Search results for: binary-signal mechanics

Authors: Felix Eyben, Simon Schaffrath, Markus Feldmann

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A building should maximize the potential for use through its design. Therefore, flexible use is always important when designing a steel structure. To create flexibility, steel beams with web openings are increasingly used, because these offer the advantage that cables, pipes and other technical equipment can easily be routed through without detours, allowing for more space-saving and aesthetically pleasing construction. This can also significantly reduce the height of ceiling systems. Until now, beams with web openings were not explicitly considered in the European standard. However, this is to be done with the new EN 1993-1-13, in which design rules for different opening forms are defined. In order to further develop the design concepts, beams with web openings under bending are therefore to be investigated in terms of damage mechanics as part of a German national research project aiming to optimize the verifications for steel structures based on a wider database and a validated damage prediction. For this purpose, first, fundamental factors influencing the load-bearing behavior of girders with web openings under bending load were investigated numerically without taking material damage into account. Various parameter studies were carried out for this purpose. For example, the factors under study were the opening shape, size and position as well as structural aspects as the span length, arrangement of stiffeners and loading situation. The load-bearing behavior is evaluated using resulting load-deformation curves. These results are compared with the design rules and critically analyzed. Experimental tests are also planned based on these results. Moreover, the implementation of damage mechanics in the form of the modified Bai-Wierzbicki model was examined. After the experimental tests will have been carried out, the numerical models are validated and further influencing factors will be investigated on the basis of parametric studies.

Keywords: damage mechanics, finite element, steel structures, web openings

Procedia PDF Downloads 139

Authors: Ugo Galvanetto, Pirto G. Pavan, Mirco Zaccariotto

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The discipline of Computer-integrated surgery (CIS) will provide equipment able to improve the efficiency of healthcare systems and, which is more important, clinical results. Surgeons and machines will cooperate in new ways that will extend surgeons’ ability to train, plan and carry out surgery. Patient specific CIS of the brain requires several steps: 1 - Fast generation of brain models. Based on image recognition of MR images and equipped with artificial intelligence, image recognition techniques should differentiate among all brain tissues and segment them. After that, automatic mesh generation should create the mathematical model of the brain in which the various tissues (white matter, grey matter, cerebrospinal fluid …) are clearly located in the correct positions. 2 – Reliable and fast simulation of the surgical process. Computational mechanics will be the crucial aspect of the entire procedure. New algorithms will be used to simulate the mechanical behaviour of cutting through cerebral tissues. 3 – Real time provision of visual and haptic feedback A sophisticated human-machine interface based on ergonomics and psychology will provide the feedback to the surgeon. The present work will address in particular point 2. Modelling the cutting of soft tissue in a structure as complex as the human brain is an extremely challenging problem in computational mechanics. The finite element method (FEM), that accurately represents complex geometries and accounts for material and geometrical nonlinearities, is the most used computational tool to simulate the mechanical response of soft tissues. However, the main drawback of FEM lies in the mechanics theory on which it is based, classical continuum Mechanics, which assumes matter is a continuum with no discontinuity. FEM must resort to complex tools such as pre-defined cohesive zones, external phase-field variables, and demanding remeshing techniques to include discontinuities. However, all approaches to equip FEM computational methods with the capability to describe material separation, such as interface elements with cohesive zone models, X-FEM, element erosion, phase-field, have some drawbacks that make them unsuitable for surgery simulation. Interface elements require a-priori knowledge of crack paths. The use of XFEM in 3D is cumbersome. Element erosion does not conserve mass. The Phase Field approach adopts a diffusive crack model instead of describing true tissue separation typical of surgical procedures. Modelling discontinuities, so difficult when using computational approaches based on classical continuum Mechanics, is instead easy for novel computational methods based on Peridynamics (PD). PD is a non-local theory of mechanics formulated with no use of spatial derivatives. Its governing equations are valid at points or surfaces of discontinuity, and it is, therefore especially suited to describe crack propagation and fragmentation problems. Moreover, PD does not require any criterium to decide the direction of crack propagation or the conditions for crack branching or coalescence; in the PD-based computational methods, cracks develop spontaneously in the way which is the most convenient from an energy point of view. Therefore, in PD computational methods, crack propagation in 3D is as easy as it is in 2D, with a remarkable advantage with respect to all other computational techniques.

Keywords: computational mechanics, peridynamics, finite element, biomechanics

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Authors: YuPei Chang

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In recent years, moral judgement tasks have served as an increasingly popular plot mechanism in digital gameplay. As a moral agency, the player's choice judgment in digital games is to shuttle between the real world and the game world. The purpose of the research is to explore the moral difficulties brewed by the interactive mechanism of the game and the moral choice of players. In the theoretical level, this research tries to combine moral disengagement, moral foundations theory, and gameplay as an aesthetic experience. And in the methodical level, this research tries to use methods that combine text analysis, diary method, and in-depth interviews. There are three research problems that will be solved in three stages. In the first stage, this project will explore how moral dilemmas are represented in game mechanics. In the second stage, this project will analyze the appearance and conflicts of moral dilemmas in game mechanics based on the five aspects of moral foundations theory. In the third stage, this project will try to understand the players' choices when they face the choices of moral dilemmas, as well as their explanations and reflections after making the decisions.

