Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Structure and phase-composition of Ti-doped gas atomized Raney-type Ni catalyst precursor alloys

Raney-type Ni precursor alloys containing 75 at.% Al and doped with 0, 0.75, 1.5 and 3.0 at.% Ti have been produced by a gas atomization process. The resulting powders have been classified by size fraction with subsequent investigation by powder XRD, SEM and EDX analysis. The undoped powders contain, as expected, the phases Ni₂Al₃, NiAl₃ and an Al-eutectic. The Ti-doped powders contain an additional phase with the TiAl₃ DO₂₂ crystal structure. However, quantitative analysis of the XRD results indicate a far greater fraction of the TiAl₃ phase is present than could be accounted for by a simple mass balance on Ti. This appears to be a (Ti_xNi_1−x)Al₃ phase in which higher cooling rates favour small x (low Ti-site occupancy by Ti atoms). SEM and EDX analysis reveal that virtually all the available Ti is contained within the TiAl₃ phase, with negligible Ti dissolved in either the Ni₂Al₃ or NiAl₃ phases.     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

A miniature triaxial apparatus for investigating the micromechanics of granular soils with in situ X-ray micro-tomography scanning

The development of a miniature triaxial apparatus is presented. In conjunction with an X-ray micro-tomography (termed as X-ray μCT hereafter) facility and advanced image processing techniques, this apparatus can be used for in situ investigation of the micro-scale mechanical behavior of granular soils under shear. The apparatus allows for triaxial testing of a miniature dry sample with a size of \mathrm{8}\hspace{0.17em}\mathrm{mm}\times \mathrm{16}\hspace{0.17em}\mathrm{mm} (diameter \times height). In situ triaxial testing of a 0.4–0.8 mm Leighton Buzzard sand (LBS) under a constant confining pressure of 500 kPa is presented. The evolutions of local porosities (i.e., the porosities of regions associated with individual particles), particle kinematics (i.e., particle translation and particle rotation) of the sample during the shear are quantitatively studied using image processing and analysis techniques. Meanwhile, a novel method is presented to quantify the volumetric strain distribution of the sample based on the results of local porosities and particle tracking. It is found that the sample, with nearly homogenous initial local porosities, starts to exhibit obvious inhomogeneity of local porosities and localization of particle kinematics and volumetric strain around the peak of deviatoric stress. In the post-peak shear stage, large local porosities and volumetric dilation mainly occur in a localized band. The developed triaxial apparatus, in its combined use of X-ray μCT imaging techniques, is a powerful tool to investigate the micro-scale mechanical behavior of granular soils.     

Effect of spatial constraints on the phase evolution of YFeO3-based nanopowders under heat treatment of glycine-nitrate combustion products

Formation and structural transformations of yttrium orthoferrite crystals have been studied using X-ray diffractometry, Mössbauer spectroscopy and transmission electron microscopy combined with electron microdiffraction. Said processes have been studied under heat treatment of glycine-nitrate combustion products. There have been identified formations of three structural yttrium orthoferrite modifications – amorphized hexagonal <h₁>-YFeO₃ (P6₃cm) and nanocrystalline hexagonal h₂-YFeO₃ (P6₃/mmc), as well as nanocrystalline orthorhombic o-YFeO₃ (Pbnm), which are selectively formed depending on available three-dimensional confinements. Based on the analysis of changes in the fluid and size composition formulation, it has been proposed mechanism for formation and transformation of YFeO₃ nanocrystals, including growth stage of h₂-YFeO₃ crystals due to amorphized phase of <h₁>-YFeO₃ up to critical size of about 15?nm and their subsequent transformation into orthorhombic form o-YFeO₃.     

Precipitating spinel into precursor glass and its assistance in crystallization

The crystallization phenomena of spinel in CaO-MgO-Al₂O₃-SiO₂-Fe₂O₃ glass have received much attention due to the particular role in preparation of glass-ceramic materials, which represent an effective option to manage hazardous waste. In this study, both preliminary spinel and secondary spinel were precipitated in the precursor glass. The formation of these spinel was meticulously assessed by a combination of X-ray diffractometry and scanning electron microscopy. The structure of the microenvironment in the precursor glass was characterized by Raman spectrums. These advanced techniques highlight the potential for one-step crystallization of the glass. The investigation, which focused on one-step crystallization, demonstrated the growth of pyroxene on spinel accompanying a migration of chromium. The results also show the microstructure of the obtained glass-ceramic was very dependent on the heat-treat temperature. This study not only unambiguously reveals the precipitation mechanisms of spinel but also provides more documentation for one-step crystallization in the glass-ceramics field.     

The robust knapsack problem with queries

We consider robust knapsack problems where item weights are uncertain. We are allowed to query an item to find its exact weight,where the number of such queries is bounded by a given parameter Q. After these queries are made, we need to pack the items robustly, i.e., so that the choice of items is feasible for every remaining possible scenario of item weights.The central question that we consider is: Which items should be queried in order to gain maximum profit? We introduce the notion of query competitiveness for strict robustness to evaluate the quality of an algorithm for this problem, and obtain lower and upper bounds on this competitiveness for interval-based uncertainty. Similar to the study of online algorithms, we study the competitiveness under different frameworks, namely we analyze the worst-case query competitiveness for deterministic algorithms, the expected query competitiveness for randomized algorithms and the average case competitiveness for known distributions of the uncertain input data. We derive theoretical bounds for these different frameworks and evaluate them experimentally. We also extend this approach to Γ-restricted uncertainties introduced by Bertsimas and Sim.Furthermore, we present heuristic algorithms for the problem. In computational experiments considering both the interval-based and the Γ-restricted uncertainty, we evaluate their empirical performance. While the usage of a Γ-restricted uncertainty improves the nominal performance of a solution (as expected), we find that the query competitiveness gets worse.     

Robust Control of Permanent Magnet Synchronous Motors

In this paper, permanent magnet synchronous motors (PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea. In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter, the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.      

Producing fully-lamellar microstructure for wrought beta-gamma TiAl alloys without single α-phase field

Fine-grained fully-lamellar (FL) microstructure is desired for TiAl components to serve as compressor/turbine blades and turbocharger turbine wheels. This study deals with the process and phase transformation to produce FL microstructure for Mo stabilized beta-gamma TiAl alloys without single α-phase field. Unlike the α + γ two-phased TiAl or beta-gamma TiAl with single α-phase field, the wrought multi-phase TiAl–4/6Nb–2Mo–B/Y alloys exhibit special annealing process to obtain FL microstructure. Short-term annealing at temperatures slightly above β-transus is recommended to produce the desired FL microstructure. The related mechanism is to guarantee the sufficient diffusion homogenization of β stabilizers during single β-phase annealing, and further avoid α decomposition by α → γ + β when cooling through α + β + γ phase field. The colony boundary β phase contributes to fine-grained nearly FL microstructure, by retarding the coarsening of the α phase grains.