Topology optimization of modular structures with multiple assemblies and applications to airborne shelves

This work is devoted to the aeronautical application of topology optimization for modular structures with multiple assemblies that consist of repeated standard modules and optional reinforcements.These kinds of structures are widely used owing to their transportability,reconfigurability,low manufacturing and service costs.In this work,the design of airborne shelves with modular structures characterized by the standard module configuration is formulated for the first time as a topology optimization problem of multiple assemblies and multiple load cases subjected to the volume constraint.It is shown that the weighted compliance design of multiple assemblies is a compromising solution compared to the optimization result of each individual assembly of standard modules.Meanwhile,the performance of optimized airborne shelves with the modular structures can effectively be ameliorated with the help of reinforcements.

Detecting and describing the modular structures of weighted networks

In the functional properties of complex networks, modules play a central role. In this paper, we propose a new method to detect and describe the modular structures of weighted networks. In order to test the proposed method, as an example, we use our method to analyse the structural properties of the Chinese railway network. Here, the stations are regarded as the nodes and the track sections are regarded as the links. Rigorous analysis of the existing data shows that using the proposed algorithm, the nodes of network can be classified naturally. Moreover, there are several core nodes in each module. Remarkably, we introduce the correlation function Grs, and use it to distinguish the different modules in weighted networks.

Investigation on Effects of Mooring Line Fractures and Connector Failures for A Hybrid Modular Floating Structure System

The present work reports a Hybrid Modular Floating Structure(HMFS)system with typical malfunction conditions.The effects of both fractured mooring lines and failed connectors on main hydrodynamic responses(mooring line tensions,module motions,connector loads and wave power production)of the HMFS system under typical sea con-ditions are comparatively investigated.The results indicate that the mooring tension distribution,certain module motions(surge,sway and yaw)and connector loads(Mz)are significantly influenced by mooring line fractures.The adjacent mooring line of the fractured line on the upstream side suffers the largest tension among the remaining mooring lines,and the case with two fractured mooring lines in the same group on the upstream side is the most dangerous among all cases of two-line failures in view of mooring line tensions,module motions and connector loads.There-fore,one emergency strategy with appropriate relaxation of a proper mooring line has been proposed and proved effective to reduce the risk of more progressive mooring line fractures.In addition,connector failures substantially affect certain module motions(heave and pitch),certain connector loads(Fz and My)and wave power production.The present work can be helpful and instructive for studies on malfunction conditions of modular floating structure(MFS)systems.

The Fundamental Relationship between Harmonic Quark Masses and Reduced Max Planck Constant

O. A. Teplov developed an approach to describe the meson quark model by establishing a mathematical quark series (harmonic quark series). With respect to the physical mesons, he made some basic hypotheses of his own and used the well-known theory of harmonic oscillation to construct a numerical mass series that obeys a rigid multiplicative pattern and allows the physical meson masses to be calculated accurately. We have found that his numerical quark series, i.e., their masses, has a fundamental relation to the reduced Max Planck constant ħand report on it in the present paper. This discovery is obviously a theoretical contribution to the correctness of Teplov’s harmonic quark model approach and at the same time a confirmation of the importance of this simple and powerful research work.

Quantitative Comparison of Modular Linear Permanent Magnet Vernier Machines with and without Partitioned Primary

A comparison of two modular linear permanent-magnet vernier(LPMV)machines is presented.A modular LPMV machine with a partitioned primary,which can significantly improve the modulation effect,is proposed.Benefitting from the partition design,the space conflict between the permanent magnet(PM)and the armature magnetic field is relieved.First,the topologies of modular LPMV machines with and without a partitioned primary are presented.Then,the effect of the partitioned primary on the modular LPMV machine is analyzed using flux modulation theory.Moreover,analytical expressions for the trapezoidal permeance are derived.In addition,the harmonic components,back electromotive forces,and thrust forces of the machines with and without the partitioned primary are comparatively analyzed.The results reveal that the thrust force density of the LPMV machine with a partitioned primary is increased by 32.3%.Finally,experiments are performed on a prototype machine for validation.

Spatial Correlation Function in Modular Networks

Due to the complexity of the interactions among the nodes of the complex networks,the properties of the networkmodules,to a large extent,remain unknown or unexplored.In this paper,we introduce the spatial correlation function Grs to describe the correlations among the modules of the weighted networks.In order to test the proposedmethod,we use ourmethod to analyze and discuss themodular structures of the ER random networks,scale-free networks and the Chinese railway network.Rigorous analysis of the existing data shows that the spatial correlation function Grs is suitable for describing the correlations among different networkmodules.Remarkably,we find that different networks display different correlations,especially,the correlation function Grs with different networks meets different degree distribution,such as the linear and exponential distributions.

A Dimensionality Reduction Framework for Detection of Multiscale Structure in Heterogeneous Networks

Graph clustering has been widely applied in exploring regularities emerging in relational data.Recently,the rapid development of network theory correlates graph clustering with the detection of community structure,a common and important topological characteristic of networks.Most existing methods investigate the community structure at a single topological scale.However,as shown by empirical studies,the community structure of real world networks often exhibits multiple topological descriptions,corresponding to the clustering at different resolutions.Furthermore,the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree.It is very challenging to detect multiscale community structure in heterogeneous networks.In this paper,we propose a novel,unified framework for detecting community structure from the perspective of dimensionality reduction.Based on the framework,we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction.We then propose a novel method to detect communities at multiple topological scales within our framework.We further show that existing algorithms fail to deal with heterogeneous node degrees.We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework.Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks.