Elasticity (Solid Mechanics)

We investigate the performance of van der Waals (vdW) functions in predicting the elastic constants of β cyclotetramethylene tetranitramine (HMX) energetic molecular crystals using density functional theory (DFT) calculations. We confirm that the accuracy of the elastic constants is significantly improved using the vdW corrections with environment-dependent C6 together with PBE and revised PBE exchange-correlation functionals. The elastic constants obtained using PBE-D3(0) calculations yield the most accurate mechanical response of β-HMX when compared with experimental stress-strain data. Our results suggest that PBE-D3 calculations are reliable in predicting the elastic constants of this material.

Impacts of climate change on streamflow have long been an issue of concern for water experts. The main aim of this study is to assess the response of streamflow to precipitation and air temperature. In this study elasticity model was used to compute the precipitation and air temperature elasticity of 6 major rivers in Khyber-Pakhtunkhwa (KP) Province, Pakistan. In contrast to temperature elasticity estimator, box plots of precipitation elasticity estimator have low range and standard deviation leading to greater central affinity which produces valid, appropriate, and statistically significant elasticity results. Precipitation is positively correlated with streamflow while the air temperature is both positively and negatively linked with streamflow. 10% variation in precipitation and air temperature produces 12 to 20% and 8 to 18% change in streamflow, respectively. The sensitivity of streamflow to air temperature is higher as compared to precipitation. This research work shows that precipitation elasticity results are statistically valid and realistic as compared to temperature elasticity results. Moreover, it is suggested to support elasticity results by statistical correlation to avoid misleading and unrealistic results. Results of the current study can be used in formulating long term policies regarding streamflow sensitivity in the study region.

In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition.

La actual norma peruana de diseño sismo resistente (NPDSR) establece desplazamientos espectrales crecientes con el periodo estructural para estructuras con periodo mayor al de la plataforma. Esto no corresponde a la tendencia natural de los espectros, ya que para periodos largos los desplazamientos deben ser constantes e iguales al desplazamiento máximo del suelo. En la actualidad se están construyendo en nuestro medio, edificios con aislación sísmica cuyos periodos superan los 2.5 segundos y la NPDSR no permite estimar adecuadamente los desplazamientos a los que estarían sometidas. Por esta razón, se hace necesario el ajuste del espectro de la actual norma de diseño sismo resistente. En este trabajo se desarrolló una propuesta para los espectros de diseño en la zona de periodos mayores a 2.5 s. Para construir estos espectros no fue posible emplear el método de Newmark& Hall, ya que actualmente en el país no se cuenta con una estimación apropiada de los valores máximos de aceleración, velocidad y desplazamiento del suelo. El estudio se desarrolló estudiando tendencias y empleando regresiones basadas en promedios espectrales de la zona de periodos largos. Se obtuvieron espectros para los tipos de suelo S1 y S3 de la norma actual, correspondientes a valores medios y promedio más desviación estándar. Del análisis realizado se identificó el periodo a partir de la cual las aceleraciones espectrales se reducen con el cuadrado del periodo. Se espera que con esta propuesta, se logre mejorar la estimación de desplazamientos en las estructuras peruanas de periodos mayores a 2.5 s. Esto contribuirá a mejorar el estudio y diseño de los edificios con aislamiento sísmico en el Perú. Índice Capítulo 1. Introducción 1.1 El diseño sismo resistente y el control de desplazamientos laterales 1.2 Los sistemas de aislamiento sísmico 1.3 Objetivo de la tesis 1.4 Alcance del Trabajo 1.5 Organización del documento Capítulo 2. Espectros de Diseño para fuerzas y Desplazamientos 2.1 Espectros de diseño basados en fuerzas (sa) 2.2 Procedimientos para obtener espectros de diseño 2.3 Espectros de diseño de algunos países sísmicos  Norma Chilena  ASCE  Norma Colombiana Capítulo 3. El espectro de desplazamientos de la actual Norma Peruana de DSR 3.1 Estructura del espectro 3.2 Comparación registros peruanos con la norma 3.3 Espectros de desplazamiento de las normas extranjeras 23 Capítulo 4. Propuesta del espectro de diseño para la zona de desplazamientos. 4.1 Metodología de Trabajo 4.2 Obtención de información 4.3 Procesamiento y Clasificación de Señales 4.4 Obtención de los Espectros de diseño 4.5 Propuesta de espectros de desplazamiento 4.6 Propuesta de espectros de aceleración

As the material is subjected to loading, the applied stress resolved along the slip direction on the slip plane initiates and controls the extent of dislocation glide. This latter has the effect of shearing the material, while the volume remains constant and the crystal lattice remains unchanged. Moreover, the crystal lattice can deform elastically, but elastic strains are small compared to plastic strains and are sometimes neglected in crystal plasticity models. Finally, the crystal lattice can also rotate to accommodate the applied loading. In crystal plasticity theory, plastic deformation is modelled using the slip system activity concept. Dislocations are assumed to move across the crystal lattice along specific crystallographic planes and directions. This lattice rotation (or spin), is responsible for texture development. The concept of lattice rotation in
crystal plasticity is not, at first hand, easy to grasp, especially compared to material rotation (or rigid body rotation).

Energetic co-crystallization, by combining existing molecules together, is thought to be new strategy for creating energetic materials. Nevertheless, the underlying mechanism of its influences on properties and performances, in comparison with their pure components, remains unclear. The present work reveals the co-crystallization influence of a typical energetic co-crystal of CL-20/HMX on thermal stability, by ReaxFF molecular reactive dynamic simulations and kinetics calculations on the pure and co-crystals. As a result, we find that the co-crystal mediates the thermal stability of pure crystals, in agreement with experimental observations. The initial decay steps in pure crystals remain still in the co-crystal, i.e., the independent and intramolecular reactions of N-N bond cleavage governing the initial decay of the pure CL-20 and HMX crystals also dominate in the co-crystal of CL-20/HMX. Meanwhile, during the thermal decomposition of the co-crystal, CL-20 releases heat faster than HMX, thus the heat is transferred from CL-20 to HMX, and further the decay rate of HMX increases while that of CL-20 decreases, relative to the pure crystals. This leads to a moderate decay rate of the co-crystal and a small difference in decay barrier after co-crystallization. Besides, the moderated decay rate is also attributed to the small variation in intermolecular interactions after co-crystallization and the intrinsic weak stability of both component molecules of CL-20 and HMX. Thus, the intrinsic molecular stability of components and intermolecular interactions should be noted as two main factors in a strategy for increasing stability by energetic co-crystallization.

