Local Load Redistribution Research Articles

An affine formulation of eigenstrain-based homogenization method and its application to polycrystal plasticity

Abstract Reduced order models (ROMs) are typically incorporated into concurrent multiscale approaches to allow for efficient nonlinear multiscale simulations and to alleviate high cost of direct nonlinear computational homogenization schemes. ROMs based on the ideas of transformation field analysis are among the most popular in the literature since they only require linear elastic simulations for model construction and typically have low number of degrees of freedom. However, these models have been shown to deliver overly stiff response in simulating wide range of materials. The present study focuses on mitigating this problem in the context of eigenstrain-based homogenization method (EHM) using instantaneous moduli information for polycrystal elastoviscoplasticity. For this purpose, a new EHM model is developed with the intention of using affine moduli for recomputation of the instantaneous localization tensors. The accuracy of the method is compared to the original EHM and direct crystal plasticity finite element simulations for several synthetic polycrystal microstructures, loading conditions and varying phase contrast. We show that the affine model delivers consistently softer response compared to the original EHM model. In particular, the affine model delivers notably more accurate response in the presence of high phase contrast. The affine EHM is able to capture local load redistribution through recomputation of the localization tensors.

Electric vehicle charging guidance based on weighted complex network

The charging station malfunction may deny the charging service for the electric vehicles at the station. As a result, the vehicles need to select other stations. How to make an optimal selection is difficult for the owners. An optimal charging guidance strategy based on a weighted complex network is proposed for the owners to select the optimal station. All the charging stations are modelled as a complex network in which the stations and the roads among them are defined as nodes and edges, respectively. Furthermore, each edge is weighted by the state of charge (SOC) of the vehicle, the charging price, and the distance and traffic conditions between these two stations. The bigger edge weight indicates the smaller probability that the owner at one node of the edge select the other node of the edge for charging, and vice versa. Based on the weighted complex network model, the local load redistribution method is presented to guide the charging of vehicles at the malfunctioning station. Consequently, the optimal scheduling of the vehicles is realized under the guidance strategy proposed in this paper. Finally, some contrast experiments are carried out to illustrate the effectiveness and the superiority of the proposed method.

Invulnerability Analysis and Optimization Strategy of Sector Network Using Cascading Failure Model

Resolving the challenge of flight delays caused by air traffic congestion renders it necessary to explore the mode of congestion propagation. By applying complex network theory, this article establishes a complex network structure where airspace sectors act as nodes, and the edges represent traffic flow relationships between sectors. In addition, a cascading failure model is proposed to analyze the airspace sector network’s invulnerability. The critical threshold and the sector abnormality rate are determined according to the cascading failure measurement indexes. Based on the remaining capacity of sector nodes, two optimization strategies are proposed: adjacent load redistribution strategy and local load redistribution strategy. The simulation results demonstrate that the local load redistribution strategy greatly improves the airspace sector network’s invulnerability to cascading failure.

Effect of load-capacity heterogeneity on cascading overloads in networks.

Heterogeneity in the load capacity of nodes is a common characteristic of many real-world networks that can dramatically affect their robustness to cascading overloads. However, most studies seeking to model cascading failures have ignored variations in nodal load capacity and functionality. The present study addresses this issue by extending the local load redistribution model to include heterogeneity in nodal load capacity and heterogeneity in the types of nodes employed in the network configuration and exploring how these variations affect network robustness. Theoretical and numerical analyses demonstrate that the extent of cascading failure is influenced by heterogeneity in nodal load capacity, while it is relatively insensitive to heterogeneity in nodal configuration. Moreover, the probability of cascading failure initiation at the critical state increases as the range of nodal load capacities increases. However, for large-scale networks with degree heterogeneity, a wide range of nodal load capacities can also suppress the spread of failure after its initiation. In addition, the analysis demonstrates that heterogeneity in nodal load capacity increases and decreases the extent of cascading failures in networks with sublinear and superlinear load distributions, respectively. These findings may provide some practical implications for controlling the spread of cascading failure.

