Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

GRMHD formulation of highly super-Chandrasekhar rotating magnetized white dwarfs: stable configurations of non-spherical white dwarfs

Here we extend the exploration of significantly super-Chandrasekhar magnetized white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetized polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetized axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2-3 solar mass, with central (deep interior) magnetic fields of the order of 10(14) G and differential rotation with surface time periods of about 1-10 s. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous Type Ia supernovae, to which observational evidence ascribes mass in the range 2.1-2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.

A hybrid finite element formulation for flexible multibody dynamics

This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.

Spallation analysis with a closed trans-scale formulation damage evolution

A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbers De* and De, Mach number M and damage number S. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is deter-mined by Deborah number De+. Deborah number De* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbers De* and De, Mach number M and damage number S is discussed.

An elastoplastic constitutive relation of whisker-reinforced composite for meso damage: Part I - formulation

An elastoplastic constitutive relation is developed for meso damage of whisker-reinforced composites. A model is constructed that includes orientation distribution of whiskers and slip systems as well as interface and crystal sliding. Evolution of damage will be addressed. Given in Part I is the formulation while examples will be illustrated in Part II.

Archaeometric evidence for the authenticity of the Jehoash inscription tablet

A gray, fine-grained arkosic sandstone tablet bearing an inscription in ancient Hebrew from the First Temple Period contains a rich assemblage of particles accumulated in the covering patina. Two types of patina cover the tablet: a thin layer of black to orange iron-oxide-rich layer, a product of micro-biogenic processes, and a light beige patina that contains feldspars, carbonate, iron oxide, subangular quartz grains, carbon ash particles and gold globules (1 to 4 microns [1 micron = 0.001 millimeter] in diameter). The patina covers the rock surface as well as the engraved lettering grooves and blankets and thus post-dates the incised inscription as well as a crack that runs across the stone and several of the engraved letters. Radiocarbon analyses of the carbon particles in the patina yield a calibrated radiocarbon age of 2340 to 2150 Cal BP. The presence of microcolonial fungi and associated pitting in the patina indicates slow growth over many years. The occurrence of pure gold globules and carbon ash particles is evidence of a thermal event in close proximity to the tablet (above 1000 degrees Celsius). This study supports the antiquity of the patina, which in turn, strengthens the contention that the inscription is authentic.

Statistical formulation and experimental determination of growth rate of micrometre cracks under impact loading

A new statistical formulation and a relevant experimental approach to determine the growth rate of microcracks were proposed. The method consists of experimental measurements and a statistical analysis' on the basis of the conservation law of number density of microcracks in phase space. As a practical example of the method, the growth rate of microcracks appearing in an aluminium alloy subjected to planar impact loading was determined to be ca. 10 mu m/mu s under a tensile stress of 1470 MPa and load duration between 0.26 mu s and 0.80 mu s.