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This paper investigates the effect of friction on the buckling behavior of a thin, shallow, elastic spherical shell under uniform external pressure based on an axisymmetric model of the finite element method. The study examines a combination of different geometric parameters with three different types of boundary conditions: clamped, hinged, and frictional ends with a wide range of friction coefficients. Friction has a significant influence on the buckling response of the spherical shell for all geometric parameters. In general, the critical pressure decreases as the friction coefficient or geometric parameter decreases. The buckling behavior of the frictional end with small friction coefficients presents an obvious difference compared to the results of high coefficients. For certain geometric parameters, the buckling mode of the spherical shell is transited because of changing the friction coefficient. A buckling map that describes the dependence of critical pressure on both friction coefficient and geometric parameter combined with buckling mode is generated. This map can be applied to the design of the spherical shell against buckling. [ABSTRACT FROM AUTHOR]

In this paper the authors analysed four single-layered braced barrel vaults with different types of bracing. Each braced barrel vault covered the area of 20 m × 28 m and was made from steel hollow sections. The static-strength analyses of the structures were conducted using the Autodesk Robot Structural Analysis program, taking into account self-weight, glass cover, snow load and wind load. In the case of wind load, wind pressure perpendicular to the longitudinal wall was determined in accordance with the EN 1991-1- 4 standard. However, the standard does not specify how to calculate wind pressure perpendicular to a gable wall for braced barrel vaults. For this reason, two variants suggested by the authors of this article were analysed for this direction of the wind. The influence of the type of bracing on force distribution in a braced barrel vault and on material consumption was analysed. The impact of the gable wall boundary conditions on force distribution in the braced barrel vault was also evaluated. Both the bracing type and the boundary conditions had an impact on the force distribution in the analysed braced barrel vault. [ABSTRACT FROM AUTHOR]

We propose an axisymmetric silicon nanoresonator with designed tapered angle well for the extraordinary enhancement of the decay rate of magnetic dipole (MD) emitters. Due to the resonant coupling of a MD emitter and the MD mode of the subwavelength resonator, the Purcell factor (PF) can easily reach 500, which is significantly higher than the PF when using a silicon nanosphere of the same size. The PF and the resonance frequency are conveniently tuned through the resonator diameter and the taper angle of the blind hole. When supported by a metallic substrate, further enhancement ( > 10 3 ) of the MD spontaneous emission is triggered by an image-induced quadrupolar high-Q mode of the nanoantenna. For the sake of comparison we include a critical analysis of the canonical problem that considers a Si spherical shell. Our results might facilitate a novel strategy for promising realizations of chip-scale nanophotonic applications. [ABSTRACT FROM AUTHOR]

Torsional vibrations of composite poroelastic dissipative spherical shell are investigated in the framework of Biot's extension theory. Here composite poroelastic spherical shell consists of two spherical shells, one is placed on other, and both are made of different poroelastic materials. Consideration of the stress-free boundaries of outer surface and the perfect bonding between two shells leads to complex valued frequency equation. Limiting case when the ratio of thickness to inner radius is very small is investigated numerically. In this case, thick walled composite spherical shell reduces to thin composite spherical shell. For illustration purpose, four composite materials, namely, Berea sandstone saturated with water and kerosene, Shale rock saturated with water and kerosene are employed. The particular cases of a poroelastic solid spherical shell and poroelastic thick walled hollow spherical shell are discussed. If the shear viscosity of fluid is neglected, then the problem reduces to that of classical Biot's theory. Phase velocity and attenuation are computed and the results are presented graphically. Comparison is made between the results of Biot's extension theory and that of classical Biot's theory. It is conclude that shear viscosity of fluid is causing the discrepancy of the numerical results. [ABSTRACT FROM AUTHOR]

In order to improve the function of driving of wheeled soccer robot and solve the time delay of the pivot steering motion of traditional robot, an artificial intelligent control algorithm for steering motion of wheeled soccer robot was proposed. Combined with the calculation of double eccentric steering motion control, the driving characteristic of wheeled soccer robot steering eccentric mass block was analyzed. Then, D'Alembert's principle was used to analyze the stress of robot and design the kinematics model of spherical shell steering of spherical mobile robot. Moreover, the stick-slip principle was used to control the steering of wheeled soccer robot. Thus, the steering motion control of robot was achieved. Experiment results prove that the steering speed of wheeled soccer robot is 30% higher than that of traditional robot, which effectively solves the problem about the time delay of traditional robot steering motion. [ABSTRACT FROM AUTHOR]

