Orthogonal Designs and Type II Codes over ℤ2k

Symmetric designs are used to construct binary extremal self-dual codes and Hadamard matrices and weighing matrices are used to construct extremal ternary self-dual codes. In this paper, we consider orthogonal designs and related matrices to construct self-dual codes over a larger alphabet. As an example, a number of extremal Type II codes over _2k are constructed.     

Rarefied gas flow in concentric annular tube: Estimation of the Poiseuille number and the exact hydraulic diameter

The fully developed flow of rarefied gases through circular ducts of concentric annular cross sections is solved via kinetic theory. The flow is due to an externally imposed pressure gradient in the longitudinal direction and it is simulated by the BGK kinetic equation, subject to Maxwell diffuse-specular boundary conditions. The approximate principal of the hydraulic diameter is investigated for first time in the field of rarefied gas dynamics. For the specific flow pattern, in addition to the flow rates, results are reported for the Poiseuille number and the exact hydraulic diameter. The corresponding parameters include the whole range of the Knudsen number and various values of the accommodation coefficient and the ratio of the inner over the outer radius. The accuracy of the results is validated in several ways, including the recovery of the analytical solutions at the hydrodynamic and free molecular limits.     

Ratcheting,wrinkling and collapse of tubes under axial cycling

Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling modes. Initially the wrinkle amplitude grows with increasing load. The wrinkles gradually induce a reduction in axial rigidity eventually leading to a limit load instability followed by collapse. The two instabilities can be separated by strain levels of a few percent. This work investigates whether a tube that develops small amplitude wrinkles can be subsequently collapsed by persistent cycling. The problem is first investigated experimentally using SAF 2507 super-duplex steel tubes with D/t of 28.5. The tubes are first compressed to strain levels high enough for mild wrinkles to form; they are then cycled axially under stress control about a compressive mean stress. This type of cycling usually results in material ratcheting or accumulation of compressive strain; here it is accompanied by accumulation of structural damage due to the growth of the amplitude of the initial wrinkles. The tube average strain initially grows nearly linearly with the number of cycles, but as a critical value of wrinkle amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially and the tube collapses. The rate of ratcheting and the number of cycles to failure depend on the initial compressive pre-strain and on the amplitude of the stress cycles. However, collapse was found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model of the tube with initial axisymmetric imperfections, coupled to a cyclic plasticity model, are presented and used to simulate the series of experiments performed successfully. A sensitivity study of the formulation to the imperfections and to key constitutive model parameters is then performed.     

Path-dependent failure of inflated aluminum tubes

Our recent investigation on the formability of Al alloy tubes under combined internal pressure and axial load is expanded by examining the effect of the loading path traced. A set of Al-6260-T4 tubes were loaded along orthogonal stress paths to failure and the results are compared to those of the corresponding radial paths. It is confirmed that failure strains are path-dependent, but also is demonstrated that failure stresses become path-dependent if the prestrain is significant. The experiments are simulated using the previously developed finite element models and the calibration of the Yld2000-2D [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.-H., Chu, E., 2003. Plane stress yield function for aluminum alloy sheets-part I: theory. Int. J. Plasticity 19, 1297--1319] anisotropic yield function shown in [Korkolis, Y.P., Kyriakides, S., 2008b. Inflation and burst of anisotropic aluminum tubes. Part II: an advanced yield function including deformation-induced anisotropy. Int. J. Plasticity 24, 1625–1637] to yield accurate predictions of rupture for nine radial paths. The models are shown to reproduce the path dependence of the failure stresses and strains quite well. A group of additional radial and corner paths are subsequently examined numerically to enrich the existing data on path-dependence of failure. It is again shown that the amount of plastic prestraining in either of the two directions influences the difference of the failure stresses and strains between the radial and the corner stress paths.     

Localization and propagation of curvature under pure bending in steel tubes with Lüders bands

The paper examines the plastic bending of steel tubes exhibiting Lüders bands through a combination of experiments and analyses. In pure bending experiments on tubes with diameter-to-thickness ratio of 18.8 tested under end-rotation control, following the elastic regime the moment initially traced a somewhat ragged plateau. At the beginning of the plateau Lüders bands appeared on the tension and compression sides of the cross section and simultaneously the curvature localized in one or two short zones while the rest of the tube maintained a much lower curvature. As the rotation of the ends was increased, one of the higher curvature zones spread at a nearly steady rate, affecting an increasingly larger part of the tube. When the whole tube was deformed to the higher curvature, the moment started to gradually increase while the tube deformed uniformly. A moment maximum was eventually attained and the structure failed by localized diffuse ovalization without any apparent effect from the initial Lüders bands-induced propagating instability. The problem was analyzed using 3D finite elements with a fine mesh. The material was modeled as an elastic–plastic solid with an up–down–up response over the extent of the Lüders strain, followed by hardening. The calculated response reproduced all major structural events observed experimentally including the initiation of the Lüders deformation, the moment plateau that followed, its extent, and the curvature localization and propagation associated with it. As in the experiments, once the high curvature extended over the whole tube length, the response of the tube became stable and the curvature uniform. With further bending the increasing ovalization induced a limit moment at a very high curvature.     

Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method

A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm’s performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods.     

Linear and nonlinear waves in surface and wedge index potentials

We study optical beams that are supported at the surface of a medium with a linear index potential and by a piecewise linear wedge-type potential. In the linear limit the modes are described by Airy functions. In the nonlinear regime we find families of solutions that bifurcate from the linear modes and study their stability for both self-focusing and self-defocusing Kerr nonlinearity. The total power of such nonlinear waves is finite without the need for apodization.