Three-dimensional Theory Research Articles

Estimation of the stress-strain state of orthotropic plates on elastic foundation using the bimoment theory

The study is devoted to the development of the bimoment theory and the method for calculating thick plates in the framework of the three-dimensional theory of elasticity. The basic relations and equations of motion of the plate presented are constructed with respect to the forces, moments and bimoments arising from the nonlinearity of the law of distribution of displacements and stresses over the plate thickness. Bending and vibrations of isotropic and orthotropic plates are considered an example of calculations. The resulting solution showed the efficiency and accuracy of the proposed bimoment theory in assessing the stress-strain state of thick plates.

Solid mechanics models in application to ophthalmology

The review presents the models on a change in the stress-strain state of the eye shell after vision correction operations and a change in intraocular pressure with the introduction of drugs into the vitreous body. All mathematical models were developed in collaboration with ophthalmologists. Mathematical models that describe the process of determining the true intraocular pressure (IOP) by applanation methods are discussed. New results in solid mechanics were obtained while studying ocular biomechanics problems. For example, the problem of the stability of a spherical shell subjected to a concentrated force and internal pressure was solved and the stability of the axisymmetric equilibrium state of annular inhomogeneous orthotropic plates under normal pressure was studied. The stress-strain states of transversely isotropic spherical and cylindrical layers subjected to internal and external pressures are discussed and the solutions obtained in the framework of the three-dimensional theory are compared with the solutions obtained by non-classical shell theories. This comparison made it possible to assess the accuracy of approximate theories.

Nonlinear deformation of concrete structure elements taking into account compensation grouting and fracturing

A formulation of the problem of compensatory injection was implemented using consistent equations of the elastic geometrically nonlinear three-dimensional theory. Algorithm for numerical solution was developed within the framework of the finite element method. A technique had been developed for the processes of crack formation in elements with prestressed reinforced polymer composite. A model problem was solved and comparison with experimental data was made.

An Analysis of the Grammar Sections of English Textbooks for Junior High Schools in China: Based on Larsen-Freeman’s Three-Dimensional Grammar Theory

This paper analyzes the grammar sections of BNUP (Beijing Normal University Press) English textbooks for junior high schools in China, aiming to investigate whether the grammar sections of BNUP English textbooks conform to Larsen-Freeman’s three-dimensional grammar theory. Seven categories are used to analyze the grammatical dimensions of grammar item presentation and grammar exercises to show the interconnections among the three dimensions from a holistic perspective. The results are as follows. The three dimensions (form, meaning, use) of grammar are reflected in both grammar item presentation and grammar exercises, but the distribution of the three dimensions is unbalanced. Both grammar item presentation and grammar exercises focus much on the ‘form’ dimension leaving the other two dimensions (meaning, use) less attentive. Thus, the composition of the grammar sections of BNUP textbooks is not in line with Larsen-Freeman’s three-dimensional grammar theory, which emphasizes that teaching and learning grammar should not be skewed toward one dimension. Based on the research findings, this paper not only sets the direction for the development of English textbooks but also provides insights for teachers on how to teach grammar well. (Hoseo University)

Power Relation and Cooperation between Actors: Issue of Nickel Mining Business Licenses in Konawe Regency

Natural resource management (SDA) such as nickel has become a logical choice for local governments to achieve results for regional development achievement. This is because nickel is one of the trade and business commodities between countries. However, a permit is required for the management of these natural resources. Meanwhile, the government cannot be separated from the cooperation between actors in the context of social situations regarding decisions about issuing permits for mining companies (IUP). Therefore, this paper aims to interpret the context of the social situation in nickel mining permit decision-making. In this paper, the data were obtained based on interviews with 26 informants, observations, and a review of documents. The study's results, in a review of the theory of manifestation of power relations, show that there is cooperation among regional heads, businesses, brokers, and village government officials. On the other hand, in the examination of the three-dimensional theory of power, the context of the social situation is that there is no latent conflict between the actors. The finding in this paper is the neglect of the role of local NGOs in the nickel IUD issuance process, particularly in defending the interests of local communities in the pre-mining phase.

