Equilibrium Equations Research Articles

Creep analysis of a cylinder subjected to 2D thermoelasticity loads and boundary conditions with inner heat generation source

This paper presents an in-depth investigation of the creep behavior of a thick-walled cylinder subjected to thermomechanical loads with internal heat generation under various boundary conditions. The cylinder is subjected to internal pressure with the incoming heat flux in the inner layer and the outgoing heat flux from the outer layer accompanied by heat generation. The displacement field follows the kinematics of the first-order shear deformation theory (FSDT). Simultaneously, the temperature field is treated as two-dimensional, exhibiting variations both along the thickness and the length of the cylinder, with a linear temperature gradient across the cylinder's thickness. Using the energy method, the equilibrium equations and general boundary conditions are derived for the cylinder. Norton's model is incorporated into rate forms of the above-mentioned equations to obtain time-dependent stress and strain results using an iterative method. The redistribution, displacements, strains and stresses over time have been obtained by the semi-analytical iteration method. Moreover, the effectiveness of the proposed method in addressing axisymmetric cylindrical shells under various boundary conditions and thermo-mechanical loading is demonstrated. A parametric study on the creep behavior has also been carried out which reveals critical insights. Notably, the study demonstrates that effective stress and radial displacement during creep can be effectively managed by optimizing the external cooling profile or the internal heating profile. Furthermore, the investigation reveals that the presence of a heat source markedly influences the effective stress and displacement within structure, highlighting the interplay between thermal and mechanical factors in determining the structural integrity. To validate the findings of this study, the finite element method was employed, with the results indicating good agreement between the two approaches.

Analytical solutions for hydrodynamic responses of arrays of floating truncated cylinders using multi-term Galerkin method and its application to a new wave energy converter device

In the context of linear water wave theory, the analytical solutions for the diffraction and radiation of a truncated cylinder array are developed in the presence of ambient incident waves. Each cylinder in the array can oscillate with five degrees of freedom (DOFs), i.e., surge, sway, heave, roll, and pitch. This paper adopts the multi-term Galerkin method to expand the fluid velocity at the interface of different regions into a set of basis functions containing Gegenbauer polynomials, which accurately and efficiently characterizes the cube root singularity of the fluid velocity near the edges of the truncated cylinders. Using the dynamic equilibrium equations, the amplitudes of each DOF of the cylinders in the array are solved. The analytical solution presented in this paper converges rapidly, and high-precision hydrodynamic response results can be obtained using just a few truncated terms (e.g., the upper bounds of m0 = 5 and p0 = 22 can yield results of five-figure accuracy). For the 4-cylinder array, under the same accuracy conditions (the error less than 1%), the computation time of the conventional method developed by Zeng et al. [“Hydrodynamic interactions between waves and cylinder arrays of relative motions composed of truncated floating cylinders with five degrees of freedom,” J. Fluids Struct. 115, 103785 (2022d)] based on the exact algebraic method [Kagemoto and Yue, “Interactions among multiple three-dimensional bodies in water waves: An exact algebraic method,” J. Fluid Mech. 166, 189–209 (1986)] is 3.9 times longer than that of the present method. As the number of cylinders increases, the advantage of the present method in terms of convergence speed becomes more apparent, e.g., for the 16-cylinder array, the conventional solution takes 6.3 times longer than the present solution. To extract wave energy more efficiently, a new 5DOF wave energy converter (WEC) device that can extract energy in 5DOFs is proposed. The present method is adopted to investigate the hydrodynamic performance of the 5DOF WEC arrays. Compared with the traditional 1DOF (heave) WEC, the 5DOF WEC can significantly improve the energy capture performance of arrays, especially in the high-frequency wave region.