Keywords: morality, moral disengagement, moral foundations theory, PC game, gameplay, moral dilemmas, player

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Authors: Vyacheslav S. Semenov, Tamara A. Rozovskaya

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The paper is devoted to the problem of the development of dry light-weight mixtures with hollow ceramics microspheres (CMS) for masonry works. For the one-layer fencing structures including effective masonry units, the use of “warm” masonry mortars is necessary. The used light-weight masonry mortars do not provide the brand strength and thermal uniformity of the fencing structures because of high average density. The CMS are effective light-weight aggregate for such mortars. The influence of the dosage of CMS on the physics-and-mechanics parameters and the technological properties of the masonry mortars were studied. The optimal mixture compositions have been obtained and their main properties have been determined. The influence of an air-entraining admixture and redispersible polymer powders on the average density and physics-and-mechanics parameters of the masonry mortars were studied. The optimal compositions of light-weight dry masonry mixtures with CMS have been suggested.

Keywords: dry mortar mixtures, light-weight dry mixtures, hollow ceramics microspheres, masonry mortars, “warm” mortars, air-entraining admixture, redispersible polymer powders

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Authors: Rafał Urbaniak, Robert Kłosowiak, Michał Ciałkowski, Jarosław Bartoszewicz

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The Chair of Thermal Engineering at Poznan University of Technology has been conducted research works on the possibilities of using carbon nanostructures in energy and mechanics applications for a couple of years. Those studies have provided results in a form of co-operation with foreign research centres, numerous publications and patent applications. Authors of this paper have studied the influence of multi-walled carbon nanostructures on changes in static friction arising when steel surfaces were moved. Tests were made using the original test stand consisting of automatically controlled inclined plane driven by precise stepper motors. Computer program created in the LabView environment was responsible for monitoring of the stand operation, accuracy of measurements and archiving the obtained results. Such a solution enabled to obtain high accuracy and repeatability of all conducted experiments. Tests and analysis of the obtained results allowed us to determine how additional layers of carbon nanostructures influenced on changes of static friction coefficients. At the same time, we analyzed the potential possibilities of applying nanostructures under consideration in mechanics.

Keywords: carbon nanotubes, static friction, dynamic friction

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Authors: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Elias Akoury

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Nuclear Magnetic Resonance (NMR) spectroscopy is an indispensable technique used in structure determination of small and macromolecules to study their physical properties, elucidation of characteristic interactions, dynamics and thermodynamic processes. Quantum mechanics defines the theoretical description of NMR spectroscopy and treatment of the dynamics of nuclear spin systems. The phenomenon of residual dipolar coupling (RDCs) has become a routine tool for accurate structure determination by providing global orientation information of magnetic dipole-dipole interaction vectors within a common reference frame. This offers accessibility of distance-independent angular information and insights to local relaxation. The measurement of RDCs requires an anisotropic orientation medium for the molecules to partially align along the magnetic field. This can be achieved by introduction of liquid crystals or attaching a paramagnetic center. Although anisotropic paramagnetic tags continue to mark achievements in the biomolecular NMR of large proteins, its application in small organic molecules remains unspread. Here, we propose a strategy for the synthesis of a lanthanide tag and the measurement of RDCs in organic molecules using paramagnetic lanthanide complexes.

Keywords: lanthanide tags, NMR spectroscopy, residual dipolar coupling, quantum mechanics of spin dynamics

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Authors: Xin Chen, Moxiao Li, Xuechao Sun, Fei Ti, Shaobao Liu, Feng Xu, Tian Jian Lu

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The composite materials with pores have the characteristics of light weight, sound insulation, and heat insulation, and have broad prospects in many fields, including aerospace. In general, the stiffness of such composite is less than the stiffness of the matrix material, limiting their applications. In this paper, we establish a theoretical model to analyze the deformation mechanism of a nano-pore. The interface between the pores and matrix material is described by the Gurtin-Murdoch model. By considering scale effect related with current deformation, we estimate the effective mechanical properties (e.g., effective shear modulus and bulk modulus) of a composite with nano-pores. Due to the scale effect, the elastic field in the composite was changed and local hardening was observed around the nano-pore, and the effective shear modulus and effective bulk modulus were found to be a function of the surface energy. The effective shear modulus increase with the surface energy and decrease with the size of the nano-pores, and the effective bulk modulus decrease with the surface energy and increase with the size of the nano-pores. These results have potential applications in the nanocomposite mechanics and aerospace field.

