Retarding the Shuttling Ions in the Electrochromic TiO2 with Extensive Crystallographic Imperfections

To understand the role of structure imperfections on the performance of electrochromic transition metal oxide (ETMO) is challenging for the design of efficient smart windows. Herein, we investigate the performance evolution with tunable crystallographic imperfections for rutile TiO₂ nanowire film (TNF). Structure imperfections, originating mainly from the copious oxygen deficiency, are apt to cumulatively retard the shuttling ions, resulting in the response rate for raw TNF being less than the half that of TNF annealed at 500 °C. We describe ion accommodation sites as a convolution of normal site and abnormal site, in which the normal site performs reversible coloration but the abnormal site contributes only to charge storage, which gives a rationale for the non-linear coloration and rate capability loss. These findings give a clear picture of the ion shuttling process, which is insightful for enhancing the electrochromic performance via structure reprogramming.     

Constructions for normal graphs and some consequences

Normal graphs can be considered as weaker perfect graphs in several ways. However, only few graphs are known yet to be normal, apart from perfect graphs, odd holes, and odd antiholes of length ≥ 9. Körner and de Simone [J. Körner, C. de Simone, On the odd cycles of normal graphs, Discrete Appl. Math. 94 (1999) 161-169] conjectured that every ()-free graph is normal. As there exist normal graphs containing C₅, C₇, or , it is worth looking for other ways to construct or detect normal graphs. For that, we treat the behavior of normal graphs under certain construction techniques (substitution, composition, and clique identification), providing several ways to construct new normal graphs from normal and even not normal ones, and consider the corresponding structural decompositions (homogeneous sets, skew partitions, and clique cutsets). Our results imply that normal graphs cannot be characterized by means of decomposition techniques as well as by forbidden subgraphs. We address negative consequences for the algorithmic behavior of normal graphs, reflected by the fact that neither the imperfection ratio can be bounded for normal graphs nor a χ-binding function exists. The latter is even true for the class of ()-free graphs and related classes. We conclude that normal graphs are indeed only “normal”.     

Imperfection sensitivity of curved panels under combined compression and shear

The initial buckling load of curved panels under compressive loads is substantially reduced by the existence of imperfections, in particular geometric imperfections. It is therefore essential that these imperfections are considered in analysing components which incorporate such panels in order to accurately predict their buckling behaviour. Finite element analysis allows fully non-linear analysis of shells containing geometric imperfections, however, to obtain accurate results information is required on the exact size and shape of the imperfection to be modelled. In most cases this data is not available. It is therefore generally recommended that the imperfections are modelled on the first eigenmode and have an amplitude selected according to the manufacturing procedure. This paper presents the effects of varying imperfection shape and amplitude on the buckling and postbuckling behaviour of one specific case, a curved panel under combined shear and compression, to test the accuracy of such recommendations.     

Hutchinson模型的塑性后分叉和缺陷敏感性

本文通过对Ｈｕｔｃｈｉｎｓｏｎ模型的初始塑性后分叉和缺陷敏感性的分析，介绍了一个分析塑性后屈曲的一般方法，这一方法非常类似Ｋｏｉｎｔｅｒ的弹性后屈曲理论。用这一方法分析缺陷敏感性和初始后分叉的过程是一致的，所得展开在渐近的意义上是精确的，和数值解符合得相当好。     

Imperfection sensitivity of hilltop branching points of systems with dihedral group symmetry

Imperfection sensitivity of a hilltop branching point occurring as a coincidence of a limit point and a double bifurcation point of a finite-dimensional, elastic, conservative system equivariant to the dihedral group is investigated. In the neighborhood of this point, the potential is expanded into a power series of independent state variables, loading parameter and imperfection magnitude. The form of the expansion is determined through exploitation of dihedral-group symmetry. For the perfect system, the hilltop branching point and bifurcated paths are shown to be all unstable. For an imperfect system, equilibrium paths in general break into a series of paths: including fundamental, complementary and aloof paths. The imperfection sensitivity laws for maximum (critical) points of loading on these paths are obtained as a novel finding of this paper. Critical points on the fundamental and complementary paths enjoy a piecewise linear law, which is less severe than a one-half or two-thirds power law for the double bifurcation point. By contrast, maximum points on aloof paths suffer more severe sensitivity. The hilltop branching point thus displays complex system of imperfection sensitivities. As numerical examples, imperfection sensitivity of simple structural models with the hilltop point is investigated to ensure the validity of the present formulation.     

