Nonlinear Geometric and Material Behavior of Shell Structures with Large Strains

Abstract

This paper presents an approach for a general laminated shell geometry describable by orthogonal curvilinear coordinates. The theory includes through‐the‐thickness parabolic distribution of transverse shear stress, transformation of Cauchy stress‐strain relations into Lagrangian coordinates, and a layered elastic‐plastic analyses. Additionally, a simplified approach that allows large displacements and rotations is incorporated. The theory is cast into a displacement‐based finite‐element formulation and then specialized to cylindrical and spherical geometry. The theory is then applied to the isotropic and transversely isotropic laminated shells. Results incorporating the Cauchy‐Lagrangian transformation with through‐the‐thickness strain show a slightly more flexible response than in published results that are based on inextensible assumptions. These problems also indicate that the usual locking associated with shell elements is eliminated.