Neutron stars in scalar torsion theories with non minimal coupling

We explore the existence and configurations of static and slowly rotating neutron stars (NSs) within a specific truncation of teleparallel scalar torsion theory. In this model, a scalar field ϕ is non-minimally coupled to the torsion scalar as ξTϕ 2, in the presence of the scalar potential V(ϕ) = -μ 2 ϕ 2/2 + λϕ 4/4. We establish the hydrostatic equilibrium equations for the static scenario and numerically solve them for both interior and exterior regions, employing appropriate boundary conditions near the center and at a distant location far away from the star's surface. Radial profiles of metric functions and the scalar field, alongside mass-radius diagrams, are plotted, utilizing four different realistic equations of state (EOS). Our results align closely with observational constraints from the GW170817 event, revealing a maximal mass of 2.37 M ⊙ achieved with the BSk21 EOS for a coupling parameter ξ = 0.25. Extending our analysis to encompass slow rotation, we establish the relationship between the star's moment of inertia and its mass. Furthermore, we explore future observations of NSs utilizing the redshift surface observable. Finally, we demonstrate the validity of the universality relation between the two forms of normalized moment of inertia within teleparallel scalar torsion theory with non minimal coupling.

The effect of the stress equilibrium factor on the composite case of the solid rocket motor

In this paper, based on the composite structure design and analysis software ANSYS ACP, the layup design for the composite cases of the equal pole hole solid rocket motor with different stress equilibrium factors is carried out. The finite element software ANSYS Workbench is used to study in detail the effects of stress equilibrium factor on the stress level, failure degree, and burst pressure prediction of the case under a certain internal pressure. The results show that reducing the value of the stress equilibrium factor can reduce the stress level of each winding layer along the main direction of the material in the motor case and gradually transfer the maximum stress of the case along the fiber direction from the weak stress zone to the cylinder section. This is beneficial for improving the burst pressure of the case and making the burst point located in the cylinder section. However, whether the case failure is related to the selected failure theory and strength criterion, the failure results and burst pressure obtained using different failure theories and strength criteria may be different, which indicates that each failure criterion has its scope of application and limitations. Under the Tsai-Wu criterion, using the stress equilibrium equation to calculate the stress equilibrium factor can just ensure that each winding layer of the motor case does not fail under the working pressure. In summary, when designing a composite case and predicting its failure, in addition to considering whether the stress equilibrium factor taken is conducive to meeting the design requirements for the strength of the case, it is also necessary to consider the use of multiple failure criteria to study the failure of the case. Obviously, arbitrarily selecting the stress equilibrium factor is not appropriate in the above process. By analyzing the influence of the stress equilibrium factor on the strength and failure condition of the motor case, it can provide an effective reference for the design of a composite case for SRM.

Simulating Capillary Folding of Thin Elastic Sheets with Pinned Contact Lines

We consider the capillary folding of thin elastic sheets with pinned contact lines in three dimensions. The folding occurs due to the interaction between the elastic sheet and a droplet deposited on top of it. Firstly, we derive the equilibrium equations by minimizing the total energy of the system. This energy comprises the interfacial energies and the elastic energy, which is described by the nonlinear Koiter's model. Then we develop a time-splitting numerical scheme to solve the gradient flow dynamics. Following this dynamics, the system evolves towards the equilibrium state. At each time step, we first determine the droplet surface with a constant mean curvature by minimizing a squared area functional, subject to the boundary condition at the pinned contact line. The elastic sheet, discretized by the C1-conforming subdivision element method, is then evolved by taking into account the fluid pressure and the capillary force. We propose a novel remeshing strategy to avoid the need for interpolating the capillary force on the sheet boundary and to prevent simulations from breakdown due to distorted meshes. We perform numerical tests to demonstrate the accuracy of the numerical method, as well as its ability to predict folded structures for various types of sheets.

К ПРЕДЕЛЬНОМУ РАВНОВЕСИЮ МОНОЛИТНЫХ ЖЕЛЕЗОБЕТОННЫХ ПЛИТ ПЕРЕКРЫТИЙ КАРКАСНЫХ ЗДАНИЙ В АВАРИЙНЫХ СИТУАЦИЯХ, ПРИВОДЯЩИХ К ПРОГРЕССИРУЮЩЕМУ ОБРУШЕНИЮ КОНСТРУКЦИЙ