Keywords: composite mechanics, nano-inhomogeneity, nano-pores, scale effect

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Authors: Nicola Menga, Giuseppe Carbone

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Although contact mechanics has been widely focused on the study of contacts between half-space, it has been recently pointed out that in presence of finite thickness elastic layers the results of the contact problem show significant difference in terms of the main contact quantities (e.g. contact area, penetration, mean pressure, etc.). Actually, there exist a wide range of industrial application demanding for this kind of studies, such as seals leakage prediction or pressure-sensitive coatings for electrical applications. In this work, we focus on the contact between a rigid profile and an elastic layer of thickness h confined under two different configurations: rigid constrain and applied uniform pressure. The elastic problem at hand has been formalized following Green’s function method and then numerically solved by means of a matrix inversion. We study different contact conditions, both considering and neglecting adhesive interactions at the interface. This leads to different solution techniques: Adhesive contacts equilibrium solution is found, in term of contact area for given penetration, making stationary the total free energy of the system; whereas, adhesiveless contacts are addressed defining an equilibrium criterion, again on the contact area, relying on the fracture mechanics stress intensity factor KI. In particular, we make the KI vanish at the edges of the contact area, as peculiar for adhesiveless elastic contacts. The results are obtained in terms of contact area, penetration, and mean pressure for both adhesive and adhesiveless contact conditions. As expected, in the case of a uniform applied pressure the slab turns out much more compliant than the rigidly constrained one. Indeed, we have observed that the peak value of the contact pressure, for both the adhesive and adhesiveless condition, is much higher for the rigidly constrained configuration than in the case of applied uniform pressure. Furthermore, we observed that, for little contact area, both systems behave the same and the pull-off occurs at approximately the same contact area and mean contact pressure. This is an expected result since in this condition the ratio between the layers thickness and the contact area is very high and both layer configurations recover the half-space behavior where the pull-off occurrence is mainly controlled by the adhesive interactions, which are kept constant among the cases.

Keywords: contact mechanics, adhesion, friction, thick layer

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Authors: Peter Jean-Paul, Shanaz Wahid

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The problem of division by zero can be stated as: “what is the value of 0 x 1/0?” This expression has been considered undefined by mathematicians because it can have two equally valid solutions either 0 or 1. Recently semi-structured complex number set was invented to solve “division by zero”. However, whilst the number set had some merits it was considered to have a poor theoretical foundation and did not provide a quality solution to “division by zero”. Moreover, the set lacked consistency in simple algebraic calculations producing contradictory results when dividing by zero. To overcome these issues this research starts by treating the expression " 0 x 1/0" as a quantum mechanical system that produces two tangled results 0 and 1. Dirac Notation (a tool from quantum mechanics) was then used to redefine the unstructured unit p in semi-structured complex numbers so that p represents the superposition of two results (0 and 1) and collapses into a single value when used in algebraic expressions. In the process, this paper describes a new number set called Quantum Semi-structured Complex Numbers that provides a valid solution to the problem of “division by zero”. This research shows that this new set (1) forms a “Field”, (2) can produce consistent results when solving division by zero problems, (3) can be used to accurately describe systems whose mathematical descriptions involve division by zero. This research served to provide a firm foundation for Quantum Semi-structured Complex Numbers and support their practical use.

Keywords: division by zero, semi-structured complex numbers, quantum mechanics, Hilbert space, Euclidean space

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Authors: Rajat Mittal, Jung Hee Seo, Jacob Turner, Harshal Raut

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The perpetual advancement in computational capabilities, coupled with the continuous evolution of software tools and numerical algorithms, is creating novel avenues for research, exploration, and application at the nexus of computational fluid and structural mechanics. Fish leverage their remarkably flexible bodies and fins to harness energy from vortices, propelling themselves with an elegance and efficiency that captivates engineers. Bats fly with unparalleled agility and speed by using their flexible membrane wings. Wave-assisted propulsion (WAP) systems, utilizing elastically mounted hydrofoils, convert wave energy into thrust. Each of these problems involves a complex and elegant interplay between fluid dynamics and structural mechanics. Historically, investigations into such phenomena were constrained by available tools, but modern computational advancements now facilitate exploration of these multi-physics challenges with an unprecedented level of fidelity, precision, and realism. In this work, the author will discuss projects that harness the capabilities of high-fidelity sharp-interface immersed boundary methods to address a spectrum of engineering and biological challenges involving fluid-structure interaction.