We have proposed and developed a new quadruped walking robot with a spherical shell, called "QRoSS". QRoSS is a transformable robot that can store its legs in the spherical shell. The shell not only absorbs external forces from all directions, but also improves mobile performance because of its round shape. In rescue operations at a disaster site, carrying robots into a site is dangerous for operators because doing so may result in a second accident. If QRoSS is used, instead of being carried in, robots are thrown in, making the operation safe and easy. We developed the QRoSS series and conducted basic experiments to verify performance, which includes landing, rising and walking through a series of movements. This paper reports details of a mechanical design to improve walking performance and development of the QRoSS V prototype model. We discuss the rising operation and performance of climbing over a high vertical step. [ABSTRACT FROM AUTHOR]

In this paper, we proposed an amphibious spherical robot that can search and rescue from uneven terrain and also move in narrow underwater spaces. This paper presents three control methods for an articulated amphibious spherical robot. The first is a full-dimensional that is adapted the robot to the complex amphibious terrain, in this method, relying on a novel drive mode of mecanum wheels, the power required for the movement comes from the friction generated by mecanum wheels and the spherical shell. The second control method is modeling based on a unit quaternion motion control algorithm to realized 6 Degrees of Freedoms (DoFs) movement mode. The last control algorithm is according to Archimede Buoyancy Principle (ABP) and Fuzzy Control (FC) algorithm by controlling the air density of the spherical capsules in the lower hemispheres, the relationship between buoyancy and gravity is controlled to achieve the functions of floating and diving. Experiments are performed to demonstrate the effectiveness of the proposed methods and the developed robot. [ABSTRACT FROM AUTHOR]

This article concerns a novel solution for folded reflectarray antennas which makes use of a curved (spherical) polarizer. The proposed solution provides a high gain and stable performances on a large bandwidth. A gridded substrate is also employed to minimize the dielectric losses in each reflectarray element, allowing the use of low-cost dielectric materials. Furthermore, 3-D printing technology has been used to manufacture both the polarizer and the reflectarray substrate. A linearly polarized, 28 dBi gain, Ku-band, entirely plastic prototype has been designed, manufactured, and tested. Measurements confirm the feasibility of the proposed solution and show its good performances (54% aperture efficiency and 1 dB down gain bandwidth of about 17%). [ABSTRACT FROM AUTHOR]

This paper continues a series of studies dealing with noninvasive preoperative methods for localizing eloquent areas of the human brain. The inverse problem of magnetoencephalography (MEG) is illposed and difficult for both analytical and numerical solutions. An analytical formula is derived for the solution of the forward problem that computes the magnetic field on the surface of the head from the known location and orientation of a current dipole in the low-frequency approximation in the spherical model. In addition, the paper considers the question of stability of solutions of the inverse problem of MEG to the effect of noise. The solution is unstable to the effect of noise on its angular component, but the deviation from the true solution is much less than the noise variance. [ABSTRACT FROM AUTHOR]

The C@ZrSiO4 pigments offer a viable alternative to spinel black pigments, but they have poor tinting strength due to low encapsulation rate. The aggregate and irregular morphology limits their application. Herein, as a three‐in‐one solution for the above issues, we report a highly dispersed submicronic inclusion black pigment with deep dark hue by double‐shell reaction sintering method for the first time. The morphological advantage of spherical CSs (carbon spheres) @ZrSiO4 pigments has successfully stimulated a significant increase in chromatic performance with L* value of 13.58. In addition, the suspension stability of the pigments in solution was verified, and the effect of the order of double shell on the encapsulation efficiency was studied. [ABSTRACT FROM AUTHOR]