A brief analysis of current standards concerning calculations of the resistance to progressive structural collapse of frame buildings in case of an accidental destruction is presented. Two analysis methods concern the resistance to progressive collapse of the slabs of monolithic frame buildings in case of accidental failure of one column are considered: direct method in which the entire building is calculated with a modified analysis scheme followed by checking the strength of structures with increased efforts, and calculating the slab located over the destroyed column by the ultimate equilibrium method with determination the slab destroying load. It is shown that the slab destroying load greatly depends on the model of its destruction. General equation of the ultimate equilibrium of the slab is written down. It includes not only the formation of plastic hinges in the slab, but also taking in account pushing through the slab by the column located on it. There are three possible options for an emergency destruction of the slab: from the formation of plastic hinges in the plate only, the slab pushing through by a column and formation of plastic hinges at the same time and situation when the slab is pushed through by the column. A criterion of the destruction option determination is offered. An example of calculation is given.

Modeling the deterioration of the stiffness and of the collagen fibril distribution in a discrete model of the cornea microstructure

We present a stochastic approach to model the mechanical deterioration of the reinforcing microstructure of the human cornea. The fundamental structural micro-components of the stroma, collagen and crosslinks, are assembled deterministically into an elementary trusswork cell, multiply repeated and distorted to form a three-dimensional shell with the shape of a cornea. The spatial orientation of the collagen-like elements of each cell is thus characterized stochastically with a non correlated random angle field, obeying an assigned probability density function, leading to a non-deterministic structural stiffness. It follows that the mechanical response of the model to the action of deterministic forces equivalent to the intraocular pressure is stochastic due to the random spatial orientation of collagen fibers. The deterioration of the mechanical stiffness of the collagen components is described through a scalar variable field, evolving in space and in time, representative of a progressive damage which causes heterogeneity and asymmetric behavior. The damage variable acts in two ways on the global stiffness: (i) by reducing the stiffness of the collagen components; (ii) by modifying the dispersion coefficient of the probability density function. The equilibrium equations of the damaging model are solved at discrete time steps, with a fully explicit solution scheme, by means of the stochastic finite element improved perturbation method. The results show that when the collagen fibril stiffness reduces to 10% of the healthy value, as expected in the case of the vision-impairing condition known as keratoconus, the displacement field due to intraocular pressure is significantly affected in terms of both average and variance distributions. This effect confers a typical conical shape to the cornea. In particular, the analysis shows that high values of the response variances are confined in the keratoconus area, which agrees with a high level of uncertainties due to loss of fibril organization and thickness reduction under pathologic conditions.

Analytical solution for simplifying the pile-soil interaction to a spring-damping system under horizontal vibration

An analytical solution is developed to investigate the model of simplifying the pile-soil interaction to a spring-damping system when the horizontal earthquake input or the top of the model is subjected to horizontal dynamic load. Based on Euler-Bernoulli theory, the dynamic equilibrium equations of pile in soil and air are established, respectively. Then, utilizing the corresponding boundary conditions, potential function decomposition, and transfer matrix method, the analytical expression of impedance at the pile head whether the horizontal earthquake input or the top of the system is subjected to horizontal dynamic load can be presented. Furthermore, the model of the pile-soil complex interaction can be simplified as a spring-damping system according to the stress equilibrium at the pile bottom in the air. Moreover, the rationality of the present solution (without simplification) is verified by comparison with existing methods, and then the difference between the present solution (without simplification) and the spring-damping system (simplification) is also compared. Finally, the influence of the parameter variation in the pile buried in the soil and soil free-field on the simplified model are discussed. The research results will be instructive for the simplification of numerical model for pile-soil interaction.

Pollutant transport model with large time-scale and estimation of land-use export coefficients at a watershed level.

