Rotations as primary unknowns in the nonlinear theory of shells and corresponding finite element models.

*(English)*Zbl 0595.73084
Finite rotations in structural mechanics, Proc. Euromech. Colloq. 197, Jabłonna/Pol. 1985, Lect. Notes Eng. 19, 239-258 (1986).

Summary: [For the entire collection see Zbl 0592.00032.]

A consistent geometrically nonlinear theory of shells is derived based on the formulation of a generalized variational principle. In addition to displacements and stresses, the components of a finite rotation vector are introduced as primary unknowns. This is accomplished by applying the polar decomposition of the deformation gradient. The basic equations are described in an incremental Lagrangian frame and are given in clear operator form to emphasize the additional equations of the angular momentum balance and the rigid body kinematics as a special feature of the present theory. Mixed variant tensorial components render advantages in the reduction to the shell equations in which shear effects are included. The two-dimensional principle serves then as the adequate basis for the formulation of different mixed-type finite element models. Numerical results are presented.

A consistent geometrically nonlinear theory of shells is derived based on the formulation of a generalized variational principle. In addition to displacements and stresses, the components of a finite rotation vector are introduced as primary unknowns. This is accomplished by applying the polar decomposition of the deformation gradient. The basic equations are described in an incremental Lagrangian frame and are given in clear operator form to emphasize the additional equations of the angular momentum balance and the rigid body kinematics as a special feature of the present theory. Mixed variant tensorial components render advantages in the reduction to the shell equations in which shear effects are included. The two-dimensional principle serves then as the adequate basis for the formulation of different mixed-type finite element models. Numerical results are presented.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74K15 | Membranes |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

49S05 | Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX) |

74K25 | Shells |