Generation of elastic geodesic gridshells with anisotropic cross sections

Geodesic gridshells are shell structures made of continuous elements following geodesic lines. Their properties ease the use of beams with anisotropic cross-sections by avoiding bending about their strong axis. However, such bending may arise when flattening arbitrary geodesic grids, which forbids their initial assembly on the ground. This study provides a process to design elastic geodesic gridshells, that is, gridshells that minimise bending moments in both formed and near-flat configurations. The generation process first brings a target geodesic network onto a plane by maintaining arc lengths. The flat mesh is then relaxed to minimise its main curvatures and hence bending moments in its members. The result is an elastic geodesic gridshell that can be assembled flat on the ground and then lifted up into its target surface. The method is applied to the design of six geodesic gridshells made of reclaimed skis.

Tracking changes in the area, thickness, and volume of the Thwaites tabular iceberg “B30” using satellite altimetry and imagery

Icebergs account for half of all ice loss from Antarctica and, once released, present a hazard to maritime operations. Their melting leads to a redistribution of cold fresh water around the Southern Ocean which, in turn, influences water circulation, promotes sea ice formation, and fosters primary production. In this study, we combine CryoSat-2 satellite altimetry with MODIS and Sentinel-1 satellite imagery and meteorological data to track changes in the area, freeboard, thickness, and volume of the B30 tabular iceberg between 2012 and 2018. We track the iceberg elevation when it was attached to Thwaites Glacier and on a further 106 occasions after it calved using Level 1b CryoSat data, which ensures that measurements recorded in different acquisition modes and within different geographical zones are consistently processed. From these data, we map the iceberg's freeboard and estimate its thickness taking snowfall and changes in snow and ice density into account. We compute changes in freeboard and thickness relative to the initial average for each overpass and compare these to estimates from precisely located tracks using the satellite imagery. This comparison shows good agreement (correlation coefficient 0.87) and suggests that colocation reduces the freeboard uncertainty by 1.6 m. We also demonstrate that the snow layer has a significant impact on iceberg thickness change. Changes in the iceberg area are measured by tracing its perimeter, and we show that alternative estimates based on arc lengths recorded in satellite altimetry profiles and on measurements of the semi-major and semi-minor axes also capture the trend, though with a 48 % overestimate and a 15 % underestimate, respectively. Since it calved, the area of B30 has decreased from 1500±60 to 426±27 km2, its mean freeboard has fallen from 49.0±4.6 to 38.8±2.2 m, and its mean thickness has reduced from 315±36 to 198±14 m. The combined loss amounts to an 80 %±16 % reduction in volume, two thirds (69 %±14 %) of which is due to fragmentation and the remainder (31 %±11 %) of which is due to basal melting.

Effects of intracorneal ring segments on the biomechanical response of the ectatic cornea to air-puff: A patient-specific numerical analysis

The assessment of the underlying factors that influence the biomechanics and dynamics of the cornea is essential for preserving the safety and efficacy of refractive surgeries. In the present work, the operated cornea with intracorneal ring segments (ICRSs) in a patient-specific finite-element model (FEM) was subjected to the air-puff. Then, the dynamic deformation parameters predicted by the FEM were obtained and compared with the corresponding values in clinical measurements. In this study, the effects of ICRS design, position, and implementation procedure in six different surgical scenarios were examined on the induced corneal stresses, deformation behavior, and shape regularization. While surgical scenarios with arc lengths of 160° (single and double segment), 355° implemented with the tunnel incision method provided similar maximum apical displacement (MAD) and highest concavity radius of curvature HCR), they induced significantly different flattening effects. The surgical scenarios with the segment of 160° arc-length implemented in nasal–temporal direction showed an approximately 15% higher reduction in mean corneal power ([Formula: see text]) value than the superior–inferior direction. From a solid-mechanics perspective, the study of ICRS mechanics in the cornea also confirmed the importance of the implementation position to achieve satisfactory flattening outcomes. Comparison of the two types of ICRS implementation procedures showed that, although the pocket method demonstrated a 10.23% higher MAD, it induced a higher reduction in the HCR of 21.65% compared with tunnel incision. The developed numerical model demonstrated the direct correlation of the ICRS insertion site with induced contact stresses and ICRS position stability. The study hypothesizes the significant influence of ICRS implementation position and procedure on the corneal biomechanical and dynamical behaviors. The proposed approach can be assessed as a robust and novel framework for planning optimized corneal refractive surgeries.

