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Computing the electronic energy levels of a finite system or nanostructure is more difficult than computing those of an infinite system or bulk material. In the literature, a technique for simplifying this computation has been proposed, wherein energy levels of a finite system are derived from those of the corresponding infinite system. So far, this method has been validated only for finite length one-dimensional systems and for higher-dimensional systems at k = 0. We establish that this technique, hereafter referred to as the confined Bloch wave (CBW) method, is valid for higher-dimensional symmorphic systems over the entire Brillouin zone, provided some symmetry requirements are satisfied. For this purpose we use a lateral surface superlattice as a model for the infinite system and a stripe or ribbon patterned in this superlattice as a model for the nanostructure. Finally, we compute the subbands of zigzag ribbons of one type patterned in artificial graphene and show that the CBW method predicts all the important subbands in these ribbons, and provides additional insight into the nature of their wavefunctions. � 2010 IOP Publishing Ltd.

Admissible boundary conditions are derived for an arbitrarily laminated internally pressurized cylindrical shell of finite length, under the framework of Donnell's, Love-Timoshenko's and Sanders' kinematic relations, and the CLT (based on Love's first approximation theory). Closed-form solutions for the same cylindrical shell are presented for Love-Timoshenko's theory, with two sets of asymmetrically placed prescribed boundary conditions. As the first example, internally pressurized thin hybrid general (asymmetric) four-layer cylindrical shells with RS2-C4 boundary conditions, made of glass and carbon fiber reinforced composite layers, are numerically investigated. In the second example, the numerical results for two-layer asymmetrically laminated cylindrical shells, with RS2-SS1 boundary conditions, are compared with those, computed using triangular finite elements based on the layer-wise constant shear-angle theory (LCST), in order to evaluate the limit of applicability of the CLT. � 2007 Elsevier Ltd. All rights reserved.