A new transmission theory of "global dynamic wrap angle" for friction hoist is proposed. The theory is based on a mine hoist simulation model which combines the suspended rope with the wrapped rope. Rope dynamics in a suspended section are verified by the field experiment results. The theory holds that the mechanical state of wire rope is dynamic through the whole wrap angle, including deformation, contact and friction. When the rope enters the wrap angle, it provides positive friction and changes direction at a certain boundary point. The demarcation of the boundary depends on the rope load on both sides of the friction pulley. The theory is suitable for accurately analyzing the kinetics of high-speed and heavy-load friction hoisting. [ABSTRACT FROM AUTHOR]

We give a geometric account of kinematic control of a spherical rolling robot controlled by two internal wheels just like the toy robot Sphero. Particularly, we introduce the notion of shape space and fibers to the system by exploiting its symmetry and the principal bundle structure of its configuration space; the shape space encodes the rotational angles of the wheels, whereas each fiber encodes the translational and rotational configurations of the robot for a particular shape. We show that the system is fiber controllable—meaning any translational and rotational configuration modulo shapes is reachable—as well as find exact expressions of the geometric phase or holonomy under some particular controls. We also solve an optimal control problem of the spherical robot, show that it is completely integrable, and find an explicit solution of the problem. [ABSTRACT FROM AUTHOR]

This work presents the nonlinear post-buckling behavior of carbon nanotubes (CNTs) reinforced sandwich composite annular spherical (AS) shells supported by elastic foundations in the thermal environment. This paper takes advantage of the sandwich-structured configuration with three layers: two nanocomposite face sheets and an isotropic core to analyze the static problem. Due to the precious properties, CNTs are applied to reinforce nanocomposite face sheets of AS shells. The governing equations of the nonlinear mechanical response of CNTs reinforced sandwich-structured composite (SSC) AS shells are achieved by using the classical shell theory (CST) and taking von Kármán's geometrical nonlinearity into account. Applying Airy's stress function and an approximate solution, we propose a form of stress function for CNTs reinforced SSC AS shells. The detailed effects of different types of CNTs' reinforcement and volume fractions, geometrical parameters, core to face sheet thickness ratio, Winkler and Pasternak elastic foundations on the nonlinear mechanical post-buckling analysis are examined. [ABSTRACT FROM AUTHOR]

Substructure hybrid simulation test (SHST) is a novel seismic experimental method for analyzing structures, which usually divides the global structure into two components: the experimental substructure and the numerical substructure. An SHST system based on the OpenFresco platform was established. To ensure the high accuracy of the numerical substructure in SHST, a finite element model that corresponded to a quasi-static experimental investigation on high-strength steel composite K-shaped eccentrically braced frame (K-HSS-EBF) was established and analyzed using OpenSees. A three-story and five-span spatial K-HSS-EBF was used as the prototype and the three-story steel frame with a K-eccentric brace on the left second span was taken as the experimental substructure. The remaining four-span was modeled as a numerical substructure in OpenSees. SHST was performed with a half-scale hybrid simulation model. According to the test results, the displacement loading precision of the experimental substructure was analyzed. In addition, the shear link rotations of the experimental and numerical substructures were compared. The time curve of the displacement and the base shear of the hybrid simulation model were also compared with the simulation results of the global numerical model. The results revealed that the seismic response characteristics of the K-HSS-EBF were successfully recaptured using the numerical substructure model established in OpenSees and the spatial SHST system based on OpenFresco. [ABSTRACT FROM AUTHOR]

This study deals with the dynamic instability problem of spherical shells composed of carbon nanotubes/fiber/polymer composite (CNTFPC) with delamination around a central cutout. A multiscale analysis using the Hewitt and Malherbe equation was performed to determine the carbon nanotube (CNT) weight ratios, thickness–radius ratios, thickness–length ratios, and delamination area ratios around the cutout. A delamination around a central cutout was modeled in two dimensions by introducing the continuity conditions of displacements at the delamination boundaries. The proposed approach has been verified through a comparison of the results obtained with previous ones. The parametric study showed the significance of a proper CNT ratio and curvature for better structural performance on the dynamic stability of delaminated CNTFPC spherical shells. [ABSTRACT FROM AUTHOR]

