A model of geometric non‐linearity in static analysis of a shell, which includes the effects of large displacements and small deformations, is presented. A non‐linear problem was solved using the updated Lagrange procedure. External load was applied in increments. An iterative solution procedure was carried out for each load increment until a vector of residual forces became arbitrary small. At the end of the each iteration step states of variables were updated in comparison to their states at the end of the previous iteration step. Impact of large displacements was included by transformation of variables between the global and local coordinate systems. The shell was simulated by 8 and 9 node curved degenerated finite elements, free of membrane and shear locking. A layered model along the shell thickness was used. Presented numerical model was verified on the results of three experimentally tested very slender steel cantilever beams, with elastic behaviour of material for all applied loads. Cantilever beams were loaded by eccentric force at their ends. Example 1 shows the cantilever beam placed horizontally and loaded by bending. In Example 2, cantilever beam was placed vertically and loaded by longitudinal compressive force (Fig. 1). In Example 3, cantilever beam was placed horizontally and loaded by bending and torsion. |