Keywords: immersed boundary methods, CFD, bioflight, fluid structure interaction

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Authors: Atoui Oussama, Maazoun Azer, Belkassem Bachir, Pyl Lincy, Lecompte David

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For many decades, researchers have been focused on understanding the dynamic behavior of different structures and materials subjected to fragment impact or blast loads separately. The explosion mechanics, as well as the impact physics studies dealing with the numerical modeling of the response of protective structures under the synergistic effect of a blast wave and the impact of fragments, are quite limited in the literature. This article numerically evaluates the nonlinear dynamic behavior and damage mechanisms of Aluminum plates EN AW-1050A- H24 under different combined loading scenarios varied by the sequence of the applied loads using the commercial software LS-DYNA. For one hand, with respect to the terminal ballistic field investigations, a Lagrangian (LAG) formulation is used to evaluate the different failure modes of the target material in case of a fragment impact. On the other hand, with respect to the blast field analysis, an Arbitrary Lagrangian-Eulerian (ALE) formulation is considered to study the fluid-structure interaction (FSI) of the shock wave and the plate in case of a blast loading. Four different loading scenarios are considered: (1) only blast loading, (2) only fragment impact, (3) blast loading followed by a fragment impact and (4) a fragment impact followed by blast loading. From the numerical results, it was observed that when the impact load is applied to the plate prior to the blast load, it suffers more severe damage due to the hole enlargement phenomenon and the effects of crack propagation on the circumference of the damaged zone. Moreover, it was found that the hole from the fragment impact loading was enlarged to about three times in diameter as compared to the diameter of the projectile. The validation of the proposed computational model is based in part on previous experimental data obtained by the authors and in the other part on experimental data obtained from the literature. A good correspondence between the numerical and experimental results is found.

Keywords: computational analysis, combined loading, explosion mechanics, hole enlargement phenomenon, impact physics, synergistic effect, terminal ballistic

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Authors: Gaurav Bisht, Rahul Rathnakumar, Ravikumar Duggirala

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Predictive simulations are one of the key focus areas in safety-critical industries such as aerospace and high-performance automotive engineering. The stone-chipping study is one such effort taken up by the industry to predict and evaluate the damage caused due to gravel impact on vehicles. This paper describes a finite elements based method that can simulate the ejection of gravel chips from a vehicle tire. The FE simulations were used to obtain the initial ejection velocity of the stones for various driving conditions using a computational contact mechanics approach. To verify the accuracy of the tire model, several parametric studies were conducted. The FE simulations resulted in stone loft velocities ranging from 0–8 m/s, regardless of tire speed. The stress on the tire at the instant of initial contact with the stone increased linearly with vehicle speed. Mesh convergence studies indicated that a highly resolved tire mesh tends to result in better momentum transfer between the tire and the stone. A fine tire mesh also showed a linearly increasing relationship between the tire forward speed and stone lofting speed, which was not observed in coarser meshes. However, it also highlighted a potential challenge, in that the ejection velocity vector of the stone seemed to be sensitive to the mesh, owing to the FE-based contact mechanical formulation of the problem.

Keywords: abaqus, contact mechanics, foreign object debris, stone chipping

Procedia PDF Downloads 243

Authors: Luis Marquez, Ge Zhu, Vikas Srivastava

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High-density polyethylene (HDPE) is one of the most commonly used thermoplastic polymer materials for water and gas pipelines. Slow crack growth failure is a well-known phenomenon in high-density polyethylene material and causes brittle failure well below the yield point with no obvious sign. The failure of transportation pipelines can cause catastrophic environmental and economic consequences. Using the non-destructive testing method to predict slow crack growth failure behavior is the primary preventative measurement employed by the pipeline industry but is often costly and time-consuming. Phenomenological slow crack growth models are useful to predict the slow crack growth behavior in the polymer material due to their ability to evaluate slow crack growth under different temperature and loading conditions. We developed a quantitative method to assess the slow crack growth behavior in the high-density polyethylene pipeline material under different thermal conditions based on existing physics-based phenomenological models. We are also working on developing an experimental protocol and quantitative model that can address slow crack growth behavior under different chemical exposure conditions to improve the safety, reliability, and resilience of HDPE-based pipeline infrastructure.

Keywords: mechanics of materials, physics-based modeling, civil engineering, fracture mechanics

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Authors: A. Armin, R. Fotouhi, W. Szyszkowski

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This paper is part of a study to develop robots for farming. As such power requirement to operate equipment attach to such robots become an important factor. Soil-tool interaction play major role in power consumption, thus predicting accurately the forces which act on the blade during the farming is prime importance for optimal designing of farm equipment. In this paper a finite element investigation for tillage tools and soil interaction is described by using an inelastic constitutive material law for agriculture application. A 3-dimentional (3D) nonlinear finite element analysis (FEA) is developed to examine behavior of a blade with different rake angles moving in a block of soil, and to estimate the blade force. The soil model considered is an elastic-plastic with non-associated Drucker-Prager material model. Special use of contact elements are employed to consider connection between soil-blade and soil-soil surfaces. The FEA results are compared with experiment ones, which show good agreement in accurately predicting draft forces developed on the blade when it moves through the soil. Also, a very good correlation was obtained between FEA results and analytical results from classical soil mechanics theories for straight blades. These comparisons verified the FEA model developed. For analyzing complicated soil-tool interactions and for optimum design of blades, this method will be useful.

