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1

The stress analysis effect on structural health monitoring in functionally graded shell

Madeh Ahmed Raee, Abd-Ali Nabel Kadum

Diagnostyka

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2022

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Vol. 23, No. 3

art. no. 2022302

EN

The common damage in engineering structures, especially in functionally graded materials, such as failure resulting from fiber breaking or cracking in the matrix or deboning between fibers and matrix, as well as the delamination between the composite material plies and between its layers, may be due to thermal effects, vibration, load concentration as a result of stress and strain for provides information’s about structural health monitoring. Virtual energy method such as Hamilton's was used to investigate the effect of the design parameters such as side to thickness and modular as well as material graduation index ratio on the stress-strain relationships, displacement, resultants of stresses, and resultants of mid plane strain. The analysis and simulation of the FGM shells is done in this paper utilizing MATLAB19 code and ABAQUS20 programs. The distribution of characteristics across shell thickness had also been determined using a power law. Normal stress was varied gradually from 5.74 MPa to 9.55 MPa with material index (n) from 0 to 10 respectively, while shear stress varied from 4.2 to 8.23 MPa for the same value of (n). The strain percent increased slightly from 0.00059 to 0.0012 with displacement 0.22 and 1.2 respectively for the same value of (n).

2

Structural analysis of functionally graded material using sigmioadal and power law

Abd-Ali Nabel Kadum, Madeh Ahmed Raee

Diagnostyka

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2021

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Vol. 22, No. 4

59--65

EN

The stress-strain relations, displacement distribution, stress resultants and mid plane strain resultants of a functionally graded material plate are studied using Hamilton’s principle. A simply supported rectangular thick shell direct stress, inplane shear stress, transverse stress and displacement are investigated. The analysis and modeling of five layers FGM shell is carried out using MATLAB19 code with ABAQUS20 software. Using distinct materials on the top and bottom layers of the shell, a transverse uniform load in five degrees - of - freedom is applied with a specific Poisson's ratio and Young's modulus in a power and sigmoidal law function through the thickness direction. A power law was used to determine the distribution of properties through shell thickness. The results showed that the bottom layer affected significantly most stress due to subjected to the most in-plane stress while the displacement is greatest at the top layer.

3

Subdiffusion of volcanic earthquakes

Abe S., Suzuki N.

Acta Geophysica

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2017

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Vol. 65, no. 3

481--489

EN

A comparative study is performed on volcanic seismicities at Icelandic volcano, Eyjafjallajökull, and Mt. Etna in Sicily from the viewpoint of complex systems science, and the discovery of remarkable similarities between them is reported. In these seismicities as point processes, the jump probability distributions of earthquakes (i.e., distributions of the distance between the hypocenters of two successive events) are found to obey the exponential law, whereas the waiting-time distributions (i.e., distributions of inter-occurrence time of two successive events) follow the power law. A careful analysis is made about the finite size effects on the waiting-time distributions, and the previously reported results for Mt. Etna (Abe and Suzuki 2015) are reinterpreted accordingly. It is shown that the growth of the seismic region in time is subdiffusive at both volcanoes. The aging phenomenon is commonly observed in the “event-time-averaged” mean-squared displacements of the hypocenters. A comment is also made on (non-)Markovianity of the processes.

4

Lagrangian simulation and analysis of the power-law fluid mixing in the two-blade circular mixers using a modified WCSPH method

Shamsoddini R., Sefid M.

Polish Journal of Chemical Technology

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2015

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Vol. 17, nr 2

1--10

EN

In the present study, we introduce a robust modified Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method in order to examine miscible mixing within a two-blade paddle mixer. Since it has a Lagrangian nature and it is based on particles, Smoothed Particle Hydrodynamics (SPH) is an appropriate and convenient method for simulating the moving boundary problems and tracking the particles in the mixing process. The present study thus introduces a convenient SPH method for modelling the mixing process for the power-law fluids. Two geometries for the mixer are examined and the effects of the power-law index on the fluid mixing are investigated. The results show that the geometric change from circular chamber to twin chamber considerably increases the mixing rate (by at least 49%). The results also indicate that the twin chamber mixer is more efficient for the fluids with higher power-law index.

5

Comparison between bilinear and power low softening curve of concrete using inverse analysis

Danhash G., Kousa M., Wardeh G.