The pollutant transport equilibrium in a watershed can be analyzed on a large time scale, and land-use export coefficients can be calculated directly under certain hydrologic and transport conditions, by ignoring hydrologic and transport processes at small space and time scales on hydrologic response units. In this study, the water environment system of a watershed was deconstructed into three parts (source, source-sink, and runoff transport) to construct a pollutant transportation equilibrium model on a large time scale. A watershed with an annual source-sink accumulation of zero was defined as a completely transported watershed; therefore, we derived a completely transported equilibrium equation. The problem of seeking the land export coefficient was converted into a problem of seeking the optimal solution of linear programming, which can be estimated according to the variation in pollutant output processes. The feasibility of the solution can be analyzed using multi-year stochastic rainfall processes. The model was used to analyze the transport equilibrium of chemical oxygen demand (COD), total nitrogen (TN), and total phosphorus (TP) upstream of the monitored cross-sections in a watershed, which covered 3145.66 km2. The land export coefficients were calculated according to the model. The model calculations indicated that the watershed was completely transported during perennial years. The calculated export coefficients of COD, TN, and TP for farmland, primary vegetation, and urban land were within the range of general empirical values. The calculated maximum accumulations of COD, TN, and TP were 0.19 × 107, 0.063 × 107, and 0.049 × 106 kg, respectively, for perennial rainfall. PRACTITIONER POINTS: A completely transported watershed was defined, and a model of pollutant transportation equilibrium with large time-scale was constructed. A problem of seeking the optimal solution of a linear programming was designed to estimate the land export coefficient of COD, TN, and TP. The runoff transport and accumulation processes of COD, TN, and TP in a watershed was analyzed.

Geometrically nonlinear vibration of toroidal sandwich shells with auxetic honeycomb core under periodic/impulsive pressure

The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool.

An Analysis of the Kinematics and Dynamics Performance of a New Type of Three-Pronged Sliding Universal Coupling

The three-pronged sliding universal coupling is a new kind of three-pronged coupling. The purpose of this study is to demonstrate that, compared with a traditional unequal angular velocity universal coupling (such as the Hooke universal coupling), the universal coupling has the superior characteristics of constant angular speed transmission, simple structure and strong transmission capacity by performing kinematic and dynamic analysis of the new three-pronged sliding constant angular velocity universal coupling. It provides a broad prospect for applications in automotive and other fields. To study its kinematic and dynamic characteristics, directional cosine matrices are utilized as tools to analyze the coordinate systems by establishing simplified geometric models and corresponding motions. Through the analysis of the motions of the input and output shafts and employing the method of single-force element, a set of equilibrium equations for the forces acting on the output shaft and the input shaft are formulated for solution analysis. The research indicates that during the rotation process, there exists a small angular difference between the input shaft and the intermediate shaft, demonstrating the quasi-constant angular velocity characteristics of the new tripod sliding universal coupling. The curves of the forces and force moment acting on each component of the coupling approximate sinusoidal curves. The optimal operating angle range for the new tripod universal coupling is at angle , during which the system exhibits good transmission and mechanical performance. It can be widely used in the automobile industry, tie steel industry and other occasions that require angular transmission. It is especially used in high-speed operation and large transmission capacity.

On the Efficient and Accurate Non-linear Computational Modeling of Multilayered Bending Plates. State of the Art and a Novel Proposal: The 2D+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ ext {D}+$$\\end{document} Multiscale Approach

After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness.Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy).The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application of the Hill–Mandel principle, grounded in the well-established physical assumption imposing mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models, at the computational cost of 2D models.

Numerical modeling and analysis of fluid-filled truncated conical shells with ring stiffeners

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders’ shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli’s equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research.

Continuum strain of point defects

We propose a new Regularized Green's Function Method (RGFM) derived from electron densities and captures the disturbance due to point defects, successfully extending the elastic strain determination to the lattice scales. The RGFM circumvents the use of concentrated point forces, which results in unrealistic singular fields. The objective is to determine the force variations at the atomic scales from Ab-initio calculations as Quantum Mechanical Force Density (QMFD). QMFD encodes the information regarding the electronic structure of the defect since it is related to the gradients of electron wavefunctions generated from the Density Functional Theory (DFT) calculations. Once the QMFD is calculated, RGFM solves the force equilibrium equation via Fourier transforms to compute elastic fields. Therefore, the present treatment reflects the electronic structure of the atomic positions, hence the complex elastic deformations and interactions at short range, which represents a significant advancement compared to previous studies. The RGFM can also capture the long-range fields since it calculates the decay of the force fields away from the nuclei. Previous theories, such as the elastic dipole method, face two main shortcomings: they can only handle the long-range elastic fields, and contain an unphysical singularity at the center of the point defect. Our novel derivation of distributed forces addresses both challenges, i.e., it renders non-singular displacement and strain fields at the nuclei, and can also describe the elastic response accurately far from the nuclei center. The application of the method to the NV (nitrogen-vacancy) center in SiC is demonstrated in comparison with the elastic dipole theory, showing the advantages of the present methodology.