Keywords: finite element analysis, soil-blade contact modeling, blade force, mechanical engineering

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Authors: Debadi Chakraborty, John E. Sader

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Nanomechanical devices have emerged as a versatile platform for a host of applications due to their extreme sensitivity to environmental conditions. For example, mass measurements with sensitivity at the atomic level have recently been demonstrated. Ultrafast laser spectroscopy coherently excite the vibrational modes of metal nanoparticles and permits precise measurement of the vibration characteristics as a function of nanoparticle shape, size and surrounding environment. This study reports that the vibration of metal nanoparticles in simple liquids, like water and glycerol are not described by conventional fluid mechanics, i.e., Navier Stokes equations. The intrinsic molecular relaxation processes in the surrounding liquid are found to have a profound effect on the fluid-structure interaction of mechanical devices at nanometre scales. Theoretical models have been developed based on the non-Newtonian viscoelastic fluid-structure interaction theory to investigate the vibration of nanoparticles immersed in simple fluids. The utility of this theoretical framework is demonstrated by comparison to measurements on single nanowires and ensembles of metal rods. This study provides a rigorous foundation for the use of metal nanoparticles as ultrasensitive mechanical sensors in fluid and opens a new paradigm for understanding extremely high frequency fluid mechanics, nanoscale sensing technologies, and biophysical processes.

Keywords: fluid-structure interaction, nanoparticle vibration, ultrafast laser spectroscopy, viscoelastic damping

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Authors: Nandini B. Nagaraju, Punya D. Gowda, S. Aishwarya, Benjamin Rohit

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This paper attempts to understand the structural behavior of non-prismatic channel beams subjected to bending through finite element (FE) analysis. The present study aims at shedding some light on how tapered channel beams behave by studying the effect of taper ratio on structural behavior. As a weight reduction is always desired in aerospace structures beams are tapered in order to obtain highest structural efficiency. FE analysis has been performed to study the effect of taper ratio on linear deflection, lateral torsional buckling, non-linear parameters, stresses and dynamic parameters. Taper ratio tends to affect the mechanics of tapered beams innocuously and adversely. Consequently, it becomes important to understand and document the mechanics of channel tapered beams. Channel beams generally have low torsional rigidity due to the off-shear loading. The effect of loading type and location of applied load have been studied for flange taper, web taper and symmetric taper for different conditions. Among these, as the taper ratio is increased, the torsional angular deflection increases but begins to decrease when the beam is web tapered and symmetrically tapered for a mid web loaded beam. But when loaded through the shear center, an increase in the torsional angular deflection can be observed with increase in taper ratio. It should be considered which parameter is tapered to obtain the highest efficiency.

Keywords: channel beams, tapered beams, lateral torsional bucking, shear centre

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Authors: Mark T. Hanson, Alan T. Varughese

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Osteoporosis is a disease affecting bone quality which in turn can increase the risk of low energy fractures. Treatment of osteoporosis using Bisphosphonates has the beneficial effect of increasing bone mass while at the same time has been linked to the formation of atypical femoral fractures. This has led to the increased study of micro-fractures in bones of patients using Bisphosphonate treatment. One of the mechanics related issues which have been identified in this regard is the loss in stiffness of bones containing one or many micro-fractures. Different theories have been put forth using fracture mechanics to determine the effect of crack presence on elastic properties such as modulus. However, validation of these results in a deterministic way has not been forthcoming. The present analysis seeks to provide this deterministic evaluation of fracture’s effect on the elastic modulus. In particular, the effect of crack size, crack orientation and crack number on elastic modulus is investigated. In particular, the Finite Element method is used to explicitly determine the elastic modulus reduction caused by the presence of cracks in a representative volume element. Single cracks of various lengths and orientations are examined as well as cases of multiple cracks. Cracks in tension as well as under shear stress are considered. Although the focus is predominantly two-dimensional, some three-dimensional results are also presented. The results obtained show the explicit reduction in modulus caused by the parameters of crack size, orientation and number noted above. The present results allow the interpretation of the various theories which currently exist in the literature.