Weight trades in the design of a composite wing box: effect of various design choices

A process to efficiently design composite wing boxes is presented. It uses analytical and semi-empirical equations for failure modes such as material strength, plate buckling, stiffener column buckling and stiffener flange or web crippling. Laminate layups for the different components are selected in accordance with basic engineering rules and guidelines and are updated as necessary to meet the local loads. The emphasis is in allowing buckling of skins at any fraction of the ultimate load and allowing local load redistribution from buckled to non-buckled panels to save weight. The design process is automated and the design can be automatically transferred over to a commercial finite-element code for detailed design and validation. The effects on weight of number of spars, ribs, and stiffeners as well as the fraction of ultimate load at which buckling is allowed are examined and insight is gained to which of these the weight is most sensitive to. In addition, the effect of minimum gage on weight was found to be a driver.

An efficient local cascade defense method in complex networks

Cascading failures in networked systems often lead to catastrophic consequence. Defending cascading failure propagation by employing local load redistribution method is an efficient way. Given initial load of every node, the key of improving network robustness against cascading failures is to maximally defend cascade propagation with minimum total extra capacity of all nodes. With finite total extra capacity of all nodes, we first discuss three general extra capacity distributions including degree-based distribution (DD), average distribution (AD) and random distribution (RD). To sufficiently use the total spare capacity (SC) of all neighboring nodes of a failed node, then we propose a novel SC-based local load redistribution mechanism to improve the cascade defense ability of network. We investigate the network robustness against cascading failures induced by a single node failure under the three extra capacity distributions in both scale-free networks and random networks. Compared with the degree-based (DB) local load redistribution method, our SC method achieves higher robustness under all of the three extra capacity distributions. The extensive simulation results can well confirm the effectiveness of the SC local load redistribution method.

Cascading failures with local load redistribution in interdependent Watts–Strogatz networks

Cascading failures of loads in isolated networks have been studied extensively over the last decade. Since 2010, such research has extended to interdependent networks. In this paper, we study cascading failures with local load redistribution in interdependent Watts–Strogatz (WS) networks. The effects of rewiring probability and coupling strength on the resilience of interdependent WS networks have been extensively investigated. It has been found that, for small values of the tolerance parameter, interdependent networks are more vulnerable as rewiring probability increases. For larger values of the tolerance parameter, the robustness of interdependent networks firstly decreases and then increases as rewiring probability increases. Coupling strength has a different impact on robustness. For low values of coupling strength, the resilience of interdependent networks decreases with the increment of the coupling strength until it reaches a certain threshold value. For values of coupling strength above this threshold, the opposite effect is observed. Our results are helpful to understand and design resilient interdependent networks.

Vulnerability analysis of the US power grid based on local load-redistribution

In this paper, local load-redistribution is employed to study the vulnerability of the US power grid subjected to attacks, and the initial load of power node is assumed as the linear summation of its degree and the sum of its neighbors’ degrees. Based on the simulation results, we find that with the decrease of the initial load of power node, the critical threshold of tolerance parameter increases subjected to the highest load node-based attack, but the critical threshold decreases subjected to the lowest load node-based attacks. Meanwhile, we discover that the critical threshold subjected to the lowest load node-based attack is larger than that subjected to the highest load node-based attack when the tunable parameter α∈[0.1,0.9]. Moreover, this paper compares the new model with the other two existing models, and the results illustrate that there are many similarities between these two existing models, but they are different from the new model presented in this paper. Furthermore, the infimum of tolerance parameter is proposed to portray the minimum cost of power grid, which can give a method to construct more robust power grids in the future.

