APPLICATION OF THE MAPLE PACKAGE FOR CALCULATING THE RIBBED PLATE FOR STRENGTH, TAKING INTO ACCOUNT THE DISCRETE LOCATION OF THE RIBS

This paper presents an analytical calculation of the stress-strain state of a ribbed plate supported by a cross system of stiffeners. The calculation was carried out by the Ritz method using the Maple mathematical package

Scalable Vertiport Hub Location Selection for Air Taxi Operations in a Metropolitan Region

On-demand air mobility services, often called air taxis, are on the way to revolutionize our urban/regional transportation sector by lifting transportation to the third dimension and thus possibly contribute to solving the congestion-induced transportation deadlock many metropolitan regions face today. Although existing research mainly focuses on the design of efficient vehicles and specifically battery technology, in the near future, a new question will arise: Where to locate the vertiports/landing pads for such air taxis? In this study, we propose a vertiport location selection problem. In contrast to existing studies, we allow the demand to be distributed over the whole metropolitan area, modeled as a grid, and exclude certain grid cells from becoming hubs, for example, because of safety/geographical constraints. The combination of these two contributions makes the problem intriguingly difficult to solve with standard solution techniques. We propose a novel variable neighborhood search heuristic, which is able to solve 12 × 12 grid instances within a few seconds of computation time and zero gaps in our experiments, whereas CPLEX needs up to 10 hours. We believe that our study contributes toward the scalable selection of vertiport locations for air taxis. Summary of Contribution: The increasing interest in opening the third dimension, that is, altitude, to transportation inside metropolitan regions raises new research challenges. Existing research mainly focuses on the design of efficient vehicles and control problems. In the near future, however, the actual operation of air taxis will lead to new set of operations research problems for so-called air taxi operations. Our contribution focuses on the optimization of vertiports for air taxi operations in a metropolitan region. We choose to model the problem over a grid-like demand structure, with a novel side constraint: selected grid cells are unavailable as hubs, for example, because of environmental, technical, cultural, or other reasons. This makes our model a special case in between the two traditional models: discrete location and continuous location. Our model is inherently difficult to solve for exact methods; for instance, solving a grid of 12 × 12 grid cells needs more than 10 hours with CPLEX, when modeled as a discrete location problem. We show that a straightforward application of existing neighborhood search heuristics is not suitable to solve this problem well. Therefore, we design an own variant of mixed variable neighborhood search, which consists of novel local search steps, tailored toward our grid structure. Our evaluation shows that by using our novel heuristic, almost all instances can be solved toward optimality.

Influence of reinforcing ribs on the deformed state of ellipsoidal shells under distributed load

This paper presents the problem about non-stationary oscillations of reinforced ellipsoidal shells, taking into account the discrete location of the ribs. Problem bases on a geometrically nonlinear variant of the Tymoshenko theory for shells and rods. A numerical method for solving problems of this class has been developed and substantiated. This article focuses on the location of the reinforcing ribs. On the basis of the developed numerical method the deformed state of discretely supported ellipsoidal shells for internal, external and internal-external placement of ribs is investigated. Boundary conditions for rigidly clamped edges of the shell were studied.

Multiscale Topology Optimization With Gaussian Process Regression Models

Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

Solving Classic Discrete Facility Location Problems Using Excel Spreadsheets

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the best possible subset of p facilities out of n possible candidates. I developed an Excel workbook that allows students to interactively evaluate the quality of different subsets, to run a VBA macro that finds the optimal subset, or to solve an ILP formulation that finds the optimal subset. Spreadsheets are available for five classic discrete location models: (1) the location set-covering problem, (2) the maximal covering location problem, (3) the p-median problem, (4) the p-centers problem, and (5) the simple plant location problem. The results from an assignment in a master’s-level business analytics course indicate that the workbook facilitates a better conceptual understanding of the precise nature of the discrete facility location problems by showing that they can be solved via enumeration of all possible combinations of p subsets that can be drawn from n candidate locations. More important, students directly observe the superiority of ILP as a solution approach as n increases and as p approaches n/2.

Lastverteilungen in Kugelgewindetrieben/Consideration of locally discrete loads in the service life calculation of ball screws

Kugelgewindetriebe (KGT) weisen abhängig von ihrer Geometrie und der vorherrschenden Belastung deutlich variable innere Lastverteilungen auf. Finite-Elemente-Modelle erlauben die Ermittlung dieser Verteilungen, die aktuell jedoch vor allem bei der Lebensdauerberechnung nur unzureichend berücksichtigt werden. Nachfolgend wird eine Methode zur Berücksichtigung ortsdiskreter Lastverteilungen in der Lebensdauerberechnung von Kugelgewindetrieben vorgestellt.   Ball screws (BS) exhibit strongly varying internal load distributions depending on their geometry and the applied load. With finite element models this distribution may be estimated, however, distributed loads are barely taken into account in applications such as service life calculation. In the following, a method to integrate discrete location load distributions into the service life calculation of ball screws is presented.

Evolution of respiratory syncytial virus genotype BA in Kilifi, Kenya, 15 years on

Respiratory syncytial virus (RSV) is recognised as a leading cause of severe acute respiratory disease and deaths among infants and vulnerable adults. Clinical RSV isolates can be divided into several known genotypes. RSV genotype BA, characterised by a 60-nucleotide duplication in the G glycoprotein gene, emerged in 1999 and quickly disseminated globally replacing other RSV group B genotypes. Continual molecular epidemiology is critical to understand the evolutionary processes maintaining the success of the BA viruses. We analysed 735 G gene sequences from samples collected from paediatric patients in Kilifi, Kenya, between 2003 and 2017. The virus population comprised of several genetically distinct variants (n = 56) co-circulating within and between epidemics. In addition, there was consistent seasonal fluctuations in relative genetic diversity. Amino acid changes increasingly accumulated over the surveillance period including two residues (N178S and Q180R) that mapped to monoclonal antibody 2D10 epitopes, as well as addition of putative N-glycosylation sequons. Further, switching and toggling of amino acids within and between epidemics was observed. On a global phylogeny, the BA viruses from different countries form geographically isolated clusters suggesting substantial localized variants. This study offers insights into longitudinal population dynamics of a globally endemic RSV genotype within a discrete location.

Generating optimal and near-optimal solutions to facility location problems

There is a decided bent toward finding an optimal solution to a given facility location problem instance, even when there may be multiple optima or competitive near-optimal solutions. Identifying alternate solutions is often ignored in model application, even when such solutions may be preferred if they were known to exist. In this paper we discuss why generating close-to-optimal alternatives should be the preferred approach in solving spatial optimization problems, especially when it involves an application. There exists a classic approach for finding all alternate optima. This approach can be easily expanded to identify all near-optimal solutions to any discrete location model. We demonstrate the use of this technique for two classic problems: the p-median problem and the maximal covering location problem. Unfortunately, we have found that it can be mired in computational issues, even when problems are relatively small. We propose a new approach that overcomes some of these computational issues in finding alternate optima and near-optimal solutions.