Elasticity (Solid Mechanics)

Crumb rubber modification has been proven to enhance the properties of pure bitumen. This paper looks at some of the international standards for producing crumb rubber modified bitumen (CRMB) and reviews the effect of crumb rubber to the rheology of crumb rubber modified bitumen. The review shows that the rheology of CRMB depends on internal factors such as crumb rubber quantity, particle size, and pure bitumen composition, and external factors such as the mixing time, temperature, and also the modification technique. These factors govern the swelling process of crumb rubber particles that lead to the increase of viscosity of the modified bitumen. However, the mixing temperature and duration can cause rubber particles to depolymerize and subsequently cause loss of viscosity. Crumb rubber modification also improves the properties of bitumen by increasing the storage and loss modulus and enhancing the high and low temperature susceptibility. The effect of crumb rubber to aging propert...

We present some new formulae for the solution of boundary value problems for a two-dimensional isotropic elastic body. In particular, using the so-called Dbar formalism and the method introduced by Fokas (2008) [4], we obtain integral representations of the Fourier type for the displacements appearing in boundary value problems formulated in an arbitrary convex polygon with n sides.

Porous pre-sintered zirconia is subject to white machining during which its elasticity, plasticity and resistance to machining-induced damage determine its machinability and final quality. This study used nanoindentation techniques and the Sakai's series elastic and plastic deformation model to extract the resistance to plastic deformation from the plane strain modulus and the contact hardness for pre-sintered zirconia. The modulus and the resistance to plasticity were used to calculate the relative amount of elasticity and plasticity. The fracture energy and the normalized indentation absorbed energy were used to deconvolute the resistance to machining-induced cracking based on the Sakai–Nowak model. All properties were extracted at a 10 mN peak load and loading rates of 0.1–2 mN/s to determine the loading rate effects on these properties. We found that the resistance to plasticity and the resistance to machining-induced cracking were independent of the loading rate (ANOVA, p > 0.05). The elastic and plastic displacements depended on the loading rate through power laws. This loading rate-dependent deformation behaviour was explained by the maximum shear stress generated underneath the indenter and the indentation energy. The plastic deformation components and the indentation absorbed energy at all loading rates were higher than the elastic deformation components and the elastic strain energy, respectively. Finally, we established the linkage among the pore structure, indentation behaviour and machinability of pre-sintered zirconia.

W szczegółowy sposób omówione zostały założenia ogólnej nieliniowej teorii sprężystości i wyprowadzenia podstawowych elementów mechaniki ośrodka ciągłego, a także przytoczone zostały dowody fundamentalnych twierdzeń rozważanej teorii w ramach kinematyki, statyki i dynamiki ciał odkształcalnych. Omówiono kwestie formułowania związków konstytutywnych dla ciał izotropowych i anizotropowych zarówno o liniowej, jak i nieliniowej charakterystyce, ze szczególnym uwzględnieniem zagadnienia energetycznego sprzężenia miar naprężenia i odkształcenia oraz zastosowania rozkładu widmowego tensorów sprężystości. Osobno omówiono liniowy wariant teorii z różnymi jego sformułowaniami oraz metodami analitycznymi, m.in. zastosowaniem funkcji naprężeń, potencjałów, metod półodwrotnych oraz analizy zespolonej. Rozważania te poszerzono o opis teorii ogólniejszych – mechanikę ośrodka mikropolarnego Cosseratów oraz mechanikę ośrodka mikromorficznego Mindlina. W ramach teorii liniowej przedstawiono matematyczny opis zjawisk elastooptyki, propagacji płaskich i sferycznych fal sprężystych, a także propagacji sprężystych fal powierzchniowych. Przytoczono i udowodniono twierdzenia wariacyjne teorii liniowej oraz omówiono ich zastosowanie w ramach numerycznych metod rozwiązywania zagadnień tej teorii. Przeanalizowano rozwiązania trzynastu klasycznych zagadnień liniowej teorii sprężystości oraz zagadnień pokrewnych, ze szczególnym uwzględnieniem zagadnień dynamicznych. Całość uzupełniona została rozbudowanym dodatkiem poświęconym rachunkowi tensorowemu i absolutnemu rachunkowi różniczkowemu.

