Freeform Skeletal Shape Optimization of Compliant Mechanisms

Compliant mechanisms are elastic continua used to transmit or transform force and motion mechanically. The topology optimization methods developed for compliant mechanisms also give the shape for a chosen parameterization of the design domain with a fixed mesh. However, in these methods, the shapes of the flexible segments in the resulting optimal solutions are restricted either by the type or the resolution of the design parameterization. This limitation is overcome in this paper by focusing on optimizing the skeletal shape of the compliant segments in a given topology. It is accomplished by identifying such segments in the topology and representing them using Bezier curves. The vertices of the Bezier control polygon are used to parameterize the shape-design space. Uniform parameter steps of the Bezier curves naturally enable adaptive finite element discretization of the segments as their shapes change. Practical constraints such as avoiding intersections with other segments, self-intersections, and restrictions on the available space and material, are incorporated into the formulation. A multi-criteria function from our prior work is used as the objective. Analytical sensitivity analysis for the objective and constraints is presented and is used in the numerical optimization. Examples are included to illustrate the shape optimization method.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Nonlinear optical absorption in a graphene infrared photodetector

The photoresponse of the graphene photodetector elucidated strong dependence on several optical parameters, such as the angle of incidence and the incident power of infrared exposure at room temperature. The sinusoidal dependence of the photoresponse on incidence angle, which had not been realized before, has now been revealed. The combined effect of the photo excited charge carrier and the photon drag effect explain this nonlinear optical absorption in graphene at lower incident power. The nonlinear dependence of the charge carrier generation on the incident power revealed that this process contributed to the nonlinear photoresponse. However, a deviation is observed at a higher incident power due to the induction of thermal effects in the graphene lattice. This work demonstrates the tunability of the graphene photodetector under a systematic variation that involves both parameters.

Optimization of degree of sphericity of primary phase during cooling slope casting of A356 Al alloy: Taguchi method and regression analysis

The present work presents the results of experimental investigation of semi-solid rheocasting of A356 Al alloy using a cooling slope. The experiments have been carried out following Taguchi method of parameter design (orthogonal array of L-9 experiments). Four key process variables (slope angle, pouring temperature, wall temperature, and length of travel of the melt) at three different levels have been considered for the present experimentation. Regression analysis and analysis of variance (ANOVA) has also been performed to develop a mathematical model for degree of sphericity evolution of primary alpha-Al phase and to find the significance and percentage contribution of each process variable towards the final outcome of degree of sphericity, respectively. The best processing condition has been identified for optimum degree of sphericity (0.83) as A(3), B-3, C-2, D-1 i.e., slope angle of 60 degrees, pouring temperature of 650 degrees C, wall temperature 60 degrees C, and 500 mm length of travel of the melt, based on mean response and signal to noise ratio (SNR). ANOVA results shows that the length of travel has maximum impact on degree of sphericity evolution. The predicted sphericity obtained from the developed regression model and the values obtained experimentally are found to be in good agreement with each other. The sphericity values obtained from confirmation experiment, performed at 95% confidence level, ensures that the optimum result is correct and also the confirmation experiment values are within permissible limits. (c) 2014 Elsevier Ltd. All rights reserved.

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

Single fluid schemes that rely on an interface function for phase identification in multicomponent compressible flows are widely used to study hydrodynamic flow phenomena in several diverse applications. Simulations based on standard numerical implementation of these schemes suffer from an artificial increase in the width of the interface function owing to the numerical dissipation introduced by an upwind discretization of the governing equations. In addition, monotonicity requirements which ensure that the sharp interface function remains bounded at all times necessitate use of low-order accurate discretization strategies. This results in a significant reduction in accuracy along with a loss of intricate flow features. In this paper we develop a nonlinear transformation based interface capturing method which achieves superior accuracy without compromising the simplicity, computational efficiency and robustness of the original flow solver. A nonlinear map from the signed distance function to the sigmoid type interface function is used to effectively couple a standard single fluid shock and interface capturing scheme with a high-order accurate constrained level set reinitialization method in a way that allows for oscillation-free transport of the sharp material interface. Imposition of a maximum principle, which ensures that the multidimensional preconditioned interface capturing method does not produce new maxima or minima even in the extreme events of interface merger or breakup, allows for an explicit determination of the interface thickness in terms of the grid spacing. A narrow band method is formulated in order to localize computations pertinent to the preconditioned interface capturing method. Numerical tests in one dimension reveal a significant improvement in accuracy and convergence; in stark contrast to the conventional scheme, the proposed method retains its accuracy and convergence characteristics in a shifted reference frame. Results from the test cases in two dimensions show that the nonlinear transformation based interface capturing method outperforms both the conventional method and an interface capturing method without nonlinear transformation in resolving intricate flow features such as sheet jetting in the shock-induced cavity collapse. The ability of the proposed method in accounting for the gravitational and surface tension forces besides compressibility is demonstrated through a model fully three-dimensional problem concerning droplet splash and formation of a crownlike feature. (C) 2014 Elsevier Inc. All rights reserved.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations

The periodic 3D Navier-Stokes equations are analyzed in terms of dimensionless, scaled, L-2m-norms of vorticity D-m (1 <= m <= infinity). The first in this hierarchy, D-1, is the global enstrophy. Three regimes naturally occur in the D-1-D-m plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime 1]; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar, Dukkipati, & Bhatnagar, 2014), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on SF algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms. (C) 2014 Elsevier Ltd. All rights reserved.