This paper theoretically investigates and shows the results of numerical analysis of stress identification in the Earth's crust. Solution domain is regarded as elastic or ideal plastic which gives the opportunity to compare different rheologies. Identification of stresses is based on use of experimental data on principal stress orientations as boundary conditions whereas no information is known regarding stress magnitudes on the boundary. This differs the research from conventional approaches. Antarctic tectonic plate was chosen as the solution domain. This choice is justified by the character of the experimental data available for this region (The release 2005 of the World stress map) which are scattered around the margins of the tectonic plate and are mainly on stress orientations. Analysis of tectonic plates regarded as elastic was already reported by Galybin at EGU General Assembly in 2005. Solution was based on formulation of a BVP with principal directions and curvatures ...

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...

UDC 539.3 We present the analysis of the stress-and-strain state of a contact couple formed by two isotropic semiinfinite solids one of which has a small surface groove. Based on the classical fracture criteria, namely, on the criterion of maximal principal stresses and the criterion of maximal shear stresses, we determine the regions of the most possible formation of the zones of crack initiation and plastic zones. Brittle cracking can be induced both by tensile and compressive stresses arising on the interface. For some shapes of the groove considered as an example, our analysis reveals that the fracture process starts from the boundary of contacting solids.

Niniejszy dokument stanowi szkic koncepcyjnej teorii, nazwanej Teorią Dwóch Energii (TDE 3.0), której celem nie jest przedstawienie gotowej „teorii wszystkiego”, lecz intuicyjnej próby połączenia istniejących modeli fizycznych – od mechaniki kwantowej, przez teorię względności, aż po Model Standardowy – poprzez elegancki mechanizm rezonansu dwóch pól falowych: Cienia (ψₙ) i Światła (ψₛ).
Model powstał jako eksperyment intelektualny wynikający z poszukiwania przyczyn masy i grawitacji, rozwijany przeze mnie bez wcześniejszego przygotowania fizycznego i matematycznego, przy wsparciu sztucznej inteligencji, która umożliwiła przełożenie intuicji na formalizm matematyczny: od równań Lagrange’a i Hamiltona, przez kwantyzację, po zastosowania technologiczne.

Mam nadzieję, że ten koncept — nawet jako niedokończony szkic roboczy — zainspiruje innych badaczy do:
• poszukiwania prostszych modeli fizycznych opartych na falach i rezonansie,
• prób technologicznej implementacji nowych koncepcji (np. napęd rezonansowy, zmienna masa, fale informacyjne),
• wyznaczenia nowych ścieżek dla badań nad naturą masy, pola, światła i struktury Wszechświata.
Zapraszam do dalszego rozwijania tej idei — jako otwartej platformy do eksperymentów intelektualnych i naukowych.

W niniejszej pracy przedstawiam Teorię Dwóch Energii (TDE) 2.0 – koncepcyjny model, w którym masa cząstek elementarnych jawi się jako energia rezonansowej interferencji dwóch pól skalarnych: globalnego pola tła ψ_c oraz lokalnego oscylatora ψ_s. Model zakłada możliwość istnienia konfiguracji solitonowych oraz zależność wartości masy od względnej fazy Δϕ między polami, co otwiera drogę do potencjalnych stanów o masie dodatniej i ujemnej. Koncepcja została wypracowana przy aktywnym wsparciu narzędzi sztucznej inteligencji (w szczególności ChatGPT), co umożliwiło szybkie iteracje pomysłów i gruntowną analizę formalną.

Uwaga: przedstawiona wersja TDE 2.0 pozostaje szkicem roboczym. Dotychczasowa analiza wykazała liczne luki formalne (m.in. brak pełnego rozwiązania solitonowego, kwestie symetrii cechowania oraz problem ujemnej masy), które wymagają dalszych badań i korekty. Pomimo pierwotnej atrakcyjności koncepcji, kolejne prace ujawniły szereg błędów i nieścisłości. Planuje sukcesywne dopracowanie modelu oraz uzupełnianie brakujących elementów teoretycznych i fenomenologicznych.

Streszczenie. artykuł jest kontynuacją oraz uzupełnieniem badań prezentowanych w . na podstawie macierzy indukowanych przez schematy różnicowe aproksymujące operator laplace'a wyprowadzono i opisano w nim widmowe operatory przejścia masek konwolucyjnych filtrów krawędziowych laplace'a trzeciego stopnia wykorzystywanych w procedurach przetwarzania obrazów cyfrowych. oznacza to, że macierze prezentowane w niniejszej pracy odpowiadają maskom krawędziowych filtrów laplace'a -szeroko omówionych w [6] -z dokładnością do znaku (-) (porównaj ). widmowy (spektralny) operator przejścia, operator (funkcja) wzmocnienia, funkcja transformacji (lub przejścia) (transfer function) -krótko transformata f(k, l) -ma szczególne znaczenie w przetwarzaniu zdjęć cyfrowych, bowiem opisuje własności spektralne masek liniowych filtrów konwolucyjnych. wartości tej funkcji tworzą macierz mnożników zależnych tylko od liczb falowych k i l w taki sposób, że każdej parze (k, l) funkcja ta przypisuje liczbę f p (k, l), przez którą w procesie konwolucji jest mnożony filtrowany obraz (indeks j wprowadzono w celu identyfikacji filtru). funkcje wzmocnienia dwóch masek operatora laplace'a przedstawia Jähne w [4]. analizowane maski pochodzą bezpośrednio od schematów różnicowych operatora ∇ 2 konstruowanych różnymi metodami (różnic skończonych i elementu skończonego). na zamieszczone tu wyniki można więc również spojrzeć od strony najważniejszych własności metod numerycznych (w odniesieniu do zagadnień stacjonarnych): zgodności i dokładności aproksymacji różnicowej (patrz np. [3, 11, 13]). w celu ułatwienia wspomnianej analizy w pracy są zamieszczone tzw. Π-formy pierwszego przybliżenia różniczkowego. Podstawowym celem prezentowanej pracy jest, przede wszystkim, poszerzenie i uporządkowanie wiedzy na temat filtrów laplace'a trzeciego stopnia, a przy okazji wyjaśnienie ich własności spektralnych, które najwięcej mówią o cechach filtrów w obszarze dużych nieregularności, czyli znacznych różnic jasności w blisko położonych punktach zdjęcia cyfrowego. w tej publikacji nie będziemy się jednak