This report is a final project which is part of the requirements of the course Engineering Computing (PCS911). We study the displacement, stress and strain of objects occupying two and three dimensional domains. We used P1 finite elements (triangles and tetrahedral) for discretization. The implementation of this project is also included in detail. 1 Motivation and Background Various physical process in science and engineering can be mentioned in details of partial differential equations. Getting solutions from these equations by analytical methods for complex geometrical shapes is relatively futile. The Finite Element Method (FEM) is a numerical method to get approximate solutions to ordinary and partial differential equations, which will model physical problems in engineering and physics. FEM has found applications in fluid mechanics, thermodynamics, mechanical structure analysis and electromagnetic fields in design and performance analysis [2]. Finite element analysis is a method in engineering for the numerical analysis of complicated mechanical structures based on the properties of the material to find the stress and strain distributions, when they are subjected to loads. FEA combined with computer aided design can be used to fasten up and optimize the design and manufacturing of mechanical structures[3]. The main aim of this project is to form a finite element model to estimate an elastic mechanical response of 2D and 3D linear elastic isotropic materials. Here we are using Matlab to execute P1 finite element procedures for numerical solutions of elasticity situations. The basic five steps involved in applying FEM are : 1. Preprocessing : Dividing the problem domain into finite elements (Discretization). 2. Formulation of Elements: Development of equations for the finite elements. 3. Assembly of element equations: Achieving the equations of the whole system from the equations of the individual elements. 4. Finding the numerical solution of the equations. 5. Post processing: Finding the stress and strain, and attaining graphical representation of the solution.

Lo studio tensionale di un corpo è un argomento di grande interesse nell'Ingegneria Civile: l'analisi di tale problema è infatti necessaria al fine di garantire una sicurezza strutturale. Lo scopo è quello di cercare la risposta di un corpo alle sollecitazioni e verificare che le reazioni resistenti del corpo siano sempre maggiori delle sollecitazioni applicate. Il problema trattato in questo elaborato è un problema di elastostatica: nel riferimento [18], tale termine è definito come "parte dell'elastomeccanica che si occupa dei problemi dell'equilibrio elastico". Si considera, in particolare, un caso di stato tensionale piano (static-planestress), descritto da un'Equazione Differenziale alle Derivate Parziali (PDE). Le leggi che governano la risposta del corpo alle sollecitazioni non sono facilmente risolvibili: si sfrutta dunque un metodo numerico che fornisce una soluzione approssimata, ma che garantisce coerenza con i vincoli imposti al bordo. Il metodo che viene presentato nell'elaborato è il Metodo degli Elementi Finiti. Tale metodo costruisce una soluzione approssimata attraverso le seguenti fasi principali: 1. Discretizzazione del dominio di definizione della PDE mediante una triangolazione regolare; 2. Definizione di opportuni vincoli al bordo; 3. Derivazione della Formulazione Variazionale del problema; 4. Approssimazione mediante elementi finiti lineari a tratti; 5. Risoluzione del sistema lineare finale associato al metodo numerico. Dopo una panoramica teorica relativa all'elasticità lineare e al Metodo degli Elementi Finiti, si presenta lo studio della reazione di un corpo soggetto a tensioni esterne, sotto opportuni vincoli al bordo. Le simulazioni numeriche sono state effettuate in ambiente MATLAB® con l'utilizzo del pacchetto Partial Differential Equation Toolbox. Con il software sono stati costruiti e confrontati due algoritmi: il primo basato sull'utilizzo di un "pacchetto di funzioni" predefinite di MATLAB® dove è stato necessario inserire semplicemente le caratteristiche del materiale e le condizioni al bordo; il secondo, invece, basato sulla creazione di un'apposita struttura per la descrizione della PDE, sull'imposizione delle condizioni al bordo e sul calcolo della matrice e del termine noto del sistema lineare finale associato al metodo numerico. Tali algoritmi sono stati utilizzati per la simulazione numerica di un particolare problema modello e per la validazione di quest'ultimo attraverso il calcolo di quantità significative, quali la tensione interna al corpo e lo stress effettivo di Von Mises.

In this paper, we proposed a simple mathematical procedure to solve the differential equations governing the buckling and bending analysis of FG thick rectangular plates resting on two-parametric foundation based on Mindlin assumption. All edges are set on the simply supported conditions. Young modulus of the FG plate was assumed to vary according to a simple four-parameter power law across the thickness direction. For bending analysis, the plate was subjected to two kinds of loading: sinusoidal and uniform. For bucking analysis, two kinds of in-plane loading were applied to the plate: uniaxial and biaxial. Variations of FG material variation profile, thickness ratio, and foundation parameters on buckling critical load and out-plane displacement were examined. The distribution of axial and shear stress across the thickness, when the plate is exposed to uniform transverse loading, was further studied.