Keywords: cracks, elastic, fracture, modulus

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Authors: Blair D. Macdonald

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After nearly one hundred years of its origin, foundational quantum mechanics remains one of the greatest unexplained mysteries in physicists today. Within this time, chaos theory and its geometry, the fractal, has developed. In this paper, the propagation behaviour with an iteration of a simple fractal, the Koch Snowflake, was described and analysed. From an arbitrary observation point within the fractal set, the fractal propagates forward by oscillation—the focus of this study and retrospectively behind by exponential growth from a point beginning. It propagates a potentially infinite exponential oscillating sinusoidal wave of discrete triangle bits sharing many characteristics of light and quantum entities. The model's wave speed is potentially constant, offering insights into the perception and a direction of time where, to an observer, when travelling at the frontier of propagation, time may slow to a stop. In isolation, the fractal is a superposition of component bits where position and scale present a problem of location. In reality, this problem is experienced within fractal landscapes or fields where 'position' is only 'known' by the addition of information or markers. The quantum' measurement problem', 'uncertainty principle,' 'entanglement,' and the classical-quantum interface are addressed; these are a problem of scale invariance associated with isolated fractality. Dual forward and retrospective perspectives of the fractal model offer the opportunity for unification between quantum mechanics and cosmological mathematics, observations, and conjectures. Quantum and cosmological problems may be different aspects of the one fractal geometry.

Keywords: measurement problem, observer, entanglement, unification

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Authors: Ibrahim M. Metwally

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Have you ever thought that earth was not the same earth we live on? Was it bigger or smaller? Was it a great continent surrounded by huge ocean as Alfred Wegener (1912) claimed? Earth is the most amazing planet in our Milky Way galaxy and may be in the universe. It is the only deformed planet that has a variable orbit around the sun and the only planet that has water on its surface. How did earth deformation take place? What does cause earth to deform? What are the results of earth deformation? How does its orbit around the sun change? First earth size computation can be achieved only considering the quantum of iron and nickel rested into earth core. This paper introduces a new theory “Earth expansion Theory”. The principles of “Earth Expansion Theory” are leading to new approaches and concepts to interpret whole earth dynamics and its geological and environmental changes. This theory is not an attempt to unify the two divergent dominant theories of continental drift, plate tectonic theory and earth expansion theory. The new theory is unique since it has a mathematical derivation, explains all the change to and around earth in terms of geological and environmental changes, and answers all unanswered questions in other theories. This paper presents the basic of the introduced theory and discusses the mechanism of earth expansion and how it took place, the forces that made the expansion. The mechanisms of earth size change from its spherical shape with radius about 3447.6 km to an elliptic shape of major radius about 6378.1 km and minor radius of about 6356.8 km and how it took place, are introduced and discussed. This article also introduces, in a more realistic explanation the formation of oceans and seas, the preparation of river formation. It also addresses the role of iron in earth size enlargement process within the continuum mechanics framework.

Keywords: earth size, earth expansion, continuum mechanics, continental and ocean formation

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Authors: Elsadig Naseraddeen Ahmed Mohamed

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In contrast to the uncertainty and complementary principle, it will be shown in the present paper that the probability of the simultaneous occupation event of any definite values of coordinates by any definite values of momentum and energy at any definite instance of time can be described by a binary definite function equivalent to the difference between their numbers of occupation and evacuation epochs up to that time and also equivalent to the number of exchanges between those occupation and evacuation epochs up to that times modulus two, these binary definite quantities can be defined at all point in the time’s real-line so it form a binary signal represent a complete mechanical description of physical reality, the time of these exchanges represent the boundary of occupation and evacuation epochs from which we can calculate these binary signals using the fact that the time of universe events actually extends in the positive and negative of time’s real-line in one direction of extension when these number of exchanges increase, so there exists noninvertible transformation matrix can be defined as the matrix multiplication of invertible rotation matrix and noninvertible scaling matrix change the direction and magnitude of exchange event vector respectively, these noninvertible transformation will be called actual transformation in contrast to information transformations by which we can navigate the universe’s events transformed by actual transformations backward and forward in time’s real-line, so these information transformations will be derived as an elements of a group can be associated to their corresponded actual transformations. The actual and information model of the universe will be derived by assuming the existence of time instance zero before and at which there is no coordinate occupied by any definite values of momentum and energy, and then after that time, the universe begin its expanding in spacetime, this assumption makes the need for the existence of Laplace’s demon who at one moment can measure the positions and momentums of all constituent particle of the universe and then use the law of classical mechanics to predict all future and past of universe’s events, superfluous, we only need for the establishment of our analog to digital converters to sense the binary signals that determine the boundaries of occupation and evacuation epochs of the definite values of coordinates relative to its origin by the definite values of momentum and energy as present events of the universe from them we can predict approximately in high precision it's past and future events.

