Nonlinear response of shell structures: effects of plasticity modelling and large rotations

Many structural applications require nonlinear finite element analyses in order to assess response and capacity. Plastic deformations may be accounted for by means of thickness integration or stress resultants. The stress resultant model employed herein is based on Ilyushinsʹ linear yield criterion for thin shells. The corners present with this criterion are circumvented by means of a simplification, hence, there is no need for multi-surface stress resultant updates. A backward Euler difference is employed in the stress resultant update, and a consistent tangent is used in the Newton–Raphson iterations on the global equilibrium. Limit points are traversed by means of an orthogonal trajectory method. The response of compression dominated shells with imperfections typically corresponds to limit point behaviour. For stress resultant plasticity, the nonlinear transition from initial yield to full plasticity in shell bending is missed. Hence, the efficiency obtained by eliminating thickness integration is countered by some inaccuracy in the response simulation. This is investigated by means of comparison with finite element simulations employing integration through thickness (with linear or nonlinear hardening). Both steel and aluminium alloys are considered. In collapse response of slender structures, the straining of the material may be moderate, but the motion may be governed by large rigid body translations and rotations. A way of accounting for this by means of the co-rotated approach is presented. Triangular high-performance facet shell elements are employed. By example computations, the importance of nonlinear geometry contributions is illustrated.