In this study we present a new strategy for the theory-guided bottom up design of b-Ti alloys for biomedical applications using a
quantum mechanical approach in conjunction with experiments. Parameter-free density functional theory calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys with respect to three constraints: (i) the use of non-toxic alloy elements; (ii) the stabilization of the body centered cubic b-phase at room temperature; (iii) the reduction of the elastic stiffness compared to existing Ti-based alloys. Following the theoretical predictions, the alloys of interest are cast and characterized with respect to their crystallographic structure, microstructure, texture, and elastic stiffness. Due to the complexity of the ab initio calculations, the simulations have been focused on a set of binary systems of Ti with two different high melting body-centered cubic metals, namely, Nb and Mo. Various levels of model approximations to describe mechanical and thermodynamic properties are tested and critically evaluated. The experiments are conducted both, on some of the binary alloys and on two more complex engineering alloy variants, namely, Ti–35 wt.% Nb–7 wt.% Zr–5 wt.% Ta and Ti–20 wt.% Mo–7 wt.% Zr–5 wt.% Ta.

Formulario de las asignaturas de Elasticidad y Resistencia de Materiales.
Se trata de un resumen de fórmulas utilizados por mi para dar clase de dichas asignaturas en Aula de Estructuras.
Cualquier comentario o aclaración será bienvenida. En el documento se encuentra nuestro correo electrónico.

We outline a general approach for extending the classical Boussinesq’s solution to the case of pressures distributed according to a polynomial law of arbitrary order over a polygonal domain. To this end we exploit a generalized version of the Gauss theorem and recent results of potential theory which consistently take into account the singularities affecting the expressions of the fields of interest, an issue which seems to have been overlooked in the existing literature. For linearly varying pressures we derive analytical expressions of displacements, strains and stresses at an arbitrary point of the half-space as a function of the loading function and of the position vectors which define the boundary of the loaded region. We briefly discuss how bilinear and more general pressure distributions can be accommodated in our formulation since the paper is mainly motivated by the interest in developing efficient computational tools for solving 3D problems in foundation engineering and contact mechanics. Finally, comparisons with existing solutions and numerical examples are discussed.

Crumb rubber modification has been proven to enhance the properties of pure bitumen. This paper looks at some of the international standards for producing crumb rubber modified bitumen (CRMB) and reviews the effect of crumb rubber to the rheology of crumb rubber modified bitumen. The review shows that the rheology of CRMB depends on internal factors such as crumb rubber quantity, particle size, and pure bitumen composition, and external factors such as the mixing time, temperature, and also the modification technique. These factors govern the swelling process of crumb rubber particles that lead to the increase of viscosity of the modified bitumen. However, the mixing temperature and duration can cause rubber particles to depolymerize and subsequently cause loss of viscosity. Crumb rubber modification also improves the properties of bitumen by increasing the storage and loss modulus and enhancing the high and low temperature susceptibility. The effect of crumb rubber to aging properties of CRMB is also discussed. Finally several techniques of chemical modification to terminal blends of CRMB and the subsequent improvement to the settling property of CRMB are explained. © 2013 Mohd Rasdan Ibrahim et al.

http://www.hindawi.com/journals/amse/2013/415246/abs/

Using the method of complex potentials we present the closed form of analytical solution for the stresses and displacements around an elliptical cavity filled with fluid in the permeable poroelastic medium. The far-field pore pressure is different from the pressure inside cavity. The fluid is allowed to diffuse through the cavity's wall towards surrounding medium. The two-dimensional plane-strain and plane-stress models are considered with steady-state distribution of diffusive pore-fluid pressure. The diffusion of fluid is coupled to the deformation of a medium using a linear theory of poroelasticity. Since in the static case the diffusion of pore fluid is controlled by an ordinary Laplace equation, the problem is reduced to elastic problem with distribution of volume forces (known as seepage forces) along gradients of pore pressure. Due to similarity between poroelasticity and thermoelasticity, the present solution is applicable both to the poroelastic and thermoelastic problems with a steady-state distribution of pore pressure and temperature, respectively. Since it is getting more common to model the deformation coupled to Darcy-flow in geosciences and no clear criteria has been suggested for verification of numerical codes, we discuss the possible application of the analytical solution as the benchmark for testing of poroelastic and thermoelastic numerical codes. To stimulate a wider use of the solution for stresses, displacements and pore-fluid pressure around an elliptical cavity are implemented in MATLAB and can be downloaded from the web.

