{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation

In this paper, we develop and analyze C(0) penalty methods for the fully nonlinear Monge-Ampere equation det(D(2)u) = f in two dimensions. The key idea in designing our methods is to build discretizations such that the resulting discrete linearizations are symmetric, stable, and consistent with the continuous linearization. We are then able to show the well-posedness of the penalty method as well as quasi-optimal error estimates using the Banach fixed-point theorem as our main tool. Numerical experiments are presented which support the theoretical results.

Model-following Neuro-adaptive approach for robust control of high performance aircrafts

Based on dynamic inversion, a relatively straightforward approach is presented in this paper for nonlinear flight control design of high performance aircrafts, which does not require the normal and lateral acceleration commands to be first transferred to body rates before computing the required control inputs. This leads to substantial improvement of the tracking response. Promising results are obtained from six degree-offreedom simulation studies of F-16 aircraft, which are found to be superior as compared to an existing approach (which is also based on dynamic inversion). The new approach has two potential benefits, namely reduced oscillatory response (including elimination of non-minimum phase behavior) and reduced control magnitude. Next, a model-following neuron-adaptive design is augmented the nominal design in order to assure robust performance in the presence of parameter inaccuracies in the model. Note that in the approach the model update takes place adaptively online and hence it is philosophically similar to indirect adaptive control. However, unlike a typical indirect adaptive control approach, there is no need to update the individual parameters explicitly. Instead the inaccuracy in the system output dynamics is captured directly and then used in modifying the control. This leads to faster adaptation, which helps in stabilizing the unstable plant quicker. The robustness study from a large number of simulations shows that the adaptive design has good amount of robustness with respect to the expected parameter inaccuracies in the model.

Effect of density variation and non-covalent functionalization on the compressive behavior of carbon nanotube arrays

Arrays of aligned carbon nanotubes (CNTs) have been proposed for different applications, including electrochemical energy storage and shock-absorbing materials. Understanding their mechanical response, in relation to their structural characteristics, is important for tailoring the synthesis method to the different operational conditions of the material. In this paper, we grow vertically aligned CNT arrays using a thermal chemical vapor deposition system, and we study the effects of precursor flow on the structural and mechanical properties of the CNT arrays. We show that the CNT growth process is inhomogeneous along the direction of the precursor flow, resulting in varying bulk density at different points on the growth substrate. We also study the effects of non-covalent functionalization of the CNTs after growth, using surfactant and nanoparticles, to vary the effective bulk density and structural arrangement of the arrays. We find that the stiffness and peak stress of the materials increase approximately linearly with increasing bulk density.

Effect of irradiation on the microstructure and mechanical behavior of nanocrystalline nickel

The effect of 4.0 MeV proton irradiation on the microstructure and mechanical properties of nanocrystalline (nc) nickel was investigated. The irradiation damage induced in the sample was of the order of 0.004 dpa. Transmission electron microscopy of irradiated samples indicated the presence of dislocation loops within the grains. An increase in hardness and strain-rate sensitivity (m) of nc-Ni with irradiation was noted. The rate-controlling deformation mechanism in irradiated nc-Ni was identified to be interaction of dislocations with irradiation-induced defects. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Behavior of Sandwich Beams With Functionally Graded Rubber Core in Three Point Bending

The three-point bending behavior of sandwich beams made up of jute epoxy skins and piecewise linear functionally graded (FG) rubber core reinforced with fly ash filler is investigated. This work studies the influence of the parameters such as weight fraction of fly ash, core to thickness ratio, and orientation of jute on specific bending modulus and strength. The load displacement response of the sandwich is traced to evaluate the specific modulus and strength. FG core samples are prepared by using conventional casting technique and sandwich by hand layup. Presence of gradation is quantified experimentally. Results of bending test indicate that specific modulus and strength are primarily governed by filler content and core to sandwich thickness ratio. FG sandwiches with different gradation configurations (uniform, linear, and piecewise linear) are modeled using finite element analysis (ANSYS 5.4) to evaluate specific strength which is subsequently compared with the experimental results and the best gradation configuration is presented. POLYM. COMPOS., 32:1541-1551, 2011. (C) 2011 Society of Plastics Engineers

Nonlinear Suboptimal Guidance with Impact Angle Constraint for Slow Moving Targets in 1-D Using MPSP

Using a recently developed method named as model predictive static programming (MPSP), a nonlinear suboptimal guidance law for a constant speed missile against a slow moving target with impact angle constraint is proposed. In this paper MPSP technique leads to a closed form solution of the latax history update for the given problem. Guidance command is the latax,which is normal to the missile velocity and the terminal constraints are miss distance and impact angle. The new guidance law is validated by considering the nonlinear kinematics with both lag-free and first order autopilot delay.

Active Vibration Suppression of One-dimensional Nonlinear Structures Using Optimal Dynamic Inversion

A flexible robot arm can be modeled as an Euler-Bernoulli beam which are infinite degrees of freedom (DOF) system. Proper control is needed to track the desired motion of a robotic arm. The infinite number of DOF of beams are reduced to finite number for controller implementation, which brings in error (due to their distributed nature). Therefore, to represent reality better distributed parameter systems (DPS) should be controlled using the systems partial differential equation (PDE) directly. In this paper, we propose to use a recently developed optimal dynamic inversion technique to design a controller to suppress nonlinear vibration of a beam. The method used in this paper determines control forces directly from the PDE model of the system. The formulation has better practical significance, because it leads to a closed form solution of the controller (hence avoids computational issues).