Three-Dimensional Thermoelasticity Analysis of Viscoelastic FGM Plate Embedded in Piezoelectric Layers under Thermal Load

Due to the high importance of viscoelastic materials in modern industrial applications, besides the intensive popularity of piezoelectric smart structures, analyzing their thermoelastic response in extreme temperature conditions inevitably becomes very important. Accordingly, this research explores the thermoviscoelastic response of sandwich plates made of a functionally-graded Boltzmann viscoelastic core and two surrounding piezoelectric face-layers subjected to electrothermal load in the platform of three-dimensional elasticity theory. The relaxation modulus of the FG viscoelastic layer across the thickness follows the power law model. the plate’s governing equations are expressed in the Laplace domain to handle mathematical complications corresponding to the sandwich plate with a viscoelastic core. Then, the state-space method, combined with Fourier expansion, is utilized to extract the plate response precisely. Finally, the obtained solution is converted to the time domain using the inverse Laplace technique. Verification of the present formulation is compared with those reported in the published papers. Finally, the influences of plate dimension, temperature gradient, and relaxation time constant on the bending response of the above-mentioned sandwich plate are examined. As an interesting finding, it is revealed that increasing the length-to-thickness ratio leads to a decrease in deflections and an increase in stresses.

To the calculation of orthotropic plates taking into account bimoments

The work is devoted to the development of the bimoment theory and the method for calculating thick plates in the framework of the three-dimensional theory of elasticity. The basic relations and equations of motion of the plate are given, constructed with respect to forces, moments and bimoments, arising from the nonlinearity of the law of distribution of displacements and stresses over its thickness. Bending and vibrations of isotropic and orthotropic plates are considered as an example of calculation. The resulting solution showed the efficiency and accuracy of the proposed bimoment theory in assessing the stress-strain state of thick plates. Figs.: Refs.: 11 titles.
 Keywords: thick orthotropic plate, three-dimensional theory of elasticity, bi-moment theory, bending and vibrations, stress-strain state.

Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a Z2 gauge theory in three dimensions

Fractional statistics of quasiparticle excitations often plays an important role in the detection and characterization of topological systems. In this paper, we investigate the case of a three-dimensional (3D) Z2 gauge theory, where the excitations take the form of bosonic spinon quasiparticle and vison flux tubes, with mutual semionic statistics. We focus on an experimentally relevant intermediate temperature regime, where sparse spinons hop coherently on a dense quasistatic and stochastic vison background. The effective Hamiltonian reduces to a random-sign bimodal tight-binding model, where both the particles and the disorder are borne out of the same underlying quantum spin liquid (QSL) degrees of freedom, and the coupling between the two is purely driven by the mutual fractional statistics. We study the localization properties and observe a mobility edge located close to the band edge, whose transition belongs to the 3D Anderson model universality class. Spinons allowed to propagate through the quasistatic vison background appear to display quantum diffusive behavior. When the visons are allowed to relax, in response to the presence of spinons in equilibrium, we observe the formation of vison depletion regions slave to the support of the spinon wavefunction. We discuss how this behavior can give rise to measurable effects in the relaxation, response and transport properties of the system and how these may be used as signatures of the mutual semionic statistics and as precursors of the QSL phase arising in the system at lower temperatures.

