Nonlinear analysis of isotropic, orthotropic and laminated plates and shells

Abstract A class of improved shear-flexible finite elements for nonlinear analyses of general plate and shell structures will be presented. The derivations are being based on degenerated plate and shell elements. In order to avoid shear locking, which is quite a problem at low-parametric elements, a special treatment of internal (spurious) constraints has been developed. The novel and essential aspect is to be seen in the splitting of the terms for stress and strain into two parts each. One part has to completely satisfy the kinematic field equations. For the remaining part the strain-displacement compatibility is merely required in a weak form. Aside from the trial functions for the displacements and rotations, trial functions for the components of the stress field have to be introduced. The weak coupling of the incremental normal displacements and the incremental rotations leads to an exact representation of constant bending even for bilinear displacement functions