In the analysis of shells, two types of geometric nonlinearities, namely large deformation and large rotation nonlinearities, may arise. Large deformation nonlinearity is attributed to the membrane stress developed due to the midplane stretching when the shell experience large displacements as compared to its dimensions. Large rotation nonlinearity is caused by large change of element slope during the analysis. This change causes the transformation matrix to change during the analysis. It also causes the relationship between the displacement field and the nodal rotation to be trigonometric, Figure (2.5).

The objective of the analysis is to evaluate the equilibrium positions of the shell, at the discrete time points or load levels , , , , ..., ** t**, . It is assumed that the solution for the kinematic and static variables for all time steps from time zero (initial configuration) to time

- Updated Lagrangian Description
- Total Lagrangian Description for Three-Dimensional Shells
- Total Lagrangian Description for Two-Dimensional Shells