Changes in the Area, Thickness, and Volume of the Thwaites B30 Iceberg Observed by Satellite Altimetry and Imagery

Icebergs account for half of all ice loss from Antarctica and, once released, present a hazard to maritime operations. Their melting leads to a redistribution of cold fresh water around the Southern Ocean which, in turn, influences water circulation, promotes sea ice formation, and fosters primary production. In this study, we combine CryoSat-2 satellite altimetry with MODIS and Sentinel-1 satellite imagery to track changes in the area, freeboard, thickness, and volume of the B30 tabular iceberg between 2012 and 2018. We track the iceberg elevation when it was attached to Thwaites Glacier and on a further 106 occasions after it calved using Level 1b CryoSat data, which ensures that measurements recorded in different modes and within different geographical zones are consistently processed. From these data, we mapped the icebergs freeboard and estimated its thickness taking snowfall and changes in snow and ice density into account. We compute changes in freeboard and thickness relative to the initial average for each overpass and compare this time series to precisely located tracks using the satellite imagery. This comparison shows that our time series of iceberg freeboard change is in good agreement with the geolocated overpasses (correlation coefficient 0.87), and suggests that geolocation reduces the uncertainty by 1.6 m. We also demonstrate that the snow layer has a significant impact on iceberg thickness change. Changes in the iceberg area are measured by tracing its perimeter and we show that alternative estimates based on arc lengths recorded in satellite altimetry profiles and on measurements of the semi-major and semi-minor axes also capture the trend, though with a 48 % overestimate and a 15 % underestimate, respectively. Since it calved, the area of B30 has decreased from 1500 +/− 60 to 426 +/− 27 km2, its mean freeboard has fallen from 49.0 +/− 4.6 to 38.8 +/− 2.2 m, and its mean thickness has reduced from 315 ± 36 to 198 ± 14 m. The combined loss amounts to an 80 +/− 16 % reduction in volume, two thirds (69 ± 14 %) of which is due to fragmentation and the remainder (31 ± 11 %) is due to basal melting.

Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

A genetic algorithm for the fuzzy shortest path problem in a fuzzy network

The shortest path problem (SPP) is an optimization problem of determining a path between specified source vertex s and destination vertex t in a fuzzy network. Fuzzy logic can handle the uncertainties, associated with the information of any real life problem, where conventional mathematical models may fail to reveal proper result. In classical SPP, real numbers are used to represent the arc length of the network. However, the uncertainties related with the linguistic description of arc length in SPP are not properly represented by real number. We need to address two main matters in SPP with fuzzy arc lengths. The first matter is how to calculate the path length using fuzzy addition operation and the second matter is how to compare the two different path lengths denoted by fuzzy parameter. We use the graded mean integration technique of triangular fuzzy numbers to solve this two problems. A common heuristic algorithm to solve the SPP is the genetic algorithm. In this manuscript, we have introduced an algorithmic method based on genetic algorithm for determining the shortest path between a source vertex s and destination vertex t in a fuzzy graph with fuzzy arc lengths in SPP. A new crossover and mutation is introduced to solve this SPP. We also describe the QoS routing problem in a wireless ad hoc network.

The Impact Behaviour of Crab Carapaces in Relation to Morphology

Brachyuran crab carapaces are protective, impact-resistant exoskeletons with elaborate material microstructures. Though several research efforts have been made to characterise the physical, material and mechanical properties of the crab carapace, there are no studies detailing how crab morphologies might influence impact resistance. The purpose of this paper is to characterise and compare Brachyuran crab carapace morphologies in relation to their impact properties, using opto-digital, experimental and numerical methods. We find that crab carapaces with both extended carapace arc-lengths and deep carapace grooves lose stiffness rapidly under cyclic impact loading, and fail in a brittle manner. Contrarily, carapaces with smaller arc lengths and shallower, more broadly distributed carapace grooves are more effective in dissipating stresses caused by impact throughout the carapace structure. This allows them to retain stiffness for longer, and influences their failure mode, which is ductile (denting), rather than brittle fracture. The findings in this paper provide new bioinspired approaches for the geometrical designs by which means material failure under cyclic impact can be controlled and manipulated.

Geometric Approach to Optimal Path Problem with Uncertain Arc Lengths

In this paper, the problem of finding the shortest paths, one of the most important problems in science and technology has been geometrically studied. Shortest path algorithm has been generalized to the shortest cycles in each homotopy class on a surface with arbitrary topology, using the universal covering space notion in the algebraic topology. Then, a general algorithm has been presented to compute the shortest cycles (geometrically rather than combinatorial) in each homotopy class. The algorithm can handle surface meshes with the desired topology, with or without boundary. It also provides a fundamental framework for other algorithms based on universal coverage space due to the capacity and flexibility of the framework.

A Study of Neutrosophic Shortest Path Problem

Shortest path problem (SPP) is an important and well-known combinatorial optimization problem in graph theory. Uncertainty exists almost in every real-life application of SPP. The neutrosophic set is one of the popular tools to represent and handle uncertainty in information due to imprecise, incomplete, inconsistent, and indeterminate circumstances. This chapter introduces a mathematical model of SPP in neutrosophic environment. This problem is called as neutrosophic shortest path problem (NSPP). The utility of neutrosophic set as arc lengths and its real-life applications are described in this chapter. Further, the chapter also includes the different operators to handle multi-criteria decision-making problem. This chapter describes three different approaches for solving the neutrosophic shortest path problem. Finally, the numerical examples are illustrated to understand the above discussed algorithms.