Level set topology optimization of structural problems with interface cohesion

This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics. Copyright © 2017 John Wiley & Sons, Ltd.     

Generation, combination and extension of random set approximations to coherent lower and upper probabilities

Random set theory provides a convenient mechanism for representing uncertain knowledge including probabilistic and set-based information, and extending it through a function. This paper focuses upon the situation when the available information is in terms of coherent lower and upper probabilities, which are encountered, for example, when a probability distribution is specified by interval parameters. We propose an Iterative Rescaling Method (IRM) for constructing a random set with corresponding belief and plausibility measures that are a close outer approximation to the lower and upper probabilities. The approach is compared with the discrete approximation method of Williamson and Downs (sometimes referred to as the p-box), which generates a closer approximation to lower and upper cumulative probability distributions but in most cases a less accurate approximation to the lower and upper probabilities on the remainder of the power set. Four combination methods are compared by application to example random sets generated using the IRM.     

What Computing with Words Means to Me [Discussion Forum]

Computing with words (CWW) means different things to different people. This article is the start of a position paper, written by some of the members of the CIS Fuzzy Systems Technical Committee Task Force on CWW, that answers the question "What does CWW mean to me?"     

A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision maker's different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.     

A Photoelastic Study of the Stress Distribution in Adhesively Bonded Joints with Prebent Adherends

A photoelastic study on lap joints with inflexible adhesive layers reveals that the load carrying capacity may be increased as much as 71 % with the use of prebent adherends.     

The value of assessing cell proliferation in breast cancer

Using three methods to measure cell proliferation, namely DNA cell cycle; anti-proliferating cell monoclonal antibody (MAb) (Ki67, P145) analysis by flow cytometry; and the histological silver (argyrophilic) staining technique to visualize nuclear-organizing regions (AgNOR), twenty-two paired samples of primary breast tumour and axillary lymph node were analysed. The results showed variable levels of correlation between the methods used for the tumour group (r = 0.915, P <0.001 for Ki677 versus P145; r = 0.42, P <0.005 for percentage S/G2/M-phase versus P145; r = 0.16, P <0.5 for percentage S/G2/M-phase versus AgNOR; r = 0.400, P < 0.1 for Ki67 versus AgNOR). The lymph-node group showed slightly poorer correlations, yet involved nodes showed a consistently higher level of proliferation than non-involved nodes by all methods used. Overall, MAb binding of Ki67 or P145 was seen to be a good indicator of cycling cells, detecting G1-phase cells in addition to S/G2/M-phase cells indentified by the other methods used. However, no advantage was found over the usual DNA flow cytometric analysis of cells, which had clear prognostic value. AgNOR scores were found to be able to discriminate between diploid and aneuploid; and dividing and non-dividing cells, but areas of score overlap limited the application of this technique to that of a positive discriminator only.     

Fuzzy Bayesian Modeling of Sea-Level Along the East Coast of Britain

A fuzzy Bayesian algorithm is introduced, allowing for the incorporation of both uncertainty and fuzziness into data derived models. This is applied to predicting the sea-level near the Thames Estuary at Sheerness, from tidal gauge measurements down the east coast, astronomical tidal prediction, and meteorological data. We show that this approach can result in accurate, low-dimensional models with low computational costs and relatively fast execution times.     

The linguistic attribute hierarchy and its optimisation for classification

A hierarchical approach to decomposing a high-dimensional model into series of low-dimensional sub-models can be an effective way to overcome the ‘curse of dimensionality’ problem. We investigate a hierarchy of linguistic decision trees (LDTs) for classification, and present linguistic interpretation of the hierarchy of LDTs. Due to the uncertain and non-linear relationship between input attributes and a goal, different hierarchies could have different performance for classification. We develop a GA with the linguistic ID3 in wrapper to optimize linguistic attribute hierarchy. The experimental results show that optimised linguistic attribute hierarchies perform better on the benchmark databases than a single LDT does, and they can greatly reduce the number of rules when the relationship between a goal variable and input attributes is highly uncertain and nonlinear. Comparing with well-known machine learning approaches, C4.5, Naive Bayes, and Neural Networks, the optimised linguistic attribute hierarchy achieves the highest accuracies for most tested databases. The trained hierarchy can be a real-time classifier if the optimization of hierarchies is performed offline.