Enhancing the Mechanical Performance of Concrete Slabs through the Incorporation of Nano-sized Iron Oxide Particles (Fe2O3)

The utilization of recycled iron in durable concrete production has gained attention for enhancing sustainability and resource efficiency. Simultaneously, incorporating nanoparticles as supplementary cementitious materials (SCMs) offers significant benefits. Introducing nano-sized iron particles (Fe2O3) into the cement paste results in a compact microstructure, improving strength, and durability. In this study, we investigate the bending behavior of concrete slabs reinforced with Fe2O3 nanoparticles using the non-local quasi-3D shear deformation theory based on Eringen's non-local differential constitutive relations. To characterize the elastic material properties of the nanocomposite, we employ Eshelby's homogenization model. In order to extend the applicability of our findings, we assume that the concrete plate rests on Kerr's foundation, which includes a shear layer connected to upper and lower springs. By deriving the equations of motion using the principle of virtual work, we establish a comprehensive framework for analyzing the bending of the concrete plate. To solve the equilibrium equations for a simply supported concrete plate, we present Navier's analytical solutions. Our investigation considers various influential parameters, such as the concentration of Fe2O3 nanoparticles in the concrete matrix, the elastic constants of the soil medium, different types of bending loads, and size-dependent nonlocal parameters. One of the most captivating findings of this study is that the incorporation of 30 wt% of iron nanoparticles in concrete leads to a remarkable improvement of 60% in the elastic properties of the material. Additionally, this same amount of iron nanoparticles has shown the potential to reduce the deflection of thin plates by over 60%.

Contribution of system elements to its static indeterminacy

The article contains an overview of the main ideas regarding the new direction of construction mechanics, which considers the issue of survivability and is intensively developing. From the point of view of redundancy, as the ability of the system to provide alternative ways of transferring the load, which is one of the main possible strategies for designing reliability and survivability, the static-kinematic analysis of rod systems is also considered. The fundamental measure of the level of redundancy of rod systems is the degree of static uncertainty. But this numerical sign does not contain information about the role of each element of the system in forming the degree of static uncertainty. This role is performed by a specially constructed distributed static indeterminacy matrix (DSI-matrix), which contains comprehensive information about the contribution of system elements to its static and kinematic properties. Using the fundamental provisions of linear algebra, the properties of the matrix of coefficients of the system of linear equilibrium equations as an operator over the vector spaces of forces and displacements are analyzed. The mechanical content of the four fundamental subspaces associated with this matrix is indicated. This analysis determines the mathematical properties of the RSN matrix and its mechanical interpretation. Methods of forming the DSI-matrix are considered both for the case of a geometrically constant system and for the analysis of geometrically variable systems, when it is necessary to resort to singular decomposition of the matrix of equilibrium equations. All theoretical explanations are accompanied by illustrative examples, although the issue of numerical implementation of the considered methods of analysis is not considered. It is obvious that they deserve independent consideration. Information is provided on the possibility of using the DSI -matrix to assess the reliability and survivability of the structural complex and its use to analyze the sensitivity of the system to the inaccuracy of manufacturing elements.

