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#### Shell knot

The expansion of a shell node leads to a set of nodes lying on a straight line. Therefore, the stretch tensor is reduced to the stretch along this line. Let be a unit vector parallel to the expansion and and unit vectors such that and . Then can be written as:

| (54)

leading to one stretch parameter . Since the stretch along and is immaterial, Equation (54) can also be replaced by

| (55)

representing an isotropic expansion. Equation (53) can now be replaced by

|  | (56)

Consequently, a knot resulting from a shell expansion is characterized by 3 translational degrees of freedom, 3 rotational degrees of freedom and 1 stretch degree of freedom.

Next: Arbitrary knot Up: Mathematical description of a Previous: Beam knot Contents