Architecture Civil Engineering Environment

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2014

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Vol. 7, no. 4

39--46

EN

Concrete is characterized by the softening behavior which is related to the increase in the crack opening with the decrease in stress. The softening curve is the relation between the stress and the crack opening and it is widely supposed to be bilinear in the international design standards. The area under the softening curve is the fracture energy GF that can be calculated according to RILEM recommendations. Unfortunately GF under RILEM recommendations is dependent on the specimen size. The size dependency problem may be solved using inverse analysis. In this research two inverse analysis procedures were applied using the analytical non linear hinge model for beams loaded in bending based on the fictitious crack model and supposing bilinear and power law softening curves. Three points bending test data for 64 beams with different sizes made from 23 concretes of wide range compressive strength and maximum aggregate size dmax were analyzed. The obtained results show that bilinear softening curve gives always a numerical maximum force larger than the experimental one about 20% whereas power law softening curve gives anumerical maximum force very close to the experimental one. This difference in predicting the numerical force is explained by the steeper drop in stress after peak force in power law softening which makes it more suitable for design purposes. Both procedures give the same GF and almost the same critical crack opening wc except for dmax = 80 [mm]. Furthermore, it is shown that macro-cracks start in the power law softening before they start in the bilinear softening and this ambiguity in crack initiation may lead to problems in predicting critical cracking cases for complicated structures.

PL

Beton charakteryzuje osłabienie związane ze zwiększaniem się rozwarcia rysy wraz ze spadkiem naprężeń. Krzywa osłabienia przedstawia związek pomiędzy naprężeniem a rozwarciem rysy i w normach projektowych powszechnie przyjmowana jest jako dwuliniowa. Powierzchnia pod tą krzywą to energia pękania, którą obliczyć można za pomoca zaleceń RILEM. Niestety jednak wartość energii pękania GF według zaleceń RILEM zależna jest of rozmiaru próbki. Problem wynikający z tej zależności można rozwiązać przez zastsosowanie analizy odwrotnej.Wtym projekcie badawczym zastosowano dwie procedury analizy odwrotnej wykorzystując analityczny nieliniowy model przegubowy dla belek zginanych w oparciu o model fikcyjnej rysy oraz zakładając dwuliniowe i potęgowe krzywe osłabienia. Analizowano dane otrzymane z testu trój-punktowego zginania 64 belek o różnych wymiarach wykonanych z 23 betonów o różnych wytrzymałościach na ściskanie i maksymalnym rozmiarze kruszywa dmax. Otrzymane wyniki pokazują, że krzywa dwuliniowa daje zawsze wartości obliczonej maksymalnej siły większe o 20% niż te uzyskane w badaniach eksperymentalnych, podczas gdy krzywa potęgowa daje wartości zbliżone do wyznaczonych w badaniach. Różnicę tą można wyjaśnić bardziej gwałtownym spadkiem naprężeń po przekroczeniu maksymalnej siły w sformułowaniu potęgowym, co czyni je bardziej adekwatnym do celów projektowych. Oba podejścia dają tę samą wartość energii pękania GF oraz niemal tę samą krytyczną szerokość rozwarcia rysy wc, z wyjątkiem dmax = 80 [mm]. Co więcej, okazuje się, że makro-rysy pojawiają się wcześniej przy sformułowaniu biliniowym niż przy sformułowaniu potęgowym, a ta dwuznaczność przy określaniu inicjacji rys może prowadzić do problemów w przewidywaniu krytycznych przypadków zarysowań w skomplikowanych konstrukcjach.

6

Numerical Study of Laminar Fully Developed Non-Newtonian Liquid Flow in Rough Circular Microchannel

Vashishtha M., Thakkar J.

Polish Journal of Chemical Technology

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2013

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Vol. 15, nr 1

30-37

EN

The present study aims to unveil the characteristics of fully developed laminar, incompressible, pressure driven non-Newtonian liquid flow in rough circular microchannels. In the present analysis Gaussian isotropic roughness distribution in circular microchannel is considered. The effect of varying surface wall roughness and flow behavior index has been studied numerically for both the pseudo plastic and dilatant fluids. It is found out that while increasing the relative roughness for a particular flow behavior index, the frictional resistance to flow in the microchannel increases and the effect is more pronounced in the case of pseudo plastic fluids. In the case of a pseudo plastic liquid flow for a constant relative surface wall roughness, on decreasing the value of flow behavior index below 1, the frictional resistance to the flow in the channel increases. While in the case of dilatant fluids with increasing the value of flow behavior index from 1 and above for a constant relative surface wall roughness the frictional resistance to the flow in the channel decreases.