The problem of the structure and the soil plastic environment interaction in the conditions of dynamic evolutionary processes

Dynamic influences are one of the important factors affecting project decisions during the construction of buildings and structures. In the case of dynamic analysis, the range of possible variations in structural response is very difficult to determine. The complexity is determined not only by the parameters of the load itself (intensity, the law of change over time), but also by the characteristics of the research object (their values and change over time), which is an interconnected system of the structure and the soil base. Dynamic factors of influence can include periodic vibration or shock loads, the effects of explosions that cause a sharp change in pressure on the structure of the building, seismic fluctuations, etc. In many cases, the load is the result of stress waves propagating in the soil base. These factors can act on the natural environment long-term, relatively short-term, short-term and instantaneous. Therefore, the development of refined approaches for assessing the stress-strain state of structures during the interaction of the structure and the soil environment under the conditions of dynamic evolutionary processes remains an actual task today. In order to effectively find a solution to the dynamics problems, it is necessary to possess the entire set of analysis tools, to clearly present the rules and limits of their application. The ability to correctly assess the engineering and geological conditions of the construction site, the properties of the soils, the joint work of these soils with the foundations and structures of the building has always been and remains the basis of reliable and effective engineering design. The given statement of the problem is a theoretical basis to build the numerical approaches to the study of the vibrational processes of heterogeneous spatial bodies during their contact interaction with an elastic-plastic medium. The paper considers the modeling aspects of the structure and the soil elastic-plastic environment interaction under the conditions of dynamic evolutionary processes. The basic geometric and physical equations of the elasticity theory for heterogeneous circular and prismatic spatial bodies are given. In the range of solving the dynamics problem, the peculiarities of the mathematical model implementation, regarding the representation of the variation of kinetic energy as part of the equations of dynamic equilibrium of linear and nonlinear mechanical systems, are considered.

Stress state analysis of a cylindrical tank with water of an under water sports palace

The paper analyzes the stress state of a cylindrical tank, which is one of the main structural elements of a sports facility - an underwater sports palace. In the calculation of the cylindrical shell of the tank of constant thickness, the moment theory was used. The reservoir is, in fact, a swimming pool for conducting training sessions on underwater swimming in fins, diving, diving, is considered fixed in its base and filled with liquid (water of a special composition, homogeneous in depth, with a given specific gravity). It is known that integration of the calculation equations of the moment theory (of circular cylindrical shells), namely: a) differential equations of equilibrium; b) equations of deformations; c) equations of forces attributed to the unit length of the coordinate line (tangential forces, bending moments), is a complex mathematical problem associated with solving a system of partial differential equations with variable coefficients. Only the calculation of the curve of a cylindrical shell ultimately leads to a system of differential equations with constant coefficients. Under the assumption of significant depth of the tank compared to the thickness of its walls and the value of the radius of the cylinder base (which allows us to consider it as infinitely long), displacements and forces (tangential and transverse), bending moments are analytically found. The locations of the cylinder surface points, in which the indicated forces and moments acquire maximum values, have been determined; sketches of their diagrams, determining the character of change of these physical quantities (parameters) along the height of the tank, have been given. The results obtained in the work can be further used to clarify and improve engineering methods of calculation of structural elements of sports facilities of this type, both at the stages of their design and in the modes of real operation in order to prevent situations associated with the loss of their strength and stability.

Permeability estimation for deformable porous media with convolutional neural network

PurposeAccurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.Design/methodology/approachA convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.FindingsThe proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R2) is 0.93 for the validation set, and the R2 for the test set A and test set B are 0.93 and 0.94, respectively.Originality/valueThis study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

Age of (152830) Dinkinesh I Selam constrained by secular tidal-BYORP theory

We constrained the age of the main belt binary asteroid system, (152830) Dinkinesh, through secular dynamics and assuming the secondary, Selam, is at equilibrium. We reproduced Selam's current semi-major axis and rotation period and Dinkinesh's current rotation period, starting from the initial conditions of the spin-up fission event. The method presented here includes the secular effects of YORP, BYORP, and tidal interactions, while also allowing for the strengths of these effects to be constrained. Based on this method, we performed a Monte Carlo simulation, which indicates that Selam's age is likely to be sim 1--10 Ma. Derivations for improved equations that describe tidal-BYORP equilibria in binary asteroid systems are also presented in this work. In particular, we derived: (1) a tidal-BYORP equilibrium equation that scales appropriately with the secondary mass and accounts for differences in the primary and secondary densities; and (2) an equation for YORP-driven primary spin stability, with the secondary being at equilibrium.