Local Load Redistribution Attacks in Power Systems With Incomplete Network Information

Power grid is one of the most critical infrastructures in a nation and could suffer a variety of cyber attacks. Recent studies have shown that an attacker can inject pre-determined false data into smart meters such that it can pass the residue test of conventional state estimator. However, the calculation of the false data vector relies on the network (topology and parameter) information of the entire grid. In practice, it is impossible for an attacker to obtain all network information of a power grid. Unfortunately, this does not make power systems immune to false data injection attacks. In this paper, we propose a local load redistribution attacking model based on incomplete network information and show that an attacker only needs to obtain the network information of the local attacking region to inject false data into smart meters in the local region without being detected by the state estimator. Simulations on the modified IEEE 14-bus system demonstrate the correctness and effectiveness of the proposed model. The results of this paper reveal the mechanism of local false data injection attacks and highlight the importance and complexity of defending power systems against false data injection attacks.

Robustness in clustering-based weighted inter-connected networks

We study the robustness of symmetrically coupled and clustering-based weighted heterogeneous inter-connected networks with respect to load-failure-induced cascades. This is done under the assumption that the flow dynamics are governed by global redistribution of loads based on weighted betweenness centrality. Our results indicate that no weighting bias should be assigned to inter-links when calculating shortest path between node pairs under the clustering-based weighting scheme; i.e., inter-links shall be treated no differently than intra-links. In contrast with local load redistribution cases, we show that increasing connectivity is preferred for the robustness against global load redistribution-based cascading failures in clustering-based weighted inter-connected networks. Furthermore, comparisons among weighting schemes reveal that, both the clustering-based and degree-based schemes outperform the random one in the sense of requiring lower initial and total investments required to ensure robustness. We also find that clustering-based scheme outperforms degree-based one in terms of requiring lower initial investments. Except in a limited range where weighting is heavily suppressed, clustering-based scheme is shown to outperform degree-based one in terms of total investments. Finally, when there exists a hard investment budget constraint, clustering-based weighting scheme would be a better choice against a two-nodes-induced failure than the degree-based weighting, and the clustering-based scheme is more stable than degree-based scheme against one-or-two-nodes-induced failure. We expect our findings to be significantly useful in designing real-world weighted inter-connected networks that are robust against load-failure-induced cascades.

Simulation study on the avalanche process of the fiber bundles with strong heterogeneities

The fiber bundle with strong heterogeneities is an extension of a fiber bundle model based on the classical fiber bundle model to describe the failure process of strongly heterogeneous materials. In order to explore the breaking dynamic properties of strongly heterogeneous materials in short-range correlation, the fiber bundle model with strong heterogeneities in local load redistribution is numerically studied in detail. The impacts of the proportion of two kinds of fibers and the distribution of the failure thresholds on the macroscopic constitutive behavior, the avalanche size distribution and increasing step number of the external load are investigated, respectively. The numerical results show that there is a local plastic plateau in the constitutive curve at a critical proportion of two kinds of fibers. Strong intensity fibers in material can nontrivially increase the intensity and stability of the system by altering the microscopic properties of the failure process.

Robustness of the western United States power grid under edge attack strategies due to cascading failures

Power systems are the basic support of modern infrastructures and protecting them from random failures or intentional attacks is an active topic of research in safety science. This paper is motivated by the following two related problems about cascading failures on power grids: efficient edge attack strategies and lower cost protections on edges. Applying the recent cascading model by adopting a local load redistribution rule, where the initial load of an edge ij is ( k i k j ) θ with k i and k j being the degrees of the nodes connected by the edge, we investigate the performance of the power grid of the western United States subject to three intentional attacks. Simulation results show that the effects of different attacks for the network robustness against cascading failures have close relations with the tunable parameter θ. Particularly, the attack on the edges with the lower load in the case of θ < 1.4 can result in larger cascading failures than the one on the edges with the higher load. In addition, compared with the other two attacks, a new attack, i.e., removing the edges with the smallest proportion between the total capacities of the neighboring edges of and the capacity of the attacked edge, usually are prone to trigger cascading failures over the US power grid. Our findings will be not only helpful to protect the key edges selected effectively to avoid cascading-failure-induced disasters, but also useful in the design of high-robustness and low-cost infrastructure networks.