7

Stochastic Populations, Power Law and Fitness Aggregation in Genetic Algorithms

Ma Z. S.

Fundamenta Informaticae

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2013

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Vol. 122, nr 3

173--206

EN

Natural populations are dynamic in both time and space. In biological populations such as insects, spatial distribution patterns are often studied as the first step to characterize population dynamics. In nature, the spatial distribution patterns of insect populations are considered as the emergent expression (property) of individual behaviors at population levels and are fine-tuned or optimized by natural selection. This inspiration prompts us to investigate the possibly similar mechanisms in Genetic Algorithms (GA) populations. In this study, we introduce the mathematical models for the spatial distribution patterns of insect populations to GA with the conjecture that the emulation of biological populations in nature may lead to computational improvement. In particular, we introduce three modeling approaches from the research of spatial distribution patterns of insect populations: (i) probability distribution modeling approach, (ii) aggregation index approach, and (iii) Taylor’s (1961, 1977) Power Law, Iwao’s (1968, 1976) Mean Crowding Model and Ma’s (1991c) population aggregation critical density (PACD), to characterize populations in GA. With these three approaches, we investigate four mappings from the research field of insect spatial distribution patterns to GA populations in order to search for possible counterpart mechanisms or features in GA. They are: (i) mapping insect spatial distribution patterns to GA populations or allowing GA populations to be controlled by stochastic distribution models that describe insect spatial distributions; (ii) mapping insect population distribution to GA population fitness distribution via Power Law and PACD modeling; (iii)mapping population aggregation dynamics to GA fitness progression across generations (or fitness aggregation dynamics in GA) via insect population aggregation index; (iv) mapping insect population sampling model to optimal GA population sizing. With regard to the mapping (i), the experiment results show the significant improvements in GA computational efficiency in terms of the reduced fitness evaluations and associated costs. This prompts us to suggest using probability distribution models, or what we call stochastic GA populations, to replace the fixed-size population settings. We also found the counterpart for the second mapping, the wide applicability of Power Law and Mean Crowding model to the fitness distribution in GA populations. The testing of the third and fourth mappings is very preliminary; we use example cases to suggest two further research problems: the potential to use fitness aggregation dynamics for controlling the number of generations iterated in GA searches, and the possibility to use fitness aggregation distribution parameters [(obtained in mapping (ii)] in determining the optimum population size in GA. A third interesting research problem is to investigate the relationship between mapping (i) and (iii), i.e., the controlling of both population sizes and population generations.

8

Testing a scaling law for the earthquake recurrence time distributions

Marekova E.

Acta Geophysica

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2012

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Vol. 60, no. 3

858-873

EN

The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.

9

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Castro-Orgaz O., Dey S.

Acta Geophysica

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2011

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Vol. 59, no. 5

993-1012

EN

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.

10

Comparing Trade-off Based Models of the Internet

Spathari A., Foudalis I., Sideri M., Papadimitriou C.

Fundamenta Informaticae

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2009

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Vol. 92, nr 4

363-372

EN

We introduce and evaluate several new models of network growth. Our models are extensions of the FKP model, modifying and improving it in various dimensions. In all these models nodes arrive one by one, and each node is connected to previous nodes by optimizing a trade-off between a geometric objective ("last mile cost") and a topological objective ("position in the network"). Our new models differ from the original FKP model in directions inspired by the real Internet: two or more edges are attached to each arriving node (while the FKP model produces a tree); these edges are chosen according to various criteria such as robustness; edges may be added to the network between old nodes; or only certain "fertile" nodes (an attribute that changes dynamically) are capable of attracting new edges. We evaluate these models, and compare them with the graph of the Internet's autonomous systems, with respect to a suite of many test parameters (such as average degree, power law exponent, and local clustering rank) proposed in the literature; to this end we have developed the network generation and measurement system Pandora.

11

Możliwość zastosowania wybranych wersji modelu Druckera-Pragera do opisu właściwości plastycznych soli kamiennej

Sobczyk J.

