In the parameterization with Rodrigues rotation vector, due to the definition in Eq. (1), the rotation angle must be restricted to −?<?<?−?<?<?. However, with an updated formulation, this is
not a limitation as rotations may not exceed ? within a single time increment. Using an updated-Lagrangian framework, displacements and rotations must be updated after each time-step.
Fig. 1 (adapted from ) shows the shell updated model. A plane shell mid-surface is assumed at the initial reference configuration. At this configuration, it Mutant IDH1-IN-1
is defined a local orthonormal system e1r,e2r,e3r , with corresponding coordinates ?1,?2,? ?1,?2,? . The vectors
e?r (?=1,2?=1,2) are placed on the shell mid-plane and e3r is normal to this plane.
Fig. 1. Shell updated model (adapted from ).Figure optionsDownload full-size imageDownload as PowerPoint slide
In this reference configuration, the position ?? of any material point can be described by the vector field:equation(7)?=?+ar?=?+arwhere the vector ?=??e?r describes the position of points on the reference mid-surface and ar=?e3r is the shell director, with ?∈H=[−hb,ht]?∈H=[−hb,ht] as the thickness coordinate and h=hb+hth=hb+ht as the shell thickness in the reference configuration.