| This research is focused on two major classes of problems: multiple-scale phenomena, and the shell-intersection problem. Included in the first class are problems of strain localization, as in plastic shear banding or the stress-channeling phenomenon due to (near) inextensiblility constraints in fiber-reinforced composites, as well as the high transverse strain gradients in the across-the-thickness of laminates. The second class of shell intersection problems often arises in practical applications involving branched shell parts, or due to very large geometric distortions in finite deformation analysis as in crashworthiness studies. All the present investigations are carried out in the context of a simple shell model of low-order quadrilateral mixed element of the first-order, shear-deformable type.;Second, the investigation of the plastic strain localization-capturing capability of the shell model is performed. The 'weak element localization test' is adopted, and the localization modes are resolved by singular-value-decomposition (SVD) technique. To a large extent, this part of the study is facilitated by the analogy between localization and wave propagation in solids. It is concluded that the underlying mixed form of shell element which naturally provides for enhanced (additional) strain modes, plays a crucial role in improving the element capability to capture diffuse and localize failure modes.;Finally, the shell-intersection problems are investigated. 6dof/node shell formulation for both linear and nonlinear analyses is consistently extended. An additional 'drill' rotational field is interpolated independently. To account for the effect of significant geometric distortions, a complete bilinear function for the independently assumed strain field is built by ideas from theory of geodesics. It is subsequently assessed in various benchmark problems.;Overall, numerical results have shown that the refined shell model is fairly reliable and computationally cost effective.;First, the issue of accurate predictions of interlaminar stresses (two-phase scheme) is addressed. A modified superconvergent patch recovery (MSPR) technique is utilized to obtain accurate nodal in-plane stresses. These are subsequently used with the thickness integration of the 3-D equilibrium to evaluate the transverse shear and normal stresses. Remarkably, the continuity of the resulting interlaminar stresses is automatically satisfied, and for flat geometry this simple two-phase procedure is completely equivalent to the far more computationally-expensive alternatives. |