We investigated a high-purity cold-rolled martensitic Fe-9wt%Mn alloy. Tensile tests performed at room temperature after tempering for 6 h at 450 C showed discontinuous yielding. Such static strain ageing phenomena in Fe are usually associated with the segregation of interstitial elements such as C or N to dislocations. Here we show by correlative transmission electron microscopy (TEM)/atom probe tomog-raphy (APT) experiments that in this case Mn segregation to edge dislocations associated with the formation of confined austenitic states causes similar effects. The local chemical composition at the dislocation cores was investigated for different tempering temperatures by APT relative to the adjacent bcc matrix. In all cases the Mn partitioning to the dislocation core regions matches to the one between ferrite and austenite in thermodynamic equilibrium at the corresponding tempering temperature. Although a stable structural and chemical confined austenitic state has formed at the dislocation cores these regions do not grow further even upon prolonged tempering. Simulation reveals that the high Mn enrichment along the edge dislocation lines (25 at.%Mn at 450 C) cannot be described merely as a Cottrell atmosphere formed by segregation driven by size interaction. Thermodynamic calculations based on a multiscale model indicate that these austenite states at the dislocation cores are subcritical and defect-stabilized by the compression stress field of the edge dislocations. Phenomenologically, these states are the 1D equivalent to the so-called complexions which have been extensively reported to be present at 2D defects, hence have been named linear complexions.

— The general solution of two dimensional problem in micropolar thermoelastic solid with fractional order derivative has been obtained .The fractional order theories of thermoelasticity with one relaxation time developed by Sherief Ezzat and Youssef have been used to investigate the problem. After developing a mathematical model, Laplace and Fourier transform techniques are used to obtain the general solution. A numerical inversion technique has been applied to obtain the solution in the physical domain and the numerical results are depicted graphically. Some particular cases of interest are also deduced from the present study.

Praca doktorska poświęcona opracowaniu kryterium stanu granicznego dla anizotropowych materiałów liniowo-sprężystych wykazujących różnicę wielkości naprężenia granicznego w zależności od jego znaku. Zaproponowane kryterium bazuje na koncepcji Rychlewskiego rozkładu głównego energii sprężystej oraz koncepcji Burzyńskiego wykorzystania zależnych od aktualnego stanu naprężenia funkcji skalujących kombinację elementów tego rozkładu. Zebrano i omówiono klasyczne kryteria dla materiałów anizotropowych oraz przeanalizowano i porównano tzw. "kryteria energetyczne". Przeprowadzono dowód twierdzenia Rychlewskiego dla wielowymiarowej przestrzeni stanów bezpiecznych. Szczegółowo scharakteryzowano poszczególne przypadki symetrii sprężystych oraz odpowiadające im postacie kryterium stanu granicznego.

Zirconia has the loading rate-dependent nanoindentation contact hardness which is a hybrid property encompassing both the elastic and plastic behaviors which affect its machinability, wear and fatigue properties. This work aimed to partition the deformation behavior into the elasticity and plasticity, and to predict the machinability of zirconia at different nanoindentation loading rates using the Sakai and the Sakai–Nowak models. The results reveal that the resistance to plasticity of zirconia was loading-rate independent (ANOVA, p 40.05). The plastic displacement showed the loading-rate dependent character following a power law while the elastic displacement revealed approximately a loading-rate independent constant. The elastic and plastic deformation components demonstrated loading-rate dependence in which at the low loading rates the two components approximately coincided but at high loading rates, the elastic deformation component was slightly dominant. Zirconia also showed higher ductility than its elasticity indices at higher loading rates. The loading-rate independent resistance to machining-induced cracking of zirconia was lower than its pre-sintered state. This study lends credence to the realization of a small-volume material removal for crack-free zirconia surface generation at high deformation rates for zirconia in abrasive machining.