On One Normal Boundary Value Problem of the Field Theory

One normal problem of the field theory on a plane for a system of Poisson equations is studied. This problem is one of implementations of the general approach to formulation of boundary value problems of the field theory, which is based on studying the kernels of trace operators and kernels of trace functionals, which are taken as the main space of desired solutions. A peculiarity of this problem is that one of the boundary conditions imposed on the desired solution is nonlocal in nature. The considered boundary condition nonlocality is due to the fact that the base space in which the solution of the problem is sought is the kernel of the regular trace functional in the Sobolev space. The need to supplement the problem on the one-dimensional cokernel of the above-mentioned functional, which arises in this case, determines the second boundary condition, which is local (pointwise) in nature. That is why, in the framework of the duality of the Sobolev space and its conjugate space, the solution to the problem is the pair (u, с), where с is a constant that compensates for the one-dimensional “defect” of the problem. It should be noted that the theory of boundary value problems for vector fields on a plane differs essentially from the theory of boundary value problems for three-dimensional vector fields. One of the reasons for the difficulties in formulating three-dimensional boundary value problems is that a number of important surfaces cannot be made parallel to each other, which rules out the possibility to consider “tangential” boundary value problems, that is, problems with boundary tangential fields. In this respect, the theory of boundary value problems of plane vector fields differs from the three-dimensional theory for the better. On the other hand, the fact that a formula that would interrelating the Laplace operator with first-order field theory operations is not available on a plane is an obstacle to identifying new non-standard boundary value problems for plane fields. Revealing of this interrelation is a separate issue, the solution of which leads to the concept of the trace of first-order field theory operators as a singular functional above the space of traces of functions from the first-order Sobolev space. Thus, boundary value problems for plane fields are a separate section of the general theory of field boundary value problems. One of the non-standard problems in the theory of plane vector fields, which contains non-local boundary conditions, is considered. A theorem for existence and uniqueness of a weak solution of the problem posed is formulated and proved. The proof of the theorem includes a few steps: using the Galerkin method, the existence of a solution to the equation is established; the passage to the limit is made, and the vector function u(x) is found; the number α is determined, and the uniqueness of the function u and the number α is established. The main result of the work is that the problem posed is correct in nature.

Isoscalar monopole strength in 100Mo: an indicator for static triaxial deformation in the ground state* *Supported by the National Natural Science Foundation of China (12075068, 11705038), the Fundamental Research Funds for the Central Universities (HIT.BRET.2021003) and the UK STFC (ST/V001108/1)

We perform deformation constraint symmetry-unrestricted three-dimensional time-dependent density functional theory (TDDFT) calculations for the isoscalar monopole (ISM) mode in 100Mo. Monopole moments are obtained as a function of time using time propagating states based on different deformations. A Fourier transform is then performed on the obtained response functions. The resulting ISM strength functions are compared with experimental data. For the static potential-energy-surface (PES) calculations, the results using the SkM* and UNEDF1 energy-density functionals (EDFs) show spherical ground states and considerable softness in the triaxial deformation. The PES obtained with the SLy4 EDF shows static triaxial deformation. The TDDFT results based on different deformations show that a quadrupole deformation (characterized by ) value of 0.25–0.30 gives a two-peak structure of the strength functions. Increasing triaxial deformation (characterized by γ) from 0 to 30 results in the occurrence of an additional peak between the two, making the general shape of the strength functions closer to that of the data. Our microscopic TDDFT analyses suggest that 100Mo is triaxially deformed in the ground state. The calculated isoscalar and strength functions show peaks at lower energies. The coupling of these two modes with the ISM mode is the reason for the three-peak/plateau structure in the strengths of 100Mo.

Effective and continuous degradation of pollutants via carbon felt loaded with Co3O4 as three-dimensional electrode: Collaboration between ROS

Combining the advantages of bipolar chemistry and three-dimensional electrode theory, this study utilized carbon felts loaded with Co3O4 nanoparticles in-situ as three-dimensional electrodes (Co/CF) to enhance the electrochemical oxidation (EO) capacity and the activation of peroxymonosulfate (PMS) of the system, thereby promoting the generation of reactive oxygen species (ROS) for the efficient and continuous degradation of various organic pollutants through advanced oxidation processes (AOPs). This synergistic system (EO-Co/CF-PMS) promoted the recycling of Co(III)/Co(II) in Co3O4 catalytic particles for the efficient and continuous utilization of 3D electrodes. The oxidative degradation of pollutants in the EO-Co/CF-PMS system was found to be mainly accomplished through the synergistic effect of reactive oxygen species (ROS), and the mechanisms of relative ROS generation pathways were fully investigated, demonstrating the superiority of the synergistic system. Notably, the contribution of each ROS in the system varied with the target pollutant, indicating the importance of the collaboration between ROS in the AOPs process for wastewater treatment efficiently.

