A new two-dimensional performance measure in purchase order sizing

Lack of knowledge about demand responses or about behavioural aspects of decision-making within procurement processes is a significant cost driver in modern supply chains. Very often, this lack of knowledge leads to a substantial increase in inventories and may endanger negotiated service levels. For instance, various studies reveal that decision- makers tend to anchor orders close to the average past demand although the target order size is significantly higher or lower. In order to improve this situation, feedback has to be systematically provided to the decision-makers. In combination with modern big data analytics and reporting instruments that enable exhaustive monitoring, effective indicators have to be applied in order to directly detect processes with significant potential for improvement. Hence, this paper proposes a new approach for measuring the intricacy in purchase order sizing that addresses self-awareness skills of decision-makers. By simultaneously analysing the amount and structure of occurring costs, processes with a significant and simple structured error pattern are identified. In order to identify these processes more reliably, a new approach that supplements former information-theoretic entropy measures by an additional cost value is proposed. By analysing costs and the structure of deviations from target values in a two-dimensional measure, a more comprehensive understanding of the considered order sizing process is pursued. In order to illustrate the application of the new approach and show limitations of one-dimensional measures, different scenarios that exemplify the new approach are presented.     

A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics

A reduction/hyper reduction framework is presented for dramatically accelerating the solution of nonlinear dynamic multiscale problems in structural and solid mechanics. At each scale, the dimensionality of the governing equations is reduced using the method of snapshots for proper orthogonal decomposition, and computational efficiency is achieved for the evaluation of the nonlinear reduced‐order terms using a carefully designed configuration of the energy conserving sampling and weighting method. Periodic boundary conditions at the microscales are treated as linear multipoint constraints and reduced via projection onto the span of a basis formed from the singular value decomposition of Lagrange multiplier snapshots. Most importantly, information is efficiently transmitted between the scales without incurring high‐dimensional operations. In this proposed proper orthogonal decomposition–energy conserving sampling and weighting nonlinear model reduction framework, training is performed in two steps. First, a microscale hyper reduced‐order model is constructed in situ, or using a mesh coarsening strategy, in order to achieve significant speedups even in non‐parametric settings. Next, a classical offline–online training approach is performed to build a parametric hyper reduced‐order macroscale model, which completes the construction of a fully hyper reduced‐order parametric multiscale model capable of fast and accurate multiscale simulations. A notable feature of this computational framework is the minimization, at the macroscale level, of the cost of the offline training using the in situ or coarsely trained hyper reduced‐order microscale model to accelerate snapshot acquisition. The effectiveness of the proposed hyper reduction framework at accelerating the solution of nonlinear dynamic multiscale problems is demonstrated for two problems in structural and solid mechanics. Speedup factors as high as five orders of magnitude are shown to be achievable. Copyright © 2017 John Wiley & Sons, Ltd.     

Medium-range order dictates local hardness in bulk metallic glasses

Bulk metallic glasses (BMGs) are materials with outstanding strength and elastic properties that make them tantalizing for engineering applications, yet our poor understanding of how their amorphous atomic arrangements control their broader mechanical properties (hardness, wear, fracture, etc.) impedes our ability to apply materials science principles in their design. In this work, we uncover the hierarchical structure that exists in BMGs across the nano- to microscale by using nanobeam electron diffraction experiments. Our findings reveal that local hardness of microscale domains decreases with increasing size and volume fraction of atomic clusters with higher local medium range order (MRO). Furthermore, we propose a model of ductile phase softening that will enable the future design of BMGs by tuning the MRO size and distribution in the nanostructure.     

A Lanczos-based method for structural dynamic reanalysis problems

In this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original system Ax = λx, procedures are developed for the modified standard eigenvalue Problem (A + ΔA)x? = λ x?, where

• 1 ΔA = Σ_jBS_jB^T, where S_j = S ∈ ?^{p × p}, p ? n and B ∈ ?^{n × p} is constant for all the perturbations S_j.
• 2 ΔA = Σ_iΣ_j B_iS_jB_i^T, where B_i ∈ ?^{n × p} may vary with the pertubations S_j.

The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate the applications of the method.     

A survey of optimal structural design under dynamic constraints

Recent published research on structural optimization subject to dynamic constraints is reviewed, and suggestions for further work are offered. Both methods for handling constraints on natural frequencies and methods for treating the more difficult constraints on quantities directly related to the dynamic response are discussed. Computational aspects are emphasized throughout.     

A graph-based model to measure structural redundancy for supply chain resilience

Globalisation and lean initiatives increase the vulnerabilities of the supply chains (SC), where disruptions in any plant in a supply chain network (SCN) can propagate throughout the whole SCN. Redundancy is part of the SC re-engineering to improve supply chain resilience (SCRES). This paper presents a conceptual model of an SCN using graph theory, considering the relationships between plants and materials. Based on the model, the structural redundancy of the SCN is measured, which is used to assess SCRES. This assessment approach focuses on the resilience of the SCN against disruptions. Case studies are discussed to illustrate the applicability of this model and show that increasing structural redundancy of the SCN improves SCRES against disruptions.     

Optical and structural investigations on iron-containing phosphate glasses

The article reports the preparation and complex characterization of iron-containing phosphate glasses considered to be ecological materials, as they contain non-toxic compounds related to environment. The oxide system Li₂O?CMgO?C(CaO)?CAl₂O₃?CP₂O₅?C(FeO/Fe₂O₃) was investigated in respect to its structural changes caused by MgO replacement with CaO and by the iron addition. UV?Cvis?CNIR (ultraviolet?Cvisible?Cnear infrared) spectroscopy as well as thermo-gravimetric (TG) measurements, differential thermo-analysis (DTA), X-ray diffraction (XRD) analysis, electronic paramagnetic resonance (EPR), and Mossbauer (nuclear gamma resonance) spectroscopy have been used to investigate redox states and coordination symmetry of iron, together with vitreous network changes during the heat treatment up to 1000 °C. UV?Cvis?CNIR transmission spectroscopy revealed no structural modifications when MgO was substituted by CaO, but noteworthy absorption bands attributed to Fe²⁺/Fe³⁺ species. TG analysis made in the 20?C1000 °C range shows low weight loss accompanied by several thermal effects, as evidenced by DTA. XRD patterns for the glass samples heat treated at about 700 °C revealed the presence of different phosphate crystalline phases containing Mg, Al, and Fe ions. EPR spectroscopy revealed the presence of paramagnetic Fe³⁺ ions and the change of the first coordination symmetry, when the samples are heated below the vitreous transition temperature. Mossbauer spectroscopy has evidenced two paramagnetic species, Fe²⁺ and Fe³⁺, both in octahedral coordination symmetry and a clustering process supported by only Fe³⁺ ions.     

Synthesis and X-ray structural investigation of undoped borate glasses

A series of undoped borate glasses: Li₂B₄O₇, LiKB₄O₇, LiB₃O₅, SrB₄O₇, and LiCaBO₃ of high optical quality and chemical purity were obtained from the corresponding polycrystalline compounds using standard glass synthesis under technological conditions developed by the authors. The glasses were obtained by rapid cooling of molten crystalline material, which was heated to 100 K above the melting point to prevent crystallization and to exceed the glass transition point. The X-ray diffraction intensity profiles of the investigated glasses were typical of glassy compounds. The most typical intensity profile, consisting of almost symmetrical peaks, was observed in the case of Li₂B₄O₇ and LiB₃O₅. Substitution and partial substitution of Li atoms by Sr and Ca atoms was accompanied by significant changes in the intensity profiles of the investigated glasses. Pair correlation functions and structural parameters (average interatomic distances and coordination number to oxygen) of the investigated glasses were evaluated and analyzed. Structural peculiarities of the investigated borate glasses are discussed in comparison with structural data available for their crystalline analogs.     

A one-step method for direct integration of structural dynamic equations

The choice on an efficient direct integration procedure for linear structural dynamic equations of motion is discussed. It is suggested that as accuracy parameter the truncation error on the exponential terms contained in the modal contributions of the exact solution be assumed. This error does not always coincide with the local truncation error. These considerations were used to design an unconditionally stable one-step method whose accuracy is 0(h⁴). Numerical comparisons with some well-known integration schemes showed the efficiency of the proposed method.     