The effect of foundation embedment on settlement calculation is a widely researched topic in which there is no scientific consensus regarding the magnitude of settlement reduction. In this paper, a non-linear three dimensional Finite Element analysis has been performed with the aim of evaluating the aforementioned effect. For this purpose, 1800 models were run considering different variables, such as the depth and dimensions of the foundation and the Young’s modulus and Poisson’s ratio of the soil. The settlements from models with foundations at surface level and at depth were then compared and the relationship between them established. The statistical analysis of this data allowed two new expressions, with a mean maximum error of 1.80%, for the embedment influence factor of a foundation to be proposed and these to be compared with commonly used corrections. The proposed equations were validated by comparing the settlements calculated with the proposed influence factors and the true settlements measured in several real foundations. From the comprehensive study of all modelled cases, an improved approach, when compared to those proposed by other authors, for the calculation of the true elastic settlements of an embedded foundation is proposed.

► A kind of Elastic Composite, Reinforced Lightweight Concrete (ECRL.C) with the mentioned specifics is a type of "Resilient Composite Systems (RCS)" in which, contrary to the basic geometrical assumption of the flexure theory in Solid Mechanics, "the strain changes in the beam height during bending" is typically "Nonlinear". (The RCS could be counted as "The Methodically Reinforced Nonlinear Porous Materials", also having the high specific modulus of resilience in flexure.)

♦ Through employing this integrated structure, with significantly high strain capability and modulus of resilience in bending, we can achieve the high bearing capacities in beams with the secure fracture pattern, in less weight.

♦ Due to the system particulars and its behavior in bending, the usual calculation of the necessary equilibrium steel amount to attain the low-steel bending sections with the secure fracture pattern in the beams and its related limitations do not become propounded. Thereby, the strategic deadlock of the high possibility of the brittle fracture pattern in the bending elements made of the usual reinforced lightweight concretes, especially about the low-thickness bending elements as slabs, is unlocked.

♦ This simple, applied technology and the related components and systems can have several applications in the road and building industries. (It can also be used in making the resilient pieces and constructions "with appropriate behavior and high resistance against severe blasts and shocks.)

♦ Regarding the "strategic importance of Lightweight and Integrated Construction in the practical increase of the resistance and safety against earthquake" and considering the appropriate behavior of this "resilient", durable structure against the dynamic loads, shakes, impacts, blasts, and shocks and the possibility of making some lightweight and insulating, non-brittle, reinforced sandwich panels and pieces, this resilient system and its components can especially be useful in the "seismic areas".

♦ This system can also be employed in constructing the vibration and impact absorber bearing pieces & slabs, which can be used in the "Railroad & Subway Structures" too.