Prace Instytutu Mechaniki Górotworu PAN

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2004

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Vol. 6, no. 1-2

59--70

PL

W pracy zaprezentowano próbę wykorzystania wybranych wersji modelu Druckera-Pragera do opisu zachowań plastycznych soli kamiennej. Do opisu zachowań sprężystych wykorzystano liniowe prawo Hooka, a do opisu zachowań lepkich – prawo potęgowe (Nortona) z umocnieniem czasowym. Analizę wykonano w oparciu o dane z typowych testów laboratoryjnych: wytrzymałości doraźnej, pełzania i relaksacji. Uzyskane wyniki wskazują, że rozszerzony model Druckera-Pragera dość dobrze opisuje zachowanie plastyczne soli kamiennej, przejawiające się w takich testach.

EN

In the paper an application of some versions of the Drucker-Prager model to description of plastic behaviour of rock salt was presented. In the considerations the Hooke’s law of elasticity was used for the description of rock salt elastic behaviour, just as the power Norton law with time hardening for the description of viscous behaviour. Some results of so called individual triaxial tests carried out for salt were studied and it was proved on their background, that the extended Drucker-Prager model might be used for the description of plastic behaviour of rock salt with fair accuracy.

12

Synthetic Web

Kłopotek M.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2003

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Nr 954

1-14

EN

We got used to the idea that Web is a collection of interlinked documents containing knowledge from almost all areas of human activity. Recent research points however that the very structure of WWW links may by its own be a rich source of diverse knowledge. Understanding of rules for Web structure and growth may have immense impact in diverse research areas, starting with theory of structure and dynamics of massive graphs, utilitarian search for effective search algorithms on WWW, to the psychological research on formation of social communities and detection of such communities on the Internet. Currently the mainstream research concentrates apparently on construction of simple models helping to explain various basic statistical phenomena observed on the Web. This paper briefly explains major models of the Web and recalls basic contradictions between properties of synthetic Web and the real Web. It also offers a way to resolve one such contradiction concerning the high correlation between PageRank and in-degrees in synthetic Web models, while such a correlation is not present in real Web.

PL

Przyzwyczailiśmy się do traktowania sieci WWW jako zbioru dokumentów zawierających wiedzę prawie ze wszystkich dziedzin naszego życia . Ostatnie badania zdają się wskazywać, że równie głębokim źródłem wiedzy może być sama struktura sieci WWW. Zrozumienie struktury i ewolucji sieci dokumentów na WWW może mieć kolosalne znaczenie dla wielu dziedzin-począwszy od badań naqd strukturą i dynamiką wielkich grafów poprzez utilitarne badania nad efektywnością programów przeczesujących sieć WWW aż po psychologiczne badania nad powstawaniem grup społecznych czy też wykrywaniem takich grup. W chwili obecnej główny nurt badań nad strukturą i rozwojem WWW skupia się na konstruowaniu prostych modeli pozwalających wyjaśnić podstawowe statystyczne własności sieci WWW. W niniejszym artykule przedstawiono ważniejsze koncepcje modelu sieci WWW i wskazano na sprzeczności między miarami rzeczywistej sieci WWW a jej syntetycznymi modelami. Zaproponowano sposób obejścia jednej z takich sprzeczności, jaką jest wysoka korelacja między PageRankiem a stopniem wejściowym stron WWW w sieciach syntetycznych, oraz brakiem takiej korelacji w rzeczywistej sieci WWW.

13

Uwarunkowania prawne w zakresie infrastruktury elektroenergetycznej na wsi

Giera M.

Wiadomości Elektrotechniczne

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2002

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R. LXX, nr 10-11

412-421

PL

Omówiono powiązanie prawa energetycznego i prawa budowlanego podczas projektowania i wykonywania inwestycji. Zwrócono uwagę na wymagania dotyczące urządzeń energetycznych i wyrobów budowlanych. Określono zasady przyłączania do sieci elektroenergetycznej oraz obowiązki właścicieli, zarządców i użytkowników odpowiedzialnych za stan techniczny i bezpieczeństwo użytkowania instalacji elektrycznych. Podano szczegółową bibliografię dotyczącą omawianych zagadnień.

EN

Discussion of the links between the power law and building law binding while designing and realizing investments. Attention paid to the requirements with regard to power equipment and building products. Principles of connecting to the mains and also duties of the owners, administrators and users responsible for the technical state and safety of using the electric systems. Detailed references relating to the problems discussed.