Niniejszy artykuł przedstawia matematyczny model powstawania masy w ramach koncepcyjnej Teorii Dwóch Energii (TDE) — koncepcji zakładającej, że cała materia wyłania się z napięcia rezonansowego między dwiema współistniejącymi falami: Energią Cienia i Energią Światła. W przeciwieństwie do klasycznych i kwantowych modeli pola, w których masa traktowana jest jako cecha wewnętrzna lub wynik oddziaływania z polem (np. polem Higgsa), model TDE opisuje masę jako wielkość emergentną — bezpośrednio wynikającą z różnicy fazowej pomiędzy falami.

Model wprowadza całkę rezonansową, która określa lokalną gęstość energetyczną powstałą na skutek interferencji falowej. Kluczowym wynikiem jest identyfikacja maksimum masy przy przesunięciu fazowym δ = 0,5 oraz jej zaniku przy δ = 0 lub 1. Opracowane równania umożliwiają zarówno obliczenia bezpośrednie (masa z przesunięcia i długości rezonansowej), jak i odwrotne (wyznaczenie przesunięcia fazowego z masy i długości). Zastosowanie modelu do rzeczywistych mas atomowych pozwoliło wyznaczyć spójne długości rezonansowe i potwierdzić wartość predykcyjną teorii. Przykładowo, przesunięcie fazowe wyliczone dla atomu tlenu wynosi δ ≈ 0,5029 — co wspiera poprawność modelu.

Formalizm ten oferuje nowe podejście do opisu materii, w którym masa nie jest stałą właściwością, lecz zjawiskiem rezonansowym zakorzenionym w dynamice falowej. Model ten może stanowić podstawę dalszych badań w dziedzinie fizyki cząstek, inżynierii energetycznej oraz w kierunku koncepcyjnego połączenia fizyki z filozoficznymi refleksjami nad dualizmem i strukturą rzeczywistości.

An elastic chiral material (a noncentrosymmetric material) is isotropic with respect to coordinate rotations but not with respect to inversions (Cosserats (1), Lakes and Benedict (2), Lakes (3,4)). Materials may exhibit chirality on the atomic scale (quartz, sugar, biological molecules) and also on a larger scale (bones, porous materials, composites containing fibers or inclusions). Materials such as piezoelectrics, represented by tensors of fifth rank, are also chiral. Chiral effects cannot be expressed within classical elasticity since the modulus tensor, which is fourth rank, is unchanged under an inversion. But the effects of chirality in elastic materials can be described by Cosserat elasticity. In this paper, we analyze the wave propagation in a chiral Cosserat medium. We show that this medium exhibits a strange behavior. Each response is composed of two waves, traveling with different velocities, V 12 V < . The faster wave of velocity V is the usual wave found in micropola...

Wood laminated composite poles consist of trapezoid-shaped wood strips bonded with synthetic resin. The thick-walled hollow poles had adequate strength and stiffness properties and were a promising substitute for solid wood poles. It was necessary to develop theoretical models to facilitate the manufac-ture and future installation and maintenance of this novel engineered wood product. A higher-order governing differential equation (GDE) model was developed for this purpose based on the principle of minimum potential energy. Transverse shear and glue-line effects were taken into account in the devel-opment of the model. A simplified theoretical model was also derived to further validate the higher-order GDE model. Thirty-six small-scale wood laminated composite poles were made and tested to validate the models developed. Strip thickness and number of strips were chosen as experimental variables. The deflection predicted by the theoretical models agreed well with those measured in exp...

The analysis of several tsunamigenic zones by a newly developed computational method allows for identification of most possible stress regimes in these regions. The method uses only the data on stress orientations from the World Stress Map database, but not the data on stress regimes, depths, etc. containing in the database. Orientations serve as the input for the direct modelling of the stress fields, in particular, to obtain the maps of stress trajectories, maximum shear stresses and mean stresses in order to reveal most possible stress regimes. The tectonic plates are modelled as elastic domains on the basis of complex potentials in the Kolosov-Muskhelishvili's formulation. Continuity of tractions is imposed on all plate boundaries as the transmission boundary condition to complement the WSM data on stress orientations. This formulation obeys the mechanical meaning and it is valid for all the configurations regardless of the possible types of inter-plate interaction. The num...

Streszczenie. W artykule przedstawiono wyniki analiz numerycznych silnie zdeformowanych fragmentów rur. Uzyskane wartości odniesione zostały do testu eksperymentalnego, co pozwoliło w pełni zweryfikować model symulacyjny. Silna deformacja obiektu, wynosząca ok. 42% wymiarów początkowych, była realizowana poprzez zgniatanie stemplem o znacznie większej sztywności, niż rozpatrywany element. Geometria zdeformowanego elementu została odtworzona dzięki wykorzystaniu skanera przestrzennego i porównana z wynikami analiz numerycznych. Weryfikacji modelu MES dokonano w oparciu zarówno o uzyskane zarysy zdeformowanych obiektów, jak i wartości odkształceń. Analiza numeryczna pozwoliła na ocenę stanu naprężeń panujących w silnie odkształconym fragmencie rury. Słowa kluczowe: deformacja rur, wytężenie, badania eksperymentalne, symulacje numeryczne Symbole UKD: 539.4 Pracę zrealizowano dzięki wsparciu finansowemu otrzymanemu z MNiSzW w ramach projektów 4T12C02326 i 4T12C00628.