♦ Here, the "Resilient Composite Systems (RCS)" and particularly, the ECRLC as a type of the RCS have been concisely presented. [By the way, an instance of the said new structure and its components and the results of some performed experiments (as bending loading and compressive loading of the slabs made of this structure, similar to ASTM E 72 Standard) have been shown in the related pictures & figures.]
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/ ● Key Words: Strength of materials (solid mechanics), Civil (construction), Materials, Earthquake (resistance and safety), Resilient concrete (flexible concrete, bendable concrete, elastic concrete), Composite concrete, Lightweight concrete, Reinforced concrete, Fibered concrete, Lightweight and integrated construction, Rail (railroad, railway), Subway, Road, Bridge, Resilience, Energy absorption, Fracture pattern, Non-linear, Strain changes, Beam, Ductility, Toughness, Insulating (insulation), Thin, Slab, Roof, Ceiling, Wall (partition), Building, Tower, Plan of mixture, Insulating reinforced lightweight pieces, 3d, Sandwich panel, Dry mix, Plaster, Foam, Expanded polystyrene (EPS), Polypropylene, Pozzolan, Porous matrix (Pored matrix), Mesh (lattice), Cement, RCS, ECRLC
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/ ► Contents:
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* ABSTRACT
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* I. INTRODUCTION
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* II. WHAT ARE THE RESILIENT COMPOSITE SYSTEMS
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- A. General Review
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- B. Components
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. - 1) Mesh or Lattice
. - 2) Fibers or Strands
. - 3) "Matrix" With the Suitable Hollow "Pores (Voids)" and/or "Lightweight Aggregates" in its Context
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- C. More Explanations About the RCS
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- D. Why Are These Systems Called "Composite"?
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- E. The General Structural Particulars and Functional Criteria as the Necessary Specifications of the Compound Materials Generally Called "Resilient Composite Systems"
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. - 1) General Structural Criteria
. - 2) Functional Criteria (Required Specifications)
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* III. "ELASTIC COMPOSITE REINFORCED LIGHTWEIGHT CONCRETE (ECRLC)" AS A TYPE OF THE RESILIENT COMPOSITE SYSTEMS (RCS)
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- An Instance of the Lightweight Concrete That Could be Used in Making the ECRLC
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* IV. REVIEW OF SOME EXPERIMENTS, AND MORE DESCRIPTION ABOUT ECRLC
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* V. SUPPLEMENTARY ELEMENTS
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* VI. APPLICATIONS
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* VII. FINAL REVIEW
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* ACKNOWLEDGEMENTS
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* REFERENCES 
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***
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/ ● General Review:
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• A kind of "Elastic Composite, Reinforced Lightweight Concrete" with the said specifics is a type of the "Resilient Composite Systems (R.C.S.)" in which, contrary to the basic geometrical assumption of flexure theory in the Solid Mechanics, the strain changes in the beam height during bending is typically "Non-linear".
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• Indeed, the RCS, as the Elastic Composite, Reinforced Lightweight Concrete (ECRLC), do not behave as most of the solid materials in bending.
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• In the "Resilient Composite Systems", distributed pores and/or appropriate lightweight aggregates or beads, accompanied by the reticular structure of the strengthened conjoined matrix, bring about the expedient internal shape changes during bending and continuing the elasticity in bending with the said nonlinearly pattern. This means better distribution of the stresses and strains and better utilizing the potential capacities of the employed reinforcements in bending and tension; whereas, in the usual lightweight concretes for instance, distributed hollow pores (such as the gas bulbs in the cellular concretes) or lightweight aggregates (such as Plastic, Rubber or polystyrene beads or any other kind of lightweight aggregates such as Perlite and Vermiculite) decrease the modulus of resilience in bending and could increase "the possibility of beam fracture of brittle and primary compressive type" in bending (compared to the concrete with higher density) according to the case.
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• In this way, by using the mentioned method to make the said particular composite systems, we could considerably increase the modulus of resilience and bearing capacity in bending "together with" significant decrease of the weight and also the possibility of beam fracture of primary compressive type. Through making these particular integrated functioning systems, for the first time, the said (paradoxical) properties have been concomitantly fulfilled in "one functioning unit" altogether.
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• Respect to the special pattern of the strain changes during bending in the particular Resilient Composite System termed ECRLC, this system as an integrated functioning unit with the reticular arrangement and texture has more strain capability (particularly within the elastic limit), energy absorption and load bearing capacities in bending compared to the usual reinforced concrete beams.
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• Thereby, through employing this applied structure, solving some of the main problems in lightweight concretes application, especially the deadlock of brittle and insecure being of fracture pattern in many of the usual reinforced lightweight concrete structures, is provided; reaching to the high bearing capacities in bending elements (even with low dimensions & weights) is to hand, and getting access to a simple and practical opportunity for "qualitative development of possibilities of using lightweight concretes" (especially with oven-dry densities of < 1350-1400kg/m3 and compressive strengths of <14-17mpa, and even with oven-dry densities of < 800kg/m3) is conceivable.
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• Naturally, by more studies in the field, these structures and their applications in various fields could be developed more.
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/ ► FULL TEXT (Open Access):
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- http://arxiv.org/abs/1510.03933 
( https://arxiv.org/ftp/arxiv/papers/1510/1510.03933.pdf ) ;
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. Kamyar Esmaeili: "Elastic Composite Reinforced Lightweight Concrete as a Type of Resilient Composite Systems";
The Internet Journal of Innovative Technology and Creative Engineering (IJITCE); 2012; 2(8): 1-22.
- http://ia800305.us.archive.org/34/items/IJITCE/vol2no801.pdf [Also archived at: http://www.webcitation.org/6B2pFPpBh ] ;
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- https://www.scribd.com/doc/11530978/Elastic-Composite-Reinforced-Lightweight-Concrete-ECRLC-as-a-type-of-Resilient-Composite-Systems-RCS-http-arxiv-org-abs-1510-03933 ; 
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- https://sites.google.com/site/NEWSTRUCTURE1 ;
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- https://sites.google.com/site/newstructure1/publications-page/ELASTIC%20COMPOSITE%2C%20REINFORCED%20LIGHTWEIGHT%20CONCRETE%20AS%20A%20TYPE%20OF%20RESILIENT%20COMPOSITE%20SYSTEMS.pdf ;
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- http://www.pdf-archive.com/2015/09/22/elasticcomposite-reinforcedlightweightconcreteasatypeofrcs/elasticcomposite-reinforcedlightweightconcreteasatypeofrcs.pdf ;
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- The link to the document in PDF format on this site:
file:///C:/Users/pc5/Downloads/ELASTIC_COMPOSITE_REINFORCED_LIGHTWEIGHT.pdf ;
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- ...

