, d)¶ Returns the shear strain vector (3rd non-linear Naghdi strain measure).
\[g = F^{T}d\]Parameters: - F – Deformation gradient.
- d – Director vector.
Returns: UFL expression of shear strain vector.