Frontal Vehicular Crash Energy Management Using Analytical Model in Multiple Conditions

When it comes to frontal vehicular crash development, matching the stiffness of the front-end structures reasonably, i.e., impact energy management, can effectively improve the safety of the vehicle. A multi-condition analytical model for a frontal vehicular crash is constructed by a three-dimensional decomposition theory. In the analytical model, the spring is used to express the equivalent stiffness of the local energy absorption space at the front-end structure. Then based on the analytical model, the dynamic responses and evaluation indexes of the vehicle in MPDB and SOB conditions are derived with the input of the crash pulse decomposition scheme. Comparing the actual vehicle crash data and the calculation results of the proposed solution method, the error is less than 15%, which verifies validity of the modeling and the accuracy of the solution. Finally, based on the solution method in the MPDB and the SOB conditions, the sensitivities of the crash pulse decomposition scheme to evaluation indexes are analyzed to obtain qualitative rules which guide crash energy management. This research reveals the energy absorption principle of the front-end structure during the frontal impact process, and provides an effective optimization method to manage the multiple conditions of the vehicle crash energy such as the FRB (frontal rigid barrier), the MPDB (mobile progressive deformable barrier), and the SOB (small overlap barrier).

Rural Spatial Differentiation and Revitalization Approaches in China: A Case Study of Qingdao City

Rural revitalization, as a major strategy with the goal of realizing the overall development of strong agriculture industries, beautiful rural areas, and rich farmers, is an effective way of alleviating the loss of talent, land, capital, and other elements in rural areas and a possible cure for "rural diseases". However, "rural diseases" faced by villages are very different, and thus exploring suitable strategies for rural revitalization is beneficial to the implementation of rural revitalization strategies and the promotion of urban-rural integration. Based on location theory, this paper constructs a point-axis-domain three-dimensional spatial location theory model that integrates market location, traffic location, and natural location and combines the coupling coordination model to comprehensively study the vitality and development directions of Qingdao's rural areas. Results found that Qingdao's high-level and medium-high-level coupling coordination areas are the main types of coupling coordination, accounting for 45.19% and 47.48%, respectively. Based on the development status of Qingdao, this study explores development directions for rural revitalization poles as well as high-level, medium-high-level, and medium-level coupling coordination areas and suggests the following: rural revitalization poles should play a demonstration role in rural revitalization in terms of industrial development, rural civilization, social governance, public service construction, etc.; high-level coupling coordination areas should focus on building modern hi-tech agriculture and rural marine tourism industries; medium-high-level coupling coordination areas should strengthen the building of satellite towns and promote industrial transformation and upgrading; medium-level coupling coordination areas should actively develop ecological environment conservation models and establish a characteristic mountainous eco-tourism industry. Thus, the findings provide important scientific reference for the implementation of rural revitalization.

Various plate theory used in the analysis of FGMs-A review

This article reviews different plate theories which are used in the structural analysis of various functionally graded structures like shells/plates. The different plate theories are compared by introducing displacement field variables. It was found that first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) are the most widely applicable theories for the structural examination of moderately thin functionally graded materials (FGMs) compared to classical laminate plate theory (CLPT). Since most researchers implemented two-dimensional theories which save considerable computational time and cost compared to three-dimensional theories. Therefore, this study is more focused on 2D-based theories. The end result of this study can be highly useful for researchers and designers in selecting appropriate theories to examine the structural behaviour of different composite materials.

Topological Differential Microscopy Based on the Spin–Orbit Interaction of Light in a Natural Crystal

We experimentally demonstrate a two-dimensional topological differential microscopy based on the spin–orbit interaction of light through a thin uniaxial crystal slab. First, a three-dimensional propagation theory is established for the light propagating through a uniaxial material. Then it is found that, due to the spin–orbit interaction, the two circularly polarized components of incident light are imposed with opposite topological charges, leading to the azimuthal splitting of spin states. Consequently, the cross-polarized field approximately amounts to the second-order spatial differentiation of the incident field. Finally, such an optical differentiation performed by a lithium niobate crystal is successfully applied to edge detection in microscopy. Further experiments validate its good performance in edge enhancement of both amplitude and phase objects. The results provide an economic, simple but robust approach to real-time, colorful, and high-contrast biological imaging in living systems.

Research on Wind Wave Simulation Technology based on Potential Flow Theory

The wave environment is the main service environment of surface aircraft in the process of surface duty. In order to comprehensively study the operating characteristics of aircraft under this condition, it is necessary to conduct research on wave parameter modeling methods and simulation technology based on different wave conditions. This paper adopts the three-dimensional potential theory and ball model to calculate the different wave cases. A high-precision numerical simulation method of complex sea conditions is formed by mastering the numerical wave-making technology of typical regular and irregular waves. The result shows that the regular simulation in this paper has a high precision that the wave height and period is in 1% error compared with theory. The calculation error of spectral peak and peak frequency of sea states at all levels are within ± 8%, and the simulation quality of irregular waves meets the calculation requirements.