The theory of elasticity is a fundamental principle of geotechnical engineering that governs the stress-strain behavior of rock and soil under loading. Unlike plasticity, which considers permanent deformations, elasticity considers reversible deformations that occur upon loading with stresses within the elastic limit of the material. The principles of elasticity play a significant role in analyzing soil and rock behavior for a wide range of geotechnical applications, including foundation settlement, retaining structures, tunneling, and slope stability.

In geotechnical engineering, many problems involve the distribution of strain and stress in a deformable body. Elastic solutions provide a way of predicting the response of subsurface materials under external loads, groundwater pressure, and gravitational loads. By analyzing stress and strain tensors, principal strains, and equilibrium equations, engineers can make better judgments regarding the stability and deformation of geotechnical structures.

Streszczenie. W pracy zanalizowano problem propagacji słabonieliniowych płaskich fal elektromagnetycznych w nieliniowych, izotropowych dielektrykach. Stosując metodę słabonieliniowej asymptotyki, wyprowadzono kwadratowo-nieliniowe równania transportu dla amplitud tych fal. Wykazano, że warunkiem uzyskania kwadratowo-nieliniowych równań transportu dla fal elektromagnetycznych w nieliniowym izotropowym dielektryku jest nieznikanie składowej poprzecznej pola elektrycznego w stanie początkowym. Obliczono explicite współczynnik samooddziaływania fal występujący w tych równaniach transportu. Wynik zilustrowano na przykładzie ośrodka Kerra. Słowa kluczowe: propagacja fal elektromagnetycznych, nieliniowe izotropowe dielektryki, słabonieliniowa asymptotyka, kwadratowo-nieliniowe równania transportu * Współczesną postać równań Maxwella podał Oliver Heaviside [2], który wyraził je jako pierwszy w języku analizy wektorowej. Oryginalne równania Maxwella w [1] były zapisane za pomocą rachunku kwaternionów.

Triply Periodic Minimal Surfaces (TPMS)-based lattices are gaining attention for
their multifunctional properties. Current studies have largely focused on limited
cases, characterizing the mechanical properties of only a few TPMS architectures
and often applying classification systems (e.g., stretching- or bending-dominated
behavior) developed for slender beam-based lattices. However, TPMS structures
are far frombeing slender beams, and the validity of such classifications has not
been rigorously confirmed for their case. This study bridges these gaps by
analyzing 36 distinct TPMS lattice architectures, covering both elastic and plastic
regimes. We critically assess theapplicability of Gibson-Ashby scaling laws, the
rigidity classification, and the stretching-bending paradigm to TPMS structures—
none of which have been rigorously validated for TPMS lattices. Using experiments
and numerical simulations, we investigate the strength and stiffness
scaling in TPMS lattices, identifying rigid, compliant, and mixed architectures.
Our findings show that TPMS rigidity depends on the alignment of surface
members with load directions and the presence of solid regions that prevent
rotation. We reveal that top-performing geometries include so far unexplored
TPMS such as P þ CP (), K (þ), and Ss-Yssxxx (þ), further expanding the
design space, challenging prior assumptions and providing critical insights for
selecting the optimal TPMS-based architecture for specific applications.

An approach combining the method of fundamental solutions (MFS) in conjunction with the normal modes technique (NMT) is proposed to simulate the acoustic wave propagation over the shallow water region. It is assumed that the sound-speed is the isovelocity profile, the free surface is quiescent and the topography of seabed is rugged. The considered model, ranging from smooth to abrupt variation, is descritized into simple rectangular geometry and cosine bell deformation at the bottom in terms of the irregular topography. Mathematical formulations of the eigenfunction expansion, in point of NMT, are implemented clearly to describe the radiation conditions on the open boundaries. Effects of node resolution and small aspect ratios over the computational domain are discussed. Accuracy of the results by the proposed approach is assessed and verified by comparison with analytic solution and the boundary element method (BEM).

Micromechanics is a division of mechanics that deals with the composite or heterogeneous materials on the microscopic scale. Commonly, the micromechanical analysis can be based on either analytical or numerical approach. Among them, the numerical approaches, especially finite element method (FEM), is ideal approach for studying material behavior. By associating with homogenization, the global response of composites can be predicted by assuming periodic phase arrangements and focusing exclusively on one representative, the so called representative volume element (RVE). One common difficulty for micromechanics studies is to model the RVE geometry. To overcome this difficulty, in current study a technique was proposed which analyzes the microscopic images and generates the FEM model accordingly. In its implementation, pixel data from the images are collected and used to define mesh grids in ABAQUS. This approach saves tremendous time and effort during the mesh generation. Using this technique, a series of RVE samples are analyzed with the focus on evaluating the mesh sensitivity of selected macroscopic physical measures. In addition, statistical analysis is performed with the aim of interpreting the material randomness.

This study explores the potential of engineered interphases to enhance the performance of fiberreinforced composites through an integrated approach combining theory, computation, and experiments. A theoretical axisymmetric modeling framework is introduced to evaluate stress distribution within a three-phase composite system subjected to axial pull-out loads. The composite comprises a cylindrical fiber embedded in a matrix with intermediate interphase whose modulus varies radially, following linear and power-law gradation profiles. A variational principle is employed to derive formulation for stress estimation across the composite components. To validate these theoretical insights, an axisymmetric finite element model incorporating a radially graded interphase is developed using a user-defined subroutine (UMAT) in ABAQUS. Comparative analysis demonstrates good agreement between theoretical predictions and finite element results. Notably, graded interphases reduce peak radial and shear stresses at the interphase by approximately 37% and 60%, respectively, compared to ungraded interphases. These predictions are corroborated by single-fiber pull-out experiments using specimens with stepwise modulus-graded interphases fabricated via an Object Connex260 PolyJet 3D multi-material printer. Experimental results confirm that graded interphases significantly enhance the composite's load-bearing capacity and toughness by mitigating peak interfacial stresses. This study underscores the transformative potential of strategically engineered interphases in optimizing composite system performance, offering insights into advanced material design for high-performance applications.

