Stress Superposition Method and Mechanical Analysis Properties of Regular Polygon Membranes

In this paper, the stress superposition method (SSM) is proposed to solve the stress distribution of regular polygon membranes. The stress-solving coefficient and the calculation formula of arbitrary point stress of regular polygon membrane are derived. The accuracy of the SSM for calculating stresses in regular polygonal membranes is verified by comparing the calculation results of the SSM with the finite element simulation results. This article is the first to propose a method to investigate the response of the arch height of the membrane curved edge to the membrane’s mechanical properties while keeping the effective area constant. It is found that the equivalent stress and the second principal stress at the midpoint of the membrane curved edge are effectively increased with the increase of the arch height of the curved edge. The second principal stress at the edge region of the membrane is relatively small, leading to the occurrence of wrinkles. When the stress at the midpoint of the curved edge is equal to that at the center of the membrane, the membrane plane attains the maximum stiffness and reduces the possibility of wrinkling at the edge.

Planar Typical Bézier Curves Made Simple

Recently, He et al. derived several remarkable properties of the so-called typical Bézier curves, a subset of constrained Bézier curves introduced by Mineur et al. In particular, He et al. proved that such curves display at most one curvature extremum, give an explicit formula of the parameter at the extremum, and show that subdividing a curve at this point furnishes two new typical curves. We recall that typical curves amount to segments of a special family of sinusoidal spirals, curves already studied by Maclaurin in the early 18th century and whose properties are well-known. These sinusoidal spirals display only one curvature extremum (i.e., vertex), whose parameter is simply that corresponding to the axis of symmetry. Subdividing a segment at an arbitrary point, not necessarily the vertex, always yields two segments of the same spiral, hence two typical curves.

Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Objective: The process of ultrasound oscillations in a relaxed environment, provided that the profiles of the acoustic wave at three time moments are known, is modeled by a three-point problem for the partial differential equation of the third order in time. This equation as a partial case contains a hyperbolic equation of the third order, which is widely used in ultrasound diagnostics. Methods: The differential-symbol method is applied to study a three-point in-time problem. The advantage of this method is the possibility to obtain a solution of the problem only through operations of differentiation. Results: We propose the formula to construct the analytic solution of the problem, which describes the process of ultrasound oscillations propagation in a relax environment. Due to this, the profile of the ultrasonic wave is known at any time and at an arbitrary point of space. The class of quasi-polynomials is distinguished as a class of uniqueness solvability of a three-point problem. Conclusion: Using the proposed method, it is possible to analyze the influence of the main parameters of ultrasound diagnostics problems on the propagation of acoustic oscillations in a relaxed environment. The research example of a specific three-point problem is given.

Soil moisture migration model based on Flux-concentration relation under steady rainfall

Moisture content distribution in soil is of great importance for understanding rainfall-induced slope failure and roadbed settlement. This study aims to develop a moisture migration model that improves the quantification of moisture content at an arbitrary point of the soil at any time for the whole process of infiltration under steady rainfall. The model was derived from the Richards' equation using the Flux-concentration relation, which was validated by numerical solutions calculated by Hydrus-1D software to evaluate the performance of the model. Results showed good accuracy and high adaptability for the moisture migration simulation of a wide range of soil types, and is applicable for short-duration and long-duration steady rainfall. Moreover, it can also reflect the stratification phenomenon for soil profile wetting by infiltration. Our analysis indicates that the flux and surface volumetric moisture content together can bound the boundary conditions of rainfall infiltration, which presents a shift from constant-flux to constant-concentration during a long-duration steady rainfall. The migration rate of the wetting front in the later stage of infiltration positively correlates with rainfall intensity under the constant-flux condition, while it finally stabilizes at Ks/(θs − θi) under the constant-concentration condition (i.e., Ks-saturated hydraulic conductivity, θs-saturated volumetric moisture content, θi-initial volumetric moisture content). HIGHLIGHT Moisture migration model was derived to improve the quantification of moisture content at an arbitrary point of the soil at any time for the whole process of infiltration under steady rainfall, which shows good accuracy and high adaptability for the moisture migration simulation of a wide range of soil types, and is applicable for short-duration and long-duration steady rainfall.

Non-integrability of a model of elastic dumbbell satellite

We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The satellite is modelled by two point masses connected by an extensible massless spring that obeys Hooke’s law. It is assumed that the distance between point masses is much smaller than the radius of the orbit, so the orbital motion of the satellite is not perturbed by its rotational motion. The gravity potential of the satellite is expanded into a series with respect to its size up to quadratic terms which describe the gravity gradient torque acting on the satellite. Two cases are considered with Hooke’s centre localised in the centre of mass of the dumbbell and at an arbitrary point along a line connecting both masses. It is shown that the first case appears to be integrable and super-integrable for selected values of the parameter of the system. In the second case, model depends effectively only on one parameter and is non-integrable. In the proof, differential Galois integrability obstructions are used. For the considered sysem, these obstructions are deduced thanks to the recently developed symplectic Kovacic’s algorithm in dimension 4. According to our knowledge, this is the first application of this tool to a physical model.