A bottom-up approach for optimization of friction stir processing parameters; a study on aluminium 2024-T3 alloy

Friction stir processing (FSP) is emerging as one of the most competent severe plastic deformation (SPD) method for producing bulk ultra-fine grained materials with improved properties. Optimizing the process parameters for a defect free process is one of the challenging aspects of FSP to mark its commercial use. For the commercial aluminium alloy 2024-T3 plate of 6 mm thickness, a bottom-up approach has been attempted to optimize major independent parameters of the process such as plunge depth, tool rotation speed and traverse speed. Tensile properties of the optimum friction stir processed sample were correlated with the microstructural characterization done using Scanning Electron Microscope (SEM) and Electron Back-Scattered Diffraction (EBSD). Optimum parameters from the bottom-up approach have led to a defect free FSP having a maximum strength of 93% the base material strength. Micro tensile testing of the samples taken from the center of processed zone has shown an increased strength of 1.3 times the base material. Measured maximum longitudinal residual stress on the processed surface was only 30 MPa which was attributed to the solid state nature of FSP. Microstructural observation reveals significant grain refinement with less variation in the grain size across the thickness and a large amount of grain boundary precipitation compared to the base metal. The proposed experimental bottom-up approach can be applied as an effective method for optimizing parameters during FSP of aluminium alloys, which is otherwise difficult through analytical methods due to the complex interactions between work-piece, tool and process parameters. Precipitation mechanisms during FSP were responsible for the fine grained microstructure in the nugget zone that provided better mechanical properties than the base metal. (C) 2014 Elsevier Ltd. All rights reserved.

Field dependent and disorder-induced nonlinear charge transport in electrochemically doped polypyrrole devices

Electric field activated charge transport is studied in the metal/polymer/metal device structure of electropolymerized polypyrrole down to 10 K with varying carrier density and disorder. Disorder induced nonlinear behaviour is observed in polypyrrole devices grown at room temperature which is correlated to delocalization of states. The slope parameter of currentvoltage characteristics (in log-log scale) increases as the temperature decreases, which indicates the onset of stronger field dependence. The field dependence of mobility becomes dominant as the carrier density decreases. The sharp dip in differential conductance indicates the localization of carriers at low temperatures which reduces the effective number of carriers involved in the transport.

Formation Flying with Nonlinear Partial Integrated Guidance and Control

Using the dynamic inversion philosophy, a nonlinear partial integrated guidance and control approach is presented in this paper for formation flying. It is based on the evolving philosophy of integrated guidance and control. However, it also retains the advantages of the conventional guidance then control philosophy by retaining the timescale separation between translational and rotational dynamics explicitly. Simulation studies demonstrate that the proposed technique is effective in bringing the vehicles into formation quickly and maintaining the formation.

Simultaneous Perturbation Newton Algorithms for Simulation Optimization

We present a new Hessian estimator based on the simultaneous perturbation procedure, that requires three system simulations regardless of the parameter dimension. We then present two Newton-based simulation optimization algorithms that incorporate this Hessian estimator. The two algorithms differ primarily in the manner in which the Hessian estimate is used. Both our algorithms do not compute the inverse Hessian explicitly, thereby saving on computational effort. While our first algorithm directly obtains the product of the inverse Hessian with the gradient of the objective, our second algorithm makes use of the Sherman-Morrison matrix inversion lemma to recursively estimate the inverse Hessian. We provide proofs of convergence for both our algorithms. Next, we consider an interesting application of our algorithms on a problem of road traffic control. Our algorithms are seen to exhibit better performance than two Newton algorithms from a recent prior work.

Adaptive Flight-Control Design Using Neural-Network-Aided Optimal Nonlinear Dynamic Inversion

A neural-network-aided nonlinear dynamic inversion-based hybrid technique of model reference adaptive control flight-control system design is presented in this paper. Here, the gains of the nonlinear dynamic inversion-based flight-control system are dynamically selected in such a manner that the resulting controller mimics a single network, adaptive control, optimal nonlinear controller for state regulation. Traditional model reference adaptive control methods use a linearized reference model, and the presented control design method employs a nonlinear reference model to compute the nonlinear dynamic inversion gains. This innovation of designing the gain elements after synthesizing the single network adaptive controller maintains the advantages that an optimal controller offers, yet it retains a simple closed-form control expression in state feedback form, which can easily be modified for tracking problems without demanding any a priori knowledge of the reference signals. The strength of the technique is demonstrated by considering the longitudinal motion of a nonlinear aircraft system. An extended single network adaptive control/nonlinear dynamic inversion adaptive control design architecture is also presented, which adapts online to three failure conditions, namely, a thrust failure, an elevator failure, and an inaccuracy in the estimation of C-M alpha. Simulation results demonstrate that the presented adaptive flight controller generates a near-optimal response when compared to a traditional nonlinear dynamic inversion controller.