Modeling Cascading Failures for Weighted Packet Networks

Cascading failures triggered by small local shocks under special condition exist in most of networks. Here we present a simple model of cascading failures for weighted packet networks, such as the Internet. In the model, links between nodes are chosen as the main research object, and local load redistribution is taken into account. Moreover, the influence factor, which is represented by betweenness centrality of neighboring links, is introduced to characterize the affection induced by jamming links. We study the model in both ER and BA networks using numerical simulation methods. We show that, in addition to the location of congestion, cascades of a packet network perturbed by a single jamming link also depend on the intrinsic topology characteristics and the current traffic load states of the network, which are of crucial factors. This is particularly important for real networks like the Internet to avoid the spread of traffic jam in the whole network.

Breakdown of fiber bundles with stochastic load-redistribution

We study fracture processes within a stochastic fiber-bundle model where it is assumed that after the failure of a fiber, each intact fiber obtains a random fraction of the failing load. Within a Markov approximation, the breakdown properties of this model can be reduced to the solution of an integral equation. As examples we consider two different versions of this model that both can interpolate between global and local load redistribution. For the strength thresholds of the individual fibers, we consider a Weibull distribution and a uniform distribution, both truncated below a given initial stress. The breakdown behavior of our models is compared with corresponding results of other fiber-bundle models.

The Influence of Ply Waviness with Nonlinear Shear on the Stiffness and Strength Reduction of Composite Laminates

The influence of ply waviness with nonlinear shear material response on the mechanical performance of composite laminates is studied. An analytic model, based on a three-dimensional laminated media analysis, is developed to predict the effective nonlinear laminate behavior associated with ply waviness. An undulating [0] ply in a [90/0/90] sublaminate configuration and undulating [±β] plies in a [90/±β/90] sub laminate configuration are two types of ply waviness considered. An incremental loading strategy is employed wherein piece-wise linear solutions are superimposed to obtain the overall nonlinear stress/strain response of composite laminates with wavy plies. The anal ysis also predicts individual ply stress and strain distributions within the wavy ply con figuration. The maximum stress failure criterion is used to predict ply failure in local re gions within the wavy ply configuration and a progressive failure methodology is adopted to permit local load redistribution. Results are presented that offer fundamental insight into the dominant mechanisms for stiffness and strength reduction in composite laminates exhibiting ply waviness and nonlinear shear material behavior.

Microstructural design of fiber composites

The optimum performance design of composite microstructures is discussed. The forces driving progress in fiber composites are examined, and recent developments in the mechanics of laminated composites are surveyed, emphasizing thick laminates, hygrothermal effects, and thermal transient effects. The strength of continuous-fiber composites is discussed, presenting analyses of local load redistribution due to fiber breakages and treatments of statistical tensile strength theories. Modes of failure of laminated composites are examined. Elastic, physical, and viscoelastic properties as well as the strength and fracture behavior of short-fiber composites are studied, and it is shown how the performance of composites can be controlled by selecting material systems and their geometric distributions. 2D textile structural composites based on woven, knitted, and braided preforms are considered, and techniques for analyzing and modeling the thermomechanical behavior of 2D textile composites are presented. Recent developments in the processing of 3D textile preforms are introduced and the processing-microstructure relationship is demonstrated. Finite elastic deformation of flexible composites is addressed.

Modeling of Size Effect in Ice Mechanics Using Fractal Concepts

Nominal failure pressure of ice decreases as the size of the contact area increases, over a wide range of scales. In this paper, the new and emerging concepts of fractals have been introduced to the problem of modeling this ice mechanics phenomenon. Models have been developed to explore effects of progressive failure with local load redistribution and uneven contact geometry. Unlike the nonsimultaneous failure models proposed to date for ice mechanics, the present progressive failure models show size effect in both mean and extreme ice failure pressures. While the present progressive failure models assume uniform contact, a separate fractal model of uneven contact geometry has also been proposed. This model provides a qualitative explanation for the size effect over the full range of scales.