Keywords: binary-signal mechanics, actual-information model of the universe, actual-transformation, information-transformation, uncertainty principle, Laplace's demon

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Authors: A. Rezaei, M. Huisman, W. Van Paepegem

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Atomic interactions in molecular systems are mainly studied by particle mechanics. Nevertheless, researches have also put on considerable effort to simulate them using continuum methods. In early 2000, simple equivalent finite element models have been developed to study the mechanical properties of carbon nanotubes and graphene in composite materials. Afterward, many researchers have employed similar structural simulation approaches to obtain mechanical properties of nanostructured materials, to simplify interface behavior of fiber-reinforced composites, and to simulate defects in carbon nanotubes or graphene sheets, etc. These structural approaches, however, are limited to small deformations due to complicated local rotational coordinates. This article proposes a method for the finite element simulation of molecular mechanics. For ease in addressing the approach, here it is called Structural Finite Element Molecular Modeling (SFEMM). SFEMM method improves the available structural approaches for large deformations, without using any rotational degrees of freedom. Moreover, the method simulates molecular conformation, which is a big advantage over the previous approaches. Technically, this method uses nonlinear multipoint constraints to simulate kinematics of the atomic multibody interactions. Only truss elements are employed, and the bond potentials are implemented through constitutive material models. Because the equilibrium bond- length, bond angles, and bond-torsion potential energies are intrinsic material parameters, the model is independent of initial strains or stresses. In this paper, the SFEMM method has been implemented in ABAQUS finite element software. The constraints and material behaviors are modeled through two Fortran subroutines. The method is verified for the bond-stretch, bond-angle and bond-torsion of carbon atoms. Furthermore, the capability of the method in the conformation simulation of molecular structures is demonstrated via a case study of a graphene sheet. Briefly, SFEMM builds up a framework that offers more flexible features over the conventional molecular finite element models, serving the structural relaxation modeling and large deformations without incorporating local rotational degrees of freedom. Potentially, the method is a big step towards comprehensive molecular modeling with finite element technique, and thereby concurrently coupling an atomistic domain to a solid continuum domain within a single finite element platform.

Keywords: finite element, large deformation, molecular mechanics, structural method

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Jovana Jankovic Pantic, Dragoslav Rakic, Tina Djuric, Irena Basaric Ikodinovic, Snezana Bogdanovic

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Regardless of the numerous activities undertaken to reduce municipal solid waste, its annual volumes continue to grow. In Serbia, the most common and the only one form of waste disposal is at municipal landfills with daily compaction and soil covering. Municipal waste compacting is one of the basic components of the disposal process. Well compacted waste takes up less volume and allows much safer storage. In order to better predict the behavior of municipal waste at landfills, it is necessary to define compaction parameters: the maximum dry unit weight and optimal moisture content. In current geotechnical practice, the most common method of determination compaction parameters is by the standard method (Proctor compaction test) used in soil mechanics, with an eventual reduction of compaction energy. Although this methodology is accepted in newer geotechnical scientific discipline "waste mechanics", different treatments of municipal waste at the landfill itself (including pretreatment), indicate the need to change this classical approach. The main reason for that is the simulation of the operation of compactors (hedgehogs) at the landfill. Therefore, during the research, various innovative solutions are introduced, such as changing the classic flat Proctor hammer, by adding spikes, whose function is, in addition to compaction, destruction and shredding of municipal waste. The paper presents the behavior of municipal waste for four synthetic waste samples with different waste compositions (Plandište landfill). The samples were tested in standard Proctor apparatus at the same compaction energy, but with two different hammers: standard flat hammer and hammer with spikes.

Keywords: compaction, hammer with spikes, landfill, municipal solid waste, proctor compaction test

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Authors: Christobel Gondwe, Yongtao Lu, Claudia Mazzà, Xinshan Li

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Skeletal muscle plays an important role in the human body system and function by generating voluntary forces and facilitating body motion. However, The mechanical properties and behaviour of skeletal muscle are still not comprehensively known yet. As such, various robust engineering techniques have been applied to better elucidate the mechanical behaviour of skeletal muscle. It is considered that muscle mechanics are highly governed by the architecture of the fibre orientations. Therefore, the aim of this study was to investigate the effect of different fibre orientations on the mechanical behaviour of skeletal muscle.In this study, a continuum mechanics approach–finite element (FE) analysis was applied to the left bicep femoris long head to determine the contractile mechanism of the muscle using Hill’s three-element model. The geometry of the muscle was segmented from the magnetic resonance images. The muscle was modelled as a quasi-incompressible hyperelastic (Mooney-Rivlin) material. Two types of fibre orientations were implemented: one with the idealised fibre arrangement, i.e. parallel single-direction fibres going from the muscle origin to insertion sites, and the other with curved fibre arrangement which is aligned with the muscle shape.The second fibre arrangement was implemented through the finite element method; non-uniform rational B-spline (FEM-NURBs) technique by means of user material (UMAT) subroutines. The stress-strain behaviour of the muscle was investigated under idealised exercise conditions, and will be further analysed under physiological conditions. The results of the two different FE models have been outputted and qualitatively compared.