We present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

Acoustic multiple scattering by a cluster of cylinders in an acoustic medium is considered. A fast recursive technique is described which takes advantage of the multilevel Block Toeplitz structure of the linear system. A parallelization technique is described that enables efficient application of the proposed recursive algorithm for solving multilevel Block Toeplitz systems on high performance computer clusters. Numerical comparisons of CPU time and total elapsed time taken to solve the linear system using the direct LAPACK and TOEPLITZ libraries on Intel FORTRAN, show the advantage of the TOEPLITZ solver. Computations are optimized by multi-threading which displays improved efficiency of the TOEPLITZ solver with the increase of the number of scatterers and frequency

The goal of this white paper is to present the theory and methodology for the non-destructive elastic moduli characterization of composites using the Impulse Excitation Technique (ASTM E1876 and correlated). This study presents a literature review and the advances achieved by ATCP Physical Engineering in what regards the application of this characterization technique applied to composites.

Layerwise theory of Reddy is utilized for investigating free-edge effects in antisymmetric angle-ply laminated shell panels under uniform axial extension. Following some physical arguments, governing displacement field is divided into local and global parts. The former is discretized through the shell thickness by a zig-zag interpolation function while the latter is calculated by a first-order shear deformation theory. Local equilibrium equations are then solved through a state space approach. Accuracy of the proposed technical solution is subsequently verified by a novel analytical elasticity solution. For this end, the problem is analytically solved for specific boundary conditions along the edges. The numerical results show excellent agreement between two theories for various composite shell panels.

We make precise some results on the cloaking of displacement fields
in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to certain high contrast small defect problems for the usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence of the solutions to the transmission problems is investigated, when the Lamé parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

We explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks' parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks's designs are strikingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigor in transposition of existing cloaks's designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks' parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars.

"Se presenta el análisis no lineal dinámico en tres direcciones de 6 edificiosde concreto reforzado de 5, 12 y 20 pisos, diseñados con la NSR-10 yla zonificación de respuesta sísmica de Bogotá del año 2010. Estos 6 edificios,con planta típica idéntica, fueron sometidos a 78 señales sísmicas del sismo deQuetame (año 2008) registradas por 26 estaciones de la red de acelerógrafosde Bogotá (RAB). Para el diseño de los edificios se utilizaron los espectros derespuesta de aceleración absoluta para las zonas: «Piedemonte-B» y «Lacustre-500» de la microzonificación sísmica de Bogotá. Posteriormente, se calcularonlas rótulas plásticas para cada elemento estructural de los 6 edificios, y en elcaso de las columnas, también sus diagramas de interacción. Luego, las edificacion estridimensionales fueron sometidas simultáneamente a los registros contra el tiempo norte-sur, este-oeste y vertical. Para cada edificio sometidoa las señales de cada estación, se obtuvieron las demandas de deriva, los desplazamientosde la cubierta, el cortante en la base y los niveles de daño segúnestimadores internacionalmente aceptados. Finalmente, se generaron mapasde demandas de deriva y aceleración por edificio en la ciudad de Bogotá D.C.Los resultados sugieren que los edificios diseñados con la amenaza sísmica dela nueva microzonificación de Bogotá y con las estipulaciones de la NSR-10,presentarán daños excesivos asociados a estados límites como son los de «seguridadde vidas» para un sismo de baja magnitud como fue el de Quetame,que equivalió a solo una fracción de aquel que corresponde al comportamientoreal bajo el escenario de diseño"

