Thermodynamic compatibility conditions of a new class of hysteretic materials

The thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions

Use of kriging to surrogate finite element models of bonded double cantilever beams

An algorithm based on kriging statistical interpolation for computing the surrogate response of a Finite Element model is presented. The interpolation model is calibrated via computation of Finite Element responses at a set of random occurrences of a material parameter. Such random generation concentrates at locations where the numerical model requires a higher amount of data to get the desired accuracy. As a model problem a standard fracture propagation test is analyzed. The proposed procedure is shown to be robust and accurate since responses obtained via a direct computation and use of the surrogate model turn out to be undistinguishable

Fixed Point Theorems for Compatible Multi-Valued and Single-Valued Mappings

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued mapping

Max-Min Fuzzy Relation Equations for a Problem of Spatial Analysis

We implement an algorithm that uses a system of max-min fuzzy  relation equations (SFRE) for solving a problem of spatial analysis. We integrate this algorithm in a Geographical information Systems (GIS) tool. We apply our  process to determine the symptoms after that an expert sets the SFRE with the values of the impact coefficients related to some parameters of a geographic zone under study. We also define an index of evaluation about the reliability of the results

Attribute dependency data analysis for massive datasets by fuzzy transforms

We present a numerical attribute dependency method for massive datasets based on the concepts of direct and inverse fuzzy transform. In a previous work, we used these concepts for numerical attribute dependency in data analysis: Therein, the multi-dimensional inverse fuzzy transform was useful for approximating a regression function. Here we give an extension of this method in massive datasets because the previous method could not be applied due to the high memory size. Our method is proved on a large dataset formed from 402,678 census sections of the Italian regions provided by the Italian National Statistical Institute (ISTAT) in 2011. The results of comparative tests with the well-known methods of regression, called support vector regression and multilayer perceptron, show that the proposed algorithm has comparable performance with those obtained using these two methods. Moreover, the number of parameters requested in our method is minor with respect to those of the cited in the above two algorithms

Fuzzy Entropy-Based Spatial Hotspot Reliability

Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off between the accuracy in the detection of the hotspot shape and the computational complexity. However, this method does not measure the reliability of the detected hotspots and therefore does not allow us to evaluate how reliable the identification of a hotspot of a circular area corresponding to the detected cluster is; a measure of the reliability of hotspots is crucial for the decision maker to assess the need for action on the area circumscribed by the hotspots. We propose a method based on the use of De Luca and Termini’s Fuzzy Entropy that uses this extension of the Fuzzy C-means algorithm and measures the reliability of detected hotspots. We test our method in a disease analysis problem in which hotspots corresponding to areas where most oto-laryngo-pharyngeal patients reside, within a geographical area constituted by the province of Naples, Italy, are detected as circular areas. The results show a dependency between the reliability and fluctuation of the values of the degrees of belonging to the hotspots

A Multilevel Fuzzy Transform Method for High Resolution Image Compression

The Multilevel Fuzzy Transform technique (MF-tr) is a hierarchical image compression method based on Fuzzy Transform, which is successfully used to compress images and manage the information loss of the reconstructed image. Unlike other lossy image compression methods, it ensures that the quality of the reconstructed image is not lower than a prefixed threshold. However, this method is not suitable for compressing massive images due to the high processing times and memory usage. In this paper, we propose a variation of MF-tr for the compression of massive images. The image is divided into tiles, each of which is individually compressed using MF-tr; thereafter, the image is reconstructed by merging the decompressed tiles. Comparative tests performed on remote sensing images show that the proposed method provides better performance than MF-tr in terms of compression rate and CPU time. Moreover, comparison tests show that our method reconstructs the image with CPU times that are at least two times less than those obtained using the MF-tr algorithm

A Novel Image Similarity Measure Based on Greatest and Smallest Eigen Fuzzy Sets

A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to a fuzzy relation equation. The original image is partitioned into squared blocks and the pixels in each block are normalized to [0, 1] in order to have a fuzzy relation. The greatest and smallest fuzzy sets, found for each block, are used to measure the similarity between the original image and the image reconstructed by joining the squared blocks. Comparison tests with other well-known image metrics are then carried out where source images are noised by applying Gaussian filters. The results show that the proposed image similarity measure is more effective and robust to noise than the PSNR and SSIM-based measures

A MITC-based procedure for the numerical integration of a continuum elastic-plastic theory of through-the-thickness-jacketed shell structures

Through-the-Thickness Jacketing (TTJ) is a technique for repairing and retrofitting shell structures by inducing in the shell core a beneficial confining stress state created by a net of broadly distributed retrofitting links crossing the shell thickness and tying externally applied layers. The paper presents the derivation, the algorithmic implementation and the numerical assessment of a predictor-corrector computational strategy for the integration of a shell FE-model obtained by combining a discrete MITC quadrilateral element with a layered continuum-based generalized shell theory of TTJ-reinforced structures, essentially based upon a Winkler-like idealization of TTJ. This theory of Through-the-Thickness-Jacketed Shells (TTJS) captures the onset of complex triaxial stress states originated by the interaction between core and TTJ reinforcements. Results of benchmark numerical applications in OpenSees with flat and curved elastic–plastic shell structures are presented in order to assess and illustrate the consistency and the general modelling features of the proposed TTJS-MITC framework endowed with the Drucker-Prager elastic-perfectly-plastic idealization of the nonlinear behavior of the material composing the shell. Numerical results exhibit quadratic convergence and show that the model captures marked strength increments over the in-plane membrane response, albeit these are lower when the response is predominantly of out-of-plane flexural type