A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites

The present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solution

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

On thermomechanics of polymers in the transition and rubber regions

A nonisothermal theory of viscoelastic media, motivated by thermomechanical behaviour of polymeric materials in the transition zone between the rubber and glassy states, was developed previously by Crochet and Naghdi (1974) and included as a special case a theory with small deformation suitable for thermorheologically simple materials. The object of the present paper is to modify the form of the previous constitutive equations slightly in order to extend the validity of the theory to the rubber region in which the medium behaves elastically.Anglai