A novel technique to measure the dynamic response of an opticalphase modulator

This paper describes a novel technique that can be used to measure the frequency response of an optical phase modulator. An interesting feature of this technique is that it does not require the use of an interferometer for phase-to-amplitude conversion, thus alleviating stability and alignment problems. Instead, the electro-optically induced birefringence of the modulator and a simple polarizer are used to transform phase modulation into intensity modulation. The latter is detected with a high-speed photodiode and, for a sinusoidal modulating signal, the resulting output power spectrum is shown to be related to the actual phase modulation index by simple mathematical expressions involving Bessel functions. Using only a spectrum analyzer, the magnitude and the variations of the modulation index are measured over a broad frequency range     

Multiresolution atomistic simulations of dynamic fracture in nanostructured ceramics and glasses

Multimillion atom molecular-dynamics (MD) simulations are performed to investigate dynamic fracture in glasses and nanostructured ceramics. Using multiresolution algorithms, simulations are carried out for up to 70 ps on massively parallel computers. MD results in amorphous silica (a-SiO₂) reveal the formation of nanoscale cavities ahead of the crack tip. With an increase in applied strain, these cavities grow and coalesce and their coalescence with the advancing crack causes fracture in the system. Recent AFM studies of glasses confirm this behavior. The MD value for the critical stress intensity factor of a-SiO₂ is in good agreement with experiments. Molecular dynamics simulations are also performed for nanostructured silicon nitride (n-Si₃N₄). Structural correlations in n-Si₃N₄ reveal that interfacial regions between nanoparticles are amorphous. Under an external strain, nanoscale cavities nucleate and grow in interfacial regions while the crack meanders through these regions. The fracture toughness of n-Si₃N₄ is found to be six times larger than that of crystalline -Si₃N₄. We also investigate the morphology of fracture surfaces. MD results reveal that fracture surfaces of n-Si₃N₄ are characterized by roughness exponents 0.58 below and 0.84 above a certain crossover length, which is of the order of the size of Si₃N₄ nanoparticles. Experiments on a variety of materials reveal this behavior. The final set of simulations deals with the interaction of water with a crack in strained silicon. These simulations couple MD with a quantum-mechanical (QM) method based on the density functional theory (DFT) so that chemical processes are included. For stress intensity factor K=0.4 MPa m^1/2, we find that a decomposed water molecule becomes attached to dangling bonds at the crack or forms a Si-O-Si structure. At K=0.5 MPa m^1/2, water molecules decompose to oxidize Si or break Si-Si bonds.     

Stationary and nonstationary absorption in lead silicate glasses with short-range order inversion

The methods of stationary and pulsed absorption spectroscopy were used to study the optical properties of xPbO·(1-x)SiO₂ glasses produced by cooling of a molten mixture of chemically pure oxides. The spectral dependence of the absorption in the range of the short-wavelength edge obeys the Urbach rule. As the PbO concentration increases, a red shift of the optical transparency cutoff is observed. At x = 0.45-0.50 the amorphous matrix undergoes a structural inversion, which is due to a transition from a silicate to a lead-oxygen glass-forming network. This transition shows up as an abrupt change in the type of optical transitions, the width of the optical gap E_g, and the Urbach energy E_U. The short-range order inversion in the glass is accompanied by an increase in the atomic correlation radius R₀ characterizing the size of the medium-range order in the system. It was found empirically that R₀ has a linear relationship with a continuum-disorder parameter E_U.It was found that pulsed electron irradiation produces short-lived color centers, which absorb at 1.65 and 2.30 eV. The relaxation of unstable absorption centers is characterized by microsecond kinetics. The nature of unstable absorption centers and their relationship with a short-range order inversion and the structure function of lead atoms have been discussed. The kinetic dependences have been interpreted in the context of a mechanism responsible for diffusion-controlled tunneling recombination of radiation-induced electronic and hole states of the matrix.