The paper focuses on the buckling of circumferentially corrugated cylindrical shells under uniform external pressure, along with the effects of corrugation on the buckling. The buckling of unstiffened and corrugated cylindrical shells are studied using a numerical method. The nonlinear numeric compares well with the existing experiment. Then, the buckling of triangle, half-circle, and sine corrugated shells are, respectively, presented, which demonstrates that the sine-shaped corrugation leads to best buckling pressure. Subsequently, several sine-shaped corrugated cylindrical shells with different corrugation amplitudes are evaluated. On this basis, preferred mass and volume equivalent corrugated shells are, respectively, used to make a comparison with the unstiffened cylindrical shell. Finally, the effects of diameter, thickness, and material properties on the buckling of preferred corrugated shells are, respectively, investigated. The results show that the circumferentially sine-shaped corrugation with the half period-to-amplitude ratio of 4.4 can enhance the buckling pressure of shell by more than four times. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the self-propelled particles confined on a spherical substrate and explore the structural and dynamic properties of self-propelled particles by controlling the packing fraction and activity. We find that these self-propelled particles freeze into the crystal with the increase in the packing fraction. We observe the pattern evolution of inevitable topological defects due to the geometric constraints of the spherical substrate. During the process of freezing, there is a transition from twelve isolated grain boundaries to the uniform distribution of defects with the increase in the self-propelled velocity. Finally, we establish a phase diagram of the freezing process. These results may deepen our understanding of active particles in complex and crowded environments. [ABSTRACT FROM AUTHOR]

The thin plate spline (TPS) is an interpolation approach that has been developed to investigate a frequently occurring problem in geosciences: the modelling of scattered data. In this paper, we carry over the concept of the thin plate spline from the plane to the sphere. To develop the spherical TPS, we utilize the idea of an elastic shell that is attributed with the bending energy and the external energy. The bending energy describes the shape of the membrane, while the external energy reflects deviations between the shell and the data to be modelled. Minimizing both energy terms leads to the variational problem with the solution in the form of the Euler–Lagrange equations. We provide the solution of the variational problem for two cases: (1) total energy minimization over the whole sphere and (2) total energy minimization over a closed region of the sphere. In case (1) we found a closed analytical solution in the form of collocation in a reproducing kernel Hilbert space. The local case (2) solution is based on a discretization of the corresponding Euler–Lagrange equation using the spherical Laplace operator. The performance of the introduced spherical TPS is demonstrated on two real world data sets. It is shown quantitative that the thin plate approach is significantly more effective than Gaussian filter in terms of the GRACE data de-striping. We also show that the TPS can be used effectively for the modelling of the vertical total electron content. It allows the reduction of the computational effort in comparison with well-established planar TPS approximation. Moreover, the harmonicity property of the TPS can be utilized to solve various issues related to Earth gravity modelling. [ABSTRACT FROM AUTHOR]

The Kiewitt spherical reticulated shell of triangular pyramid system is taken as the object of this study; a macroprogram of parametric modeling is developed by using the ANSYS Parametric Design Language. The minimum structural total weight is taken as the objective function, and a shape optimization program is proposed and compiled by adopting the sequence two-stage algorithm in FORTRAN environment. Then, the eigenvalue buckling analysis for Kiewitt spherical reticulated shell of triangular pyramid system is carried out with the span of 90 m and rise-span ratio of 1/7~1/3. On this basis, the whole nonlinear buckling process of the structure is researched by considering initial geometrical imperfection. The load-displacement curves are drawn, and the nonlinear behaviors of special nodes are analyzed. The structural nonlinear behaviors affected by rise-span ratio are discussed. Finally, the stability of reticulated shell before and after optimization is compared. The research results show that (1) users can easily get the required models only by inputting five parameters, i.e., the shell span (S), rise (F), latitudinal portions (Kn), radial loops (Nx), and thickness (T). (2) Under the conditions of different span and rise-span ratio, the optimal grid number and bar section for the Kiewitt spherical reticulated shell of triangular pyramid system existed after optimization; i.e., the structural total weight is the lightest. (3) The whole rigidity and stability of the Kiewitt spherical reticulated shell of triangular pyramid system are very nice, and the reticulated shell after optimization can still meet the stability requirement. (4) When conducting the reticulated shell design, the structural stability and carrying capacity can be improved by increasing the rise-span ratio or the rise. (5) From the perspective of stability, the rise-span ratio of the Kiewitt spherical reticulated shell of triangular pyramid system should not choose 1/7. [ABSTRACT FROM AUTHOR]