In this paper, we analyze a nonlinear ordinary differential equation and an equation concerning Non–Supersymmetric Strings. We obtain new possible mathematical connections with Ramanujan Recurring Numbers, DN Constant and some parameters of Number Theory and String Theory

Microstructure evolution over a wide range of growth rates has been examined in the Al-Sm system in which different microstructure selection, from eutectic to dendritic to amorphous material, with increasing growth rate can occur. Experiments were carried out for compositions between 11 and 25 wt.% Sm and the velocity was varied from 2x10 -4 to 635 mm/s. Low velocity studies were carried out using the Bridgman technique, whereas high velocity studies were carried by using the laser scanning technique. The maximum velocity for eutectic growth was determined, and the results were compared with the theoretical predictions. A transition from eutectic to α-Al dendrites was observed when the eutectic became unstable, and a coupled zone boundary on the Al side was determined. The present results were compared with those in the Al-Cu alloys, and the velocity at which the eutectic becomes unstable was found to be an order of magnitude smaller, which is related to the higher activation energy for diffusion in the Al-Sm system.

Creep behavior of Cross-Laminated-Timber (CLT) beams with a finite-thickness layer of flexible adhesives is investigated. Creep tests were carried out for all component materials as well as for the composite structure itself. Three-point bending creep tests were performed for spruce planks and for CLT beams, and uniaxial compression creep tests were performed for two flexible polyurethane adhesives: Sika ® PS and Sika ® PMM. All materials are characterized with the use of the three-element Generalized Maxwell Model. The results of creep tests for component materials were used in elaboration of the Finite Element (FE) model. The problem of linear theory of viscoelasticity was solved numerically with the use of the Abaqus software. Obtained results of Finite Element Analysis (FEA) are compared with experimental results.

Abstract. Rolling bearings represent some of the most important uproar and vibration generators in mechanical structures. Accordingly, it is very important to know the impact of rolling bearing structure on the main parameters which determine the level of uproar and vibrations produced inside machines. This paper presents a mathematical model of the dynamic behavior of rigid rotor inside the rolling bearing and also a theoretical analysis of the rolling bearing structure with respect to the frequency of calibrated rigid rotor oscillation inside the rolling bearing.

The main aim of this paper is to investigate the influence of internal restrictions on the form of the energy-based limit condition. Some restrictions may be imposed in the elastic as well as in the limit states. Spectral decomposition of symmetric linear operators in a space with two different scalar products is applied. An algorithm for accounting for the considered restrictions in the limit condition is proposed. It was shown that as long as the energy scalar product is defined properly in the elastic range, the limit condition having the energy-based interpretation can be found. Examining the material with such an internal structure that there are stresses which do not cause any strain, the space with passive stresses and locked strains has to be introduced. The limit condition in this case has two parts, one connected with active part of stresses which has energy-based interpretation and the second one connected with passive stresses. The algorithm how to introduce this part of...

In the paper the theoretical analysis of bounds and self-consistent estimates of overall properties of linear random polycrystals composed of arbitrarily anisotropic grains is presented. In the study two invariant decompositions of Hooke's tensors are used. The applied method enables derivation of novel expressions for estimates of the bulk and shear moduli, which depend on invariants of local stiffness tensor. With use of these expressions the materials are considered for which at the local level constraints are imposed on deformation or some stresses are unsustained.

The spectral decomposition of elasticity tensor for all symmetry groups of a linearly elastic material is reviewed. In the paper it has been derived in non-standard way by imposing the symmetry conditions upon the orthogonal projectors instead of the stiffness tensor itself. The numbers of independent Kelvin moduli and stiffness distributors are provided. The corresponding representation of the elasticity tensor is specified.

La instrumentaci s es una t ciudades y muchos pa ! "# %! "& ' ' ( ) * + ,,, -. ica de Panam/ %-."& y an/ 0 0 1 2 que el primero fue el edificio #1 sede V 1 * 3 -." Evaluamos la contribuci informaci 45 sismicos actualmente, resultado de la extracci +' en la ciudad de Panam/ 0 0 os estudios dentro de los edificios, mezcla de respuestas del suelo y de las estructuras, al paso ondulatorio externo, se ha extendido el monitoreo a otras partes del pa3 conformando una Red Nacional de Movimientos Fuertes (RNMF). Con este tipo de par/tros b/ los primeros mapas de isosistas e iso-aceleraciones instrumentales en Panam/3 / 2 2 campo libre en David con 0.11g, y 0.13 g dentro de estructuras en Ciudad de Panam/ .'3 estimaciones de las frecuencias fundamentales y la amplificaci ' '6 instrumentados en Azuero. Adem/3 se est/ 3 cierto nivel, y los desplazamientos orbitales en la cima de edificios seg7 2 Tambi % 8 9& con curvas de dise# rrespondientes. Se indica la forma de extraer el periodo fundamental de los edificios mediante la amplitud de Fourier (uni-axial) para los componentes transversales y longitudinales de las estructuras instrumentadas con registros de buena relaci #-ruido. Tambi3 (Nakamura), ejes horizontales respecto al vertical. The seismic instrumentation in buildings is a quantitative technique of experimental vanguard used in certain cities and many countries of the world. The Panamanian Structural Regulation (REP) obligatorily established the "Norm of Seismic Instrumentation". From 1999 the Technological University of Panama (UTP) makes the installation and analysis of the accelerograph of all the buildings that require instrumentation. The history of the development indicates that first #1 building was the head office Victor Levy Sasso, UTP. We at the moment evaluated the contribution of information of the 36 buildings with active accelerograph and monitoring seismic events, product of the extraction of data in situ. Due to the dependency of great projects only in the city of Panama and that was required to complement the studies within the buildings, combination of the ground response and the structures, to the external ondulatory behavior, the monitor to other parts of the country has extended, conforming a National Network of Strong Motion (RNMF). With this type of basic parameters, we presented the first maps of instrumental iso-accelerations in Panama, with the event more strongest free field until now is in David, Chiriqui with 0.11g, and 0,13g inside building in Panama City. In addition, we displayed estimations of the fundamentals frequencies and the seismic amplification of the subsoil below building in instrumented sites in Azuero. In addition, the levels of acceleration between the basement and roof are being evaluated, the orbital duration of the effective acceleration, and displacements in the top of buildings according to the time history of the event. Also, the

