In this thesis, a simple and efficient 4-node shell element based on the degenerated shell concept and the shell theory has been derived for non-linear analysis. The proposed shell element can describe finite deformations and finite rotations within small strains in a element. Transverse shear deformation with independent translational DOFs and rotational DOFs is considered according to the assumption of Mindlin-Reissner, and the induced locking problem is alleviated by the adoption of assumed strain method.
In order to model arbitrary structures including smooth surfaces, folded, and beam-shell combined structures effectively a simple and efficient finite rotation formulation eliminating the component that may give rise to singularity has been proposed. In the proposed method, convenient use of six degrees of freedom referred to global coordinate is possible without deteriorating the robustness and the convergence rate of classical 5-DOF formulation.
First of all, shell nodes are grouped into folded nodes and smooth surface nodes. This procedure is naturally concerned with establishing the directors. First the normal vectors of all elements abutting the node are calculated. If the angle between the normal vectors at the node is less than a limit, the node is considered to be on smooth surface and an average normal vector is used as a nodal normal vector. To use six degrees of freedom the projection procedure is necessary to suppress the component of singular rotation. This makes the responses of structure almost identical to those of 5-DOF formulation and precludes the instability due to the singular rotation.
The node is to be categorized into folded nodes, if any angles between the normal vectors are larger than the limit or the node is connected to a beam element. In this case the element normal vector is taken as a nodal normal vector for each elements. When the directors are updated, the projection procedure is not necessary on account of the assumption of rigid rotation that the angles between the normal vectors at a node have to be preserved during deformation processes.
Since the section eccentricity can cause significant errors in overall responses of structures, it has been considered in the element formulation. Therefore the use of rigid links or artificial layers is not necessary. The shell is assumed to be composed of an eccentric layer and a master layer to consider section eccentricity. From the shell kinematic assumptions, the deformation at an arbitrary point of the eccentric layer can be described by the degrees of freedom of the master layer.
Laminate composite structures and material non-linear responses are considered to model the buckling problem of structures more accurately. In the material non-linear analysis, von-Mises yield criterion and linear isotropic hardening has been used. To keep the efficiency of non-linear analysis numerical integration is performed in accordance with the shell theory. The consistent linearization of the virtual work principle with the generalized mid-point integration scheme leads to quadratic rate of convergence of Newton-Raphson method even in the region of plasticity.
From the numerical experiments including smooth surfaces and stiffened structures, the proposed method has shown to be applied effectively to the geometrical and/or material non-linear analysis of shell structures with finite rotation.