Gender and Identity Subversion in Oli London's Plastic is Fantastic

The release of Oli London's Plastic Is Fantastic (2021), which talks about his fantasy of plastic surgery, has been extensively criticized. One of the reasons is that his music video was released during Pride Month, a month when the LGBTQ community advocates for their rights for gender equality, followed by other videos and tweets declaring his post-surgery transition to "non-binary" and “Korean.” To dig deeper into this assertion, this study combines Fairclough's (2003) three-dimensional theory as the framework and Machin's (2010) semiotic analysis to examine the song lyrics, visuals, and sociocultural background, thereby contributing to the Multimodal Discourse Analysis studies. This study intends to investigate the construction of gender and identity in Plastic Is Fantastic, the underlying power systems present, and how the power systems subvert gender and Korean identity. Research shows that the lyrics and visuals are connected with Korean identity due to the usage of Korean in the songs and the performer's androgynous appearance and behavior throughout the video. These practices produced problems, especially when his plastic surgery-related social media activity was stirred up by mass media as he consistently equated and exploited his trans status with other minority groups, such as Koreans, LGBTQ, and transracial people. Thus, the subversion of gender and identity is present since identity production is commodified.

Integrated rupture mechanics for slow slip events and earthquakes

Slow slip events occur worldwide and could trigger devastating earthquakes, yet it is still debated whether their moment-duration scaling is linear or cubic and a fundamental model unifying slow and fast earthquakes is still lacking. Here, we show that the rupture propagation of simulated slow and fast earthquakes can be predicted by a newly-developed three-dimensional theory of dynamic fracture mechanics accounting for finite rupture width, an essential ingredient missing in previous theories. The complete spectrum of rupture speeds is controlled by the ratio of fracture energy to energy release rate. Shear stress heterogeneity can produce a cubic scaling on a single fault while effective normal stress variability produces a linear scaling on a population of faults, which reconciles the debated scaling relations. This model provides a new framework to explain how slow slip might lead to earthquakes and opens new avenues for seismic hazard assessment integrating seismological, laboratory and theoretical developments.

Convergence of the nucleation rate for first-order phase transitions

This paper investigates the importance of radiative corrections for first-order phase transitions, with particular focus on the bubble-nucleation rate. All calculations are done with a strict power-counting, and observables are consistently calculated at every order. This ensures that physical quantities are gauge and renormalization-scale invariant. Furthermore, to avoid large logarithms at high-temperatures, an effective three-dimensional theory is used. This effective theory automatically incorporates higher-order thermal masses. The results of this paper indicate that sub-leading corrections to the rate can be large. This is partly because radiative corrections are enhanced for large bubbles. To illustrate the calculations, three models are considered: a real-scalar model, a radiative-barrier model, and a model with an effective dimension $6$ operator. Relevant observables are calculated for each model, and the reliability of perturbation theory is discussed.

Hydrodynamic Response and Tension Leg Failure Performance Analysis of Floating Offshore Wind Turbine with Inclined Tension Legs

The tension legs are the essential parts of the tension legs platform-type (TLP-type) floating offshore wind turbine (FOWT) against the extra buoyancy of FOWT. Therefore, the TLP-type FOWT will face the risk of tension leg failure. However, there are seldom analyses on the hydrodynamic response and tension leg failure performance of FOWT with inclined tension legs. In this paper, a hydrodynamic model was established using three-dimensional hydrodynamic theory and applied in the motion response and tension analyses of FOWT with conventional and new tension leg arrangements on Moses. The influence of draft and tension leg arrangement on the performance of FOWT with inclined tension legs were studied. The optimum draft was the height of the column and lower tensions were obtained for the new tension leg arrangement. Moreover, the tension leg failure performance of FOWT with inclined tension legs was evaluated under different failure conditions. The results illustrated that the FOWT with the new tension leg arrangement can still operate safely after one tension leg fails.