Automated Dynamic Mascon Generation for GRACE and GRACE-FO Harmonic Processing

Commonly used mass-concentration (mascon) solutions estimated from Level-1B Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On data, provided by processing centers such as the Jet Propulsion Laboratory (JPL) or the Goddard Space Flight Center (GSFC), do not give users control over the placement of mascons or inversion assumptions, such as regularization. While a few studies have focused on regional or global mascon optimization from spherical harmonics data, a global optimization based on the geometry of geophysical signal as a standardized product with user-defined points has not been addressed. Finding the optimal configuration with enough coverage to account for far-field leakage is not a trivial task and is often approached in an ad-hoc manner, if at all. Here, we present an automated approach to defining non-uniform, global mascon solutions that focus on a region of interest specified by the user, while maintaining few global degrees of freedom to minimize noise and leakage. We showcase our approach in High Mountain Asia (HMA) and Alaska, and compare the results with global uniform mascon solutions from range-rate data. We show that the custom mascon solutions can lead to improved regional trends due to a more careful sampling of geophysically distinct regions. In addition, the custom mascon solutions exhibit different seasonal variation compared to the regularized solutions. Our open-source pipeline will allow the community to quickly and efficiently develop optimized global mascon solutions for an arbitrary point or polygon anywhere on the surface of the Earth.

Cosmological evolution and dark energy in osculating Barthel–Randers geometry

We consider the cosmological evolution in an osculating point Barthel–Randers type geometry, in which to each point of the space-time manifold an arbitrary point vector field is associated. This Finsler type geometry is assumed to describe the physical properties of the gravitational field, as well as the cosmological dynamics. For the Barthel–Randers geometry the connection is given by the Levi-Civita connection of the associated Riemann metric. The generalized Friedmann equations in the Barthel–Randers geometry are obtained by considering that the background Riemannian metric in the Randers line element is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equation is derived, and it is interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution, and that an effective cosmological constant can also be generated. Several exact cosmological solutions are also obtained. A comparison of three specific models with the observational data and with the standard $$\Lambda $$ Λ CDM model is also performed by fitting the observed values of the Hubble parameter, with the models giving a satisfactory description of the observations.

Modeling the reliability of electrical power lines of the seaport in conditions forced electricity consumption

В работе рассматривается задача оценки времени наработки силовой кабельной линии морского порта, с учетом форсирования технологического процесса в морском порту (погрузочно-разгрузочных работ) и, в связи с этим, повышения величины токовой нагрузки в силовой линии, превышающей допустимый предел, что ведет к повреждению линии. Для оценки влияния форсированного технологического процесса, на наработку силовых линий, вводятся основные факторы влияния: время длительности форсированного режима; величина тока в линии; температура окружающей среды. С их помощью вводится функция сокращающегося временного ресурса наработки силовой линии, которая отображает повреждения в силовой линии. Общая математическая модель наработки силовой кабельной линии включает повреждения в кабельной линии как основной фактор. Решение задач осуществляется с помощь разработанных программных средств и применения нечеткой математики, в среде Mathcad. Представленная математическая модель позволяет количественно оценить время наработки при использовании форсированных технологических режимов и повышенного потребления энергии, а также оценить степень снижения времени наработки, в результате суммарного действия повреждающих факторов, для произвольного момента времени в условиях эксплуатации. The paper considers the problem of estimating the operating time of the power, cable line of the seaport, taking into account the acceleration of the technological process in the seaport (loading and unloading operations) and, in this regard, the increase in the current load in the power line exceeding the permissible limit, which leads to damage lines. To assess the influence of the forced technological process on the operating time of the power lines, the main factors of influence are introduced: the duration of the forced mode; line current value; ambient temperature. With their help, the function of reducing the time resource of the operating time of the power line is introduced, which displays the damage in the power line). The general mathematical model of the power cable line operating time includes damage in the cable line as the main factor. The solution of problems is carried out with the help of the developed software and the use of fuzzy mathematics, in the Mathcad environment. The presented mathematical model makes it possible to quantitatively evaluate the operating time when using forced technological modes and increased energy consumption, as well as to assess the degree of reduction in the operating time, as a result of the total action of damaging factors, for an arbitrary point in time under operating conditions.

Construction of the destination set of a dynamic system in $\mathbb{R}^3$

The article proposes two algorithms for the numerical construction of the convex hull of a set in three-dimensional space using its support function. The first uses the hyperplane intersection method to find the pivot points of a set. The second one is based on the deformation function and allows you to find an arbitrary point of the convex hull of a set, which is convenient in many applications. The algorithms are compared, and asymptotic complexities are found. The application of the proposed apparatus to finding the destination set of dynamical systems is shown. The dynamic system will be based on differential inclusion.