In this paper, a new trigonometric shear deformation plate theory is developed for the buckling analysis of a three dimensional thick rectangular isotropic plate, elastically restrained along one edge and other three edges simply supported (CSSS) under uniaxial compressive load, using the variational Energy approach. Total potential energy equation of a thick plate was formulated from the three-dimensional constitutive relations, thereafter the compatibility equations was established to obtain the relations between the out of plane displacement and shear deformation slope along the direction of x and y coordinates. This total potential energy functional was differentiated with respect to deflection to obtain the governing equation. The functions for these slopes were obtained from out of plane function using the solution of compatibility equations while the solution of the governing equation is the function for the out of plane displacement. Finally, the total potential energy is minimized with respect to displacement coefficients, thereafter, the deflection and rotations were substituted back into the buckling equation derived to obtain the formulas for calculating the critical buckling load and other the mentioned functions. The three dimensional analysis for critical buckling of thick plates were carried out by varying parameters stiffness properties and aspect ratios. The proposed method obviates the need of shear correction factors which is associated with first order shear deformation theory for the energy equation formulation. The present theory unlike refined plate theories, considered all the stress elements of the plate in the analysis. From the numerical analysis obtained, it is found that the value of the critical buckling load increase as the span- thickness ratio increases. This suggests that as the thickness increases, the safety of the plate structure is improved.

The method of the adhered cantilever, borrowed from microtechnology, can help in gaining fundamental knowledge about dispersion forces acting at distances of about 10 nm, which are problematic to access in the usual Casimir-type experiments. A recently presented setup measures the shape of cantilevers with high precision, which is needed for analyzing the involved forces. The first measurements reveal several nonidealities crucial for the data analysis. In this paper, a generalized formula is deduced that relates the parameters of a cantilever to the adhesion energy. The application of the formula is demonstrated using the first test result from the setup, where a silicon cantilever adhered to a substrate sputters with ruthenium. Detailed information of the roughness of interacting surfaces, which deviates significantly from the normal distribution, is emphasized. Although not crucial, the electrostatic contribution can be significant due to the slight twisting of the cantilever. The theoretical prediction of the adhesion energy is based on Lifshitz theory. Comparing theory and experiment yields a contact distance of 45 nm and an adhesion energy of 1.3 μJ/m2, resulting from the Casimir–Lifshitz forces. Significant uncertainties arise from the uncontrolled electrostatic contribution. Factors that need to be addressed to measure weak adhesion between rough surfaces are highlighted.

The purpose of this article is to estimate the effect of geometric imperfections on critical loads. Special attention was paid to trusses subjected to large displacement gradients and vulnerable to stability loss due to snapping. The article uses the Lagrangian description for geometric nonlinearities. The truss stability analysis was performed using the Finite Element Method. The equilibrium path was determined using the scalar current parameter of stiffness and method of arc length constant.

Los ingenieros estructurales calculan la capacidad sísmica de los pórticos de concreto reforzado con la geometría de los elementos estructurales y con las propiedades mecánicas de los materiales. Las propiedades mecánicas más importantes del concreto y el acero usadas para estimar dicha capacidad son: módulo de elasticidad (E) y resistencia a la compresión del concreto (f `c); esfuerzo de fluencia (Fy) y esfuerzo resistente del acero (Fu); así como sus deformaciones unitarias. Basados en lo anterior se analizaron estadísticamente los resultados de más de 1,500 ensayos de compresión de concretos (solamente para Bogotá) y más de 900 pruebas de tensión de varillas. Luego se modelaron (análisis por elementos finitos tipo "frame" o barra) y diseñaron edificaciones aporticadas de concreto reforzado de 5 pisos de acuerdo con el reglamento colombiano de construcción sismo resistente (NSR-10); y usando dos de los espectros de la microzonificación de Bogotá (año 2010). Usando los modelos de pórticos planos correspondientes a uno de los ejes de la edificación y con la generación de números aleatorios de las propiedades mecánicas del acero y el concreto (de acuerdo con los análisis estadísticos de los ensayos de laboratorio) se realizaron 80,000 análisis de pushover de los pórticos planos seleccionados con el fin de establecer las derivas inelásticas y sus funciones de distribución de probabilidad para diferentes niveles de daño (simulaciones de Montecarlo). De acuerdo con los resultados, las derivas promedio para alcanzar niveles de daño de fluencia, ocupación inmediata y protección a la vida son 0.51%, 0.84% y 1. 41% respectivamente.

This thesis mainly focuses on thermal metamaterials, including thermal metadevices that can actively manipulate heat flux, and thermally responsive metamaterials that can deform in response to external heat stimuli in a controlled manner. We propose a method to design arbitrarily shaped 3D thermal cloaks with anisotropic and homogeneous material properties. Based on this approach, we study the steady-state and transient cloaking performance of multilayered cloaks. Then we propose a general road map to build thermal harvesting devices with microstructure design. The device is realized by naturally available materials. Both numerical and experimental results demonstrate good thermal harvesting performance. In addition to the above mentioned works on in-plane heat conduction control, we further propose a multilayered medium approach to flexibly manipulate out-of-plane thermal radiation. Based on this approach we realize functionalities like infrared camouflage, thermal coding and therm...