In the dynamic and quasi-static statements, the issue of non-stationary deformation and stability of the solid propellant rocket engine (SPRE) was approximately solved. It is modeled by a thin, smooth cylindrical shell, inside of which, on a part of its length, there is an elastic base corresponding to a gradually burning powder charge. A pressure wave is moving along the outer surface of the body, simulated by the running load. The deformed state of the shell is considered axisymmetric and is determined on the basis of the moment theory of the shells. For diverse variants of mounting the ends of the shell in a closed form, expressions were obtained for the critical velocity of the load. Examples were considered. [ABSTRACT FROM AUTHOR]

This paper aims to improve the collaboration ability and stability of amphibious spherical robots (ASRs). According to our previous researches, robots have no communication or control stability module. This study designed a new torque gyro control stability and an artificial electronic communication module devoted to allowing the robot to both move on land and underwater, which used a gyro sensor to design a closed-loop control module to perform terrestrial locomotion efficiently. Regarding the spherical robot mechanical structure and dynamic model, the robot communication module is designed, and the physical robot is set up to complete specific experiments. In addition, it is necessary to analyze the underwater and land motion to evaluate the performance of the robot stability motion and communication module, which includes the gait stability and velocity, and predicts the effects of the key parameters, such as electrode distance and emitter current of the amphibious spherical robot when it moves in underwater or on land. We also characterize communicate performance of the robots in still water with obstacles and natural water conditions. [ABSTRACT FROM AUTHOR]

In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter. [ABSTRACT FROM AUTHOR]

The aim of this paper is to determine the critical buckling load for simply supported thin shallow spherical shells made of functionally graded material (FGM) subjected to uniform external pressure. A metal-ceramic functionally graded (FG) shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure metal on the inner surface to pure ceramic on the outer surface. First, the total potential energy functional is obtained using the first-order shell theory of Love and Kirchhoff, Donnell-Mushtari-Vlasov kinematic equations and Hooke's Law. Then, equilibrium equations are derived through the minimization of the total potential energy functional by employing the Euler equations. The stability equations are derived by application of the adjacent - equilibrium criterion. As the nonlinear strain-displacement relations are employed, so the presented analysis is nonlinear with high accuracy. The Galerkin method is used to determine the critical buckling load. The present problem is also analyzed numerically by simulating it in Abaqus software. For validation, the present analytical results are compared with the present numerical results and with the known data in the literature. Also, the effects of some important geometrical and mechanical parameters on the hydrostatic buckling pressure are investigated. [ABSTRACT FROM AUTHOR]

Dust particles are the main aerosol component of the atmosphere, and can influence human, environmental, and ecological health. Particle size distribution is an important aerosol micro-physical parameter that denotes the concentration distribution of particles of different radii and can determine the extinction characteristics of these particles. In traditional inversion algorithms, the aerosol is generally assumed to be spherical according to Mie theory, and the relationship between aerosol optical thickness and particle size distribution is described by the Fredholm integral equation of the first kind. For non-spherical dust particles, this spherical assumption is obviously unreasonable and yields unreliable results. Therefore, we developed an algorithm assuming non-spherical particles for inversion of dust particle size distributions. In the case of non-spherical particles, the extinction efficiency factor kernel functions of the ellipsoid were calculated using the anomalous diffraction approximation method, and the kernel function of Mie scattering theory was substituted with these new kernel functions. Moreover, the Phillips–Twomey method was employed to solve the Fredholm integral equation of the first kind using aerosol optical thickness data from a CE-318 sun photometer. To verify the feasibility of the anomalous diffraction approximation method, experiments were carried out under sunny, dusty, windy and hazy weather conditions. These experiments showed that the extinction kernel function for non-spherical particles obtained using the anomalous diffraction approximation method is suitable for inversion of non-