Identification of imperfections in thin plates based on the modified potential energy principle

A procedure to identify the imperfection in thin plates is proposed in this paper. The modified potential energy principle, which serves as the theoretical basis of the identification procedure, is improved to allow for the experimental measurements in static tests. Several typical examples are studied to illustrate the effectiveness of the procedure.     

Imperfection sensitivity of optimal symmetric braced frames against buckling

Imperfection sensitivity characteristics of the non-linear buckling load factors of non-optimal and optimal symmetric frames are investigated. The frames are subjected to symmetric proportional vertical loads. The optimization problem is formulated under constraints on linear buckling load factors. Although the buckling load factors corresponding to sway and non-sway modes coincide at the optimum design, the non-sway-type asymmetric bifurcation point disappears as a result of geometrically non-linear analysis. Therefore, the maximum allowable load factors of perfect and imperfect systems should be determined by assigning displacement constraints. It is shown that quantitative evaluation is possible for imperfection sensitivity and mode interaction based on the higher order differential coefficients of the total potential energy even for frames of which the critical points should be numerically obtained. Numerical examples are presented to show that the properties of the non-sway bifurcation point are similar to those of a symmetric bifurcation point, and the interaction between sway and non-sway modes does not always lead to enhancement of imperfection sensitivity.     

Imperfection sensitivity of ultimate buckling strength of elastic-plastic square plates under compression

The mechanism of imperfection sensitivity of elastic-plastic plates under compression is complex as they undergo elastic and/or plastic buckling, dependent on their width-thickness ratio. For elastic buckling, the Koiter power law is an established means to describe the imperfection sensitivity. Yet, for plastic buckling, there is no such an established way to describe it. In this paper, the quadratic power law is advanced to describe imperfection-insensitive plastic buckling behavior. The Koiter power law is extended by implementing the quadratic law so as to describe the elastic and plastic buckling in a synthetic manner. The finite-displacement, elastic-plastic analysis was conducted on simply-supported square plates under compression by varying the plate thickness and the initial deflection of a sinusoidal form. In association with an increase of the plate slenderness parameter (decrease of plate thickness), the predominant buckling is shown to change from (1) plastic buckling to (2) unstable elastic-plastic buckling and to (3) elastic stable bifurcation followed by a maximum point of load. In accordance with the change of the mechanism of buckling, the power law is changed pertinently to describe the complex imperfection sensitivity of the compression plates in a synthetic manner. The extended imperfection sensitivity law is thus advanced as a simple and strong tool to describe the ultimate buckling strength of elastic-plastic plates.     

Characterizing and bounding the imperfection ratio for some classes of graphs

Perfect graphs constitute a well-studied graph class with a rich structure, which is reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs G where the stable set polytope STAB(G) equals the fractional stable set polytope QSTAB(G). The dilation ratio of the two polytopes yields the imperfection ratio of G. It is NP-hard to compute and, for most graph classes, it is even unknown whether it is bounded. For graphs G such that all facets of STAB(G) are rank constraints associated with antiwebs, we characterize the imperfection ratio and bound it by 3/2. Outgoing from this result, we characterize and bound the imperfection ratio for several graph classes, including near-bipartite graphs and their complements, namely quasi-line graphs, by means of induced antiwebs and webs, respectively.      

Essay on the Contributors to the Elastic Stability Theory

This paper revisits the historical aspects of the contributions made into the elastic stability theory from the structural engineering point of view.Extensive quotations are brought in order to substantiate the claims made. It is hoped that the review constitutes a contribution to the identification of the main ideas pertinent to engineering mechanics.