Plate materials play a significant role in civil engineering and its application is found in building, bridges, marine, nuclear and structural engineering. Plates are three-dimensional (3-D) structural elements and normal practice in its analysis as two-dimensional (2-D) element has produced unreliable design which is a major problem in the construction industry. In this paper, a 3-D exact elastic plate theory (alternative I refined plate theory) is developed and applied to the bending analysis of an isotropic rectangular plate with free support at the third edge and the other edges clamped (CCFC) under uniformly distributed transverse load. The energy equation is formulated using the three-dimensional constitutive relations thereafter, the compatibility equation was obtained through general variation. The solution of the compatibility equation gave an exact deflection function of the plate as presented in the trigonometric form. This deflection function which is a product of the coefficient of deflection and shape function of the plate are substituted back into the energy equation, and simplified through minimization with respect to the coefficients of deflection and shear deformation to get a realistic formula for calculating the deflection, rotations and stresses of thick rectangular plate. The results of deflections and stresses obtained at aspect ratio of 2 were compared with those of previous studies available in the literature. It was observed that the present theory varied more with those of 2-D refined plate theory (RPT) with an assumed deflection function by 6.2% whereas it varied with exact 2-D RPT by 3.1%. This shows the inefficiency of assuming the deflection function in the analysis of thick plate. Meanwhile, the recorded total percentage differences showed that 2-D RPT over predicted the bending characteristics of the plate with 4.7%. This finding provides in-depth insight about the coarseness of 2-D RPT in the thick plate analysis.

We systematically study the morphology, size and dispersion of TiB 2 particles formed in-situ from FeeTi eB based melts, as well as their chemical composition, crystal structure and mechanical properties. The effects of 5 wt.% additions of Cr, Ni, Co, Mo, W, Mn, Al, Si, V, Ta, Nb and Zr, respectively, as well as additional annealing treatments, were investigated in order to derive guidelines for the knowledge based alloy design of steels with an increased stiffness/density ratio and sufficiently high ductility. All alloying elements were found to increase the size of the coarse primary TiB 2 particles, while Co led to the most homogeneous size distribution. The size of the eutectic TiB 2 constituents was decreased by all alloying additions except Ni, while their aspect ratio was little affected. No clear relation between chemical composition, crystal structure and mechanical properties of the particles could be observed. Annealing of the as-cast alloys slightly increased the size of the primary particles, but at the same time strongly spheroidised the eutectics. Additions of Co and Cr appear thus as the best starting point for designing novel in-situ high modulus metal matrix composite steels, while using Mn in concert with thermo-mechanical processing is most suited to adapt the matrix' microstructure and optimise the particle/ matrix co-deformation processes.

Ball bearings are an integral part of many machines and mechanisms and often determine their performance limits. Vibration, friction and power loss are some of the key measures of bearing performance. Therefore, there have been many predictive analyses of bearing performance with emphasis on various aspects. The current study presents a mathematical model, incorporating bearing dynamics, mechanics of rolling element-to-races contacts as well as the elastodynamics of the bearing outer ring as a focus of the study. It is shown that the bearing power loss in cage cycles increases by as much as 4% when the flexibility of the outer ring is taken into account as a thick elastic ring, based on Timoshenko beam theory as opposed to the usual assumption of a rigid ring in other studies. Geometric optimisation has shown that the lifetime power consumption can be reduced by 1.25%, which is a significant source of energy saving when considering the abundance of machines using rolling element bearings. The elastodynamics of bearing rings significantly affects the radial bearing clearance through increased roller loads and generated contact pressures. The flexible ring dynamics is shown to generate surface waviness through global elastic wave propagation, not hitherto taken into account in contact dynamics of rollers-to-raceways which are generally considered to be subjected to only localised Hertzian deflection. The elastodynamic behaviour reduces the elastohydrodynamic film thickness, affecting contact friction, wear, fatigue, vibration, noise and inefficiency.

Triply periodic minimal surfaces (TPMS) are employed to create novel cellular materials. They include Schwarz Primitive, Schoen IWP, Neovius, Schoen Gyroid, Fischer-Koch S, and Schwarz CLP geometries. Unit cells are studied using a finite element method with periodic boundary conditions in order to predict effective electrical/thermal conductivities and elastic moduli of these TPMS-based foams. The conductivities vary linearly with relative density. The conductivities of the Primitive-, IWP-, Neovius-, Gyroid-, and S-foams are very close to each other. The conductivity of the CLP-foam needs to be described by two values because of its geometrical asymmetry while the other foams are found to be isotropic when their conductivities are studied. The uniaxial, shear and bulk moduli, Pois-son ratio and elastic anisotropy of these TPMS-foams are also computed and compared. When the mechanical properties are investigated, the CLP-foam is found to have highest anisotropy among the considered TPMS-foams. In addition, the Primitive-foam possesses highest shear modulus while the Neovius, IWP-, and Primitive-foams possess highest bulk moduli among the TPMS-foams.