In this paper, an adaptive refinement procedure is proposed to be used with Discrete Least Squares Meshless (DLSM) method for accurate solution of planar elasticity problems. DLSM method is a newly introduced meshless method based on the least squares concept. The method is based on the minimization of a least squares functional defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions at nodal points used to discretize the domain and its boundaries. A Moving Least Square (MLS) method is used to construct the shape function making the approach a fully least squares based approach. An error estimate and adaptive refinement strategy is proposed in this paper to increase the efficiency of the DLSM method. For this, a residual based error estimator is introduced and used to discover the region of higher errors. The proposed error estimator has the advantages of being available at the end of each analysis contributing to the efficiency of the proposed method. An enrichment method is then used by adding more nodes to the area of higher errors as indicated by the error estimator. A Voronoi diagram is used to locate the position of the nodes to be added to the current nodal configuration. Efficiency and effectiveness of the proposed procedure is examined by adaptively solving two benchmark problems. The results show the ability of the proposed strategy for accurate simulation of elasticity problems.

In this paper, we analyze Schrodinger Equation, Uncertainly Principle Equation, Dirac Equation positive frequency plane wave solution, Planck Equation, 11-D Supergravity equations and the Einstein Field Equation. We obtain new possible mathematical connections with DN Constant, ζ(2), the Golden Ratio and π, and some parameters of Theoretical Cosmology and String Theory

We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent angles to end up with a diagonalized Hamiltonian. Using the representation theory of the group SU(3), we explicitly determine the solutions of the energy spectrum. Considering the ground state together with reduced density matrix, we derive the corresponding purity function that is giving rise to minimal and maximal entanglement under suitable conditions. The cases of realizing one variable among three is discussed and know results in literature are recovered. PACS numbers: 03.67.Bg, 03.65.-w, 02.20.Sv

1.3. Z jakiego materiału wykonane są rurki układu pokazanego na rysunku 1.6, jeśli wiadomo, że przy obciążeniu Q=2T przemieszczenie wolnego końca wyniosło ∆l=1,2mm. Dane (wymiary poszczególnych segmentów I, II, III): l 1 =0,5m, D 1 =50mm, d 1 =45mm l 2 =1,0m, D 2 =45mm, d 2 =38mm l 3 =1,5m, D 3 =38mm, d 3 =30mm Odpowiedź: Rurki wykonano z miedzi. E [GPa] stal 210 miedź 115 aluminium 69 Rys. 1.6. 1.4. Obliczyć i porównać wartości jednostkowej sztywności rozciągania dwóch prętów przedstawionych na rysunku 1.7. Pręty wykonane są z tego samego materiału o module Younga E. Iloraz średnic jest równy α=d/D=0,8. Dla jakiej wartości α jednostkowe sztywności rozciągania obu prętów będą jednakowe? Odpowiedź: c 1 /c 2 =2,17, α=0,643. Rys.1.7. Jednostkową sztywność rozciągania określa się jako wartość siły potrzebnej do wywołania jednostkowego zwiększenia lub zmniejszenia długości pręta, czyli P c l = ∆ , ponieważ Pl l EA ∆ = , więc EA c l = 1.1. Pręty podtrzymujące elementy sztywne 1.5. Jednorodna sztywna belka AB o ciężarze Q utrzymywana jest w położeniu poziomym przez trzy pręty jak pokazuje Rys.1.8. Zaprojektować przekroje poprzeczne prętów 1, 2 i 3. Dane: Q=900 kN; k r =k c =120 MPa; α=60 0. Rys. 1.8 1.6. Sztywna nieważka belka AB utrzymywana jest przez trzy pręty. W węźle A tego układu zawieszono ciężar Q jak pokazuje Rys.1.9. Obliczyć wymagane przekroje poprzeczne prętów. Dane: Q=800 kN; k r =k c =160 MPa; α=30 0 ; β=60 0. Rys. 1.9. 1.7. Obliczyć przekrój poprzeczny pręta CD podtrzymującego jednorodną sztywną belkę AB o ciężarze Q i obciążoną na końcu siłą P jak pokazuje Rys.1.10. Dane: Q=20 kN; P=240 kN; l=5 m; a=4 m; α=30 0 ; k r =160 MPa. Rys. 1.10. 1.8. Dwie jednorodne sztywne belki AB i CD o ciężarze Q każda podtrzymywane są przez pręty AE i AF (Rys.1.11). Zaprojektować przekroje poprzeczne prętów i wybrać najbliższy dowolny kształtownik hutniczy spełniający te warunki wg PN. Obliczyć pionowe przemieszczenie punktu D. Dane: Q=40 kN; P=120 kN; l=2 m; k r =140 MPa; E=2⋅10 5 MPa. Rys. 1.11. Rys. 1.12. 1.9. Blok o ciężarze Q podparty jest prętami jak pokazuje Rys.1.12. Obliczyć przekroje poprzeczne prętów. Dane: Q=800 kN; l=1 m; α=30 0 ; k r =k c =160 MPa. 1.10. Zaprojektować pręty podtrzymujące jednorodny ciężar Q pokazany na Rys.1.13. Przyjąć pręty w postaci rur wg PN-EN 10210-2:2000. Obliczyć odchylenie od pionu ścianki AB. Dane: Q=600 kN; l=2 m; k r =k c =140 MPa; E=2⋅10 5 MPa. 1.11. Zaprojektować pręty utrzymujące pomost o ciężarze G pokazany na Rys.1.14. Dane: G=300 kN; a=1,6 m; b=80 cm; h=60 cm; c=50 cm; d=40 cm; k r =k c =160 MPa.