Keywords: FEM-NURBS, finite element analysis, Mooney-Rivlin hyperelastic, muscle architecture

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Authors: Jeries J. Abou-Hanna

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Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.

Keywords: fracture mechanics, finite element method, stress intensity factor, stress gradient

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Authors: Zain Ul Hassan, Muhammad Zain Ul Abadin, Muhammad Zubair Khan

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Unmanned aerial vehicles (UAVs) have now become of predominant importance for various operations, and an immense amount of work is going on in this specific category. The structural stability and life of these UAVs is key factor that should be considered while deploying them to different intelligent operations as their failure leads to loss of sensitive real-time data and cost. This paper presents an applied research on the development of a structural health monitoring system for a UAV designed and fabricated by deploying modular approach. Firstly, a modular UAV has been designed which allows to dismantle and to reassemble the components of the UAV without effecting the whole assembly of UAV. This novel approach makes the vehicle very sustainable and decreases its maintenance cost to a significant value by making possible to replace only the part leading to failure. Then the SHM for the designed architecture of the UAV had been specified as a combination of wings integrated with strain gauges, on-board data logger, bridge circuitry and the ground station. For the research purpose sensors have only been attached to the wings being the most load bearing part and as per analysis was done on ANSYS. On the basis of analysis of the load time spectrum obtained by the data logger during flight, fatigue life of the respective component has been predicted using fracture mechanics techniques of Rain Flow Method and Miner’s Rule. Thus allowing us to monitor the health of a specified component time to time aiding to avoid any failure.

Keywords: fracture mechanics, rain flow method, structural health monitoring system, unmanned aerial vehicle

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Authors: Pedro Ferreira, Alexandre Frugoli, Pedro Frugoli, Lucio Leonardo, Thais Cavalheri

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The teaching of fluid mechanics in engineering courses is, in general, a source of great difficulties for learning. The possibility of the use of experiments with didactic wind tunnels can facilitate the education of future professionals. The objective of this proposal is the development of a low-cost aerodynamic balance to be used in a didactic wind tunnel. The set is comprised of an Arduino microcontroller, programmed by an open source software, linked to load cells built by students from another project. The didactic wind tunnel is 5,0m long and the test area is 90,0 cm x 90,0 cm x 150,0 cm. The Weq® electric motor, model W-22 of 9,2 HP, moves a fan with nine blades, each blade 32,0 cm long. The Weq® frequency inverter, model WEGCFW 08 (Vector Inverter) is responsible for wind speed control and also for the motor inversion of the rotational direction. A flat-convex profile prototype of airfoil was tested by measuring the drag and lift forces for certain attack angles; the air flux conditions remained constant, monitored by a Pitot tube connected to a EXTECH® Instruments digital pressure differential manometer Model HD755. The results indicate a good agreement with the theory. The choice of all of the components of this proposal resulted in a low-cost product providing a high level of specific knowledge of mechanics of fluids, which may be a good alternative to teaching in countries with scarce educational resources. The system also allows the expansion to measure other parameters like fluid velocity, temperature, pressure as well as the possibility of automation of other functions.

Keywords: aerodynamic balance, wind tunnel, strain gauge, load cell, Arduino, low-cost education

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Authors: David C. Ni

Abstract:

Contemporary models for N-body systems are based on temporal, two-body, and mass point representation of Newtonian mechanics. Other mainstream models include 2D and 3D Ising models based on local neighborhood the lattice structures. In Quantum mechanics, the theories of collective modes are for superconductivity and for the long-range quantum entanglement. However, these models are still mainly for the specific phenomena with a set of designated parameters. We are therefore motivated to develop a new construction directly from the complex-variable N-body systems based on the extended Blaschke functions (EBF), which represent a non-temporal and nonlinear extension of Lorentz transformation on the complex plane – the normalized momentum spaces. A point on the complex plane represents a normalized state of particle momentums observed from a reference frame in the theory of special relativity. There are only two key parameters, normalized momentum and nonlinearity for modelling. An algorithm similar to Jenkins-Traub method is adopted for solving EBF iteratively. Through iteration, the solution sets show a form of σ + i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various distributions, such as 1-peak, 2-peak, and 3-peak etc. distributions and some of them are analog to the canonical distributions. The results of the numerical analysis demonstrate continuum-to-discreteness transitions, evolutional invariance of distributions, phase transitions with conjugate symmetry, etc., which manifest the construction as a potential candidate for the unification of statistics. We hereby classify the observed distributions on the finite convergent domains. Continuous and discrete distributions both exist and are predictable for given partitions in different regions of parameter-pair. We further compare these distributions with canonical distributions and address the impacts on the existing applications.

Keywords: blaschke, lorentz transformation, complex variables, continuous, discrete, canonical, classification

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