In the domain of current design, noteworthy development and designing ability are shown in the development of transcending structures that are designed to endure seismic powers. Two distinct approaches have emerged as a result of this endeavor: one includes the reconciliation of nonstop vertical shear walls, while the other decisively positions shear walls to brace weak delicate story areas. The huge structures that have been built with this variety of strategies are analysed very closely during the study. the application of computer simulations enabled by the the ETABS program, the work aims to broaden and improve our knowledge of the earthquake-proofing implications of these two shear wall approaches.The main objective of the exploration is to compare multi-story constructions with and without coordinated shear walls in scenarios with sensitive story weaknesses.It applies reaction range inquiry to pinpoint important boundaries like maximum displacement, maximum drift , and storey shear and narrative advancements.In designs with 15, 20, and 25 storeys, the impact of placing shear walls at building corners versus discretionary locations is investigated.The process of assessment calls notice to the similarities are the two different models: one adopting a weak story structure, and the other introducing another shear wall opposite the delicate story. Both models are put through to simulated seismic forces based on actual earthquakes as the examination unfolds. If shear walls may effectively reduce displacement and drift while also showing only minor performance changes with respect to wall position.The main ideas from the similar review are illustrated in the conclusion. the significance of arrangement schemes and the function of shear walls in maintaining seismic robustness. The findings of the pertinent inquiry for both the delicate narrative and shear wall models are presented in the section of the text devoted to results and dialogues. The greatest displacements, lateral shifts, and shear forces are detailed in thorough tabulations and illustrations at the narrative level.The development of future seismic plan rehearsals is aided by the seismic resistance of tall structures with complex story layouts.

The objective of this study was to investigate the sensitivity of the nonlinear elastic properties of cortical bone to the presence of a single submillimetric crack. Nonlinear elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in fourteen human cortical bone specimens. The specimens were parallelepiped beams (50*2*2mm). A central notch of 500 µm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters α f and α Q , and the Young's modulus E us were measured in dry condition for undamaged (control) specimens and in dry and wet conditions for damaged specimens. The length of the crack was assessed using synchrotron radiation micro-computed tomography (SR-μCT) with a voxel size of 1.4μm. The initial values of α f , measured on the intact specimens, were remarkably similar for all the specimens (α f =-5.5±1.5). After crack propagation, the nonlinear elastic coefficient α f increased significantly (p<0.006), with values ranging from-4.0 to-296.7. Conversely, no significant variation was observed for α Q and E us. A more pronounced nonlinear elastic behavior was observed in hydrated specimens compared to dry specimens (p<0.001) after propagation of a single submillimetric crack. The nonlinear elastic parameter α f was found to be significantly correlated to the crack length both in dry (R=0.79, p<0.01) and wet (R=0.84, p<0.005) conditions. Altogether these results show that nonlinear elasticity assessed by NRUS is sensitive to a single submillimetric crack induced mechanically and suggest that the humidity must be strictly controlled during measurements.

The objective of this study was to investigate the sensitivity of the nonlinear elastic properties of cortical bone to the presence of a single submillimetric crack. Nonlinear elasticity was measured by nonlinear resonant ultrasound spectroscopy (NRUS) in 14 human cortical bone specimens. The specimens were parallelepiped beams (50×2×2mm(3)). A central notch of 500µm was made to control crack initiation and propagation during four-point bending. The nonlinear hysteretic elastic and dissipative parameters αf and αQ, and Young׳s modulus Eus were measured in dry condition for undamaged (control) specimens and in dry and wet conditions for damaged specimens. The length of the crack was assessed using synchrotron radiation micro-computed tomography (SR-μCT) with a voxel size of 1.4μm. The initial values of αf, measured on the intact specimens, were remarkably similar for all the specimens (αf =-5.5±1.5). After crack propagation, the nonlinear elastic coefficient αf increased significantl...

Handling and making decisions based on data taken at different scales is a critical issue in the design of exploration and production tasks in the oil industry. Acoustic data is the classical example of the integration of dissimilar scales (i.e. seismic, well logs, lab data) where there is a scale dependent velocity. An understanding of the acoustic dispersion phenomenon in granular samples is needed. A detailed numerical work was conducted in order to establish the relationship between frequency and propagation speed for an acoustical pulse induced in simulated granular materials. The granular samples were generated with different grain size distributions while porosity and pressure were targeted and kept invariant using the grain radii expansion method. A sinusoidal burst with frequencies from 10Hz to 1MHz was applied and the corresponding acoustical speeds were estimated for each frequency. A coherent sigmoid dispersion relationship was obtained for each granular sample. The asymptotic boundaries for the dispersion function reflect the limiting cases for the wavelength/heterogeneity ratio in the granular pack. The lower speed asymptote was explained as the mean field value while upper speed asymptote can be understood based on a ray theory approximation scaled by a parameter we defined as the "acoustic tortuosity factor". This factor reflects the intricate acoustical path due to the texture of the stress network developed in the granular samples and can be used together with the sigmoid dispersive relationship to describe and clarify the scale discrepancy between different source acoustic data in granular materials.

Handling and making decisions based on data taken at different scales is a critical issue in the design of exploration and production tasks in the oil industry. Acoustic data is the classical example of the integration of dissimilar scales (i.e. seismic, well logs, lab data) where there is a scale dependent velocity. An understanding of the acoustic dispersion phenomenon in granular samples is needed. A detailed numerical work was conducted in order to establish the relationship between frequency and propagation speed for an acoustical pulse induced in simulated granular materials. The granular samples were generated with different grain size distributions while porosity and pressure were targeted and kept invariant using the grain radii expansion method. A sinusoidal burst with frequencies from 10Hz to 1MHz was applied and the corresponding acoustical speeds were estimated for each frequency. A coherent sigmoid dispersion relationship was obtained for each granular sample. The asymptotic boundaries for the dispersion function reflect the limiting cases for the wavelength/heterogeneity ratio in the granular pack. The lower speed asymptote was explained as the mean field value while upper speed asymptote can be understood based on a ray theory approximation scaled by a parameter we defined as the "acoustic tortuosity factor". This factor reflects the intricate acoustical path due to the texture of the stress network developed in the granular samples and can be used together with the sigmoid dispersive relationship to describe and clarify the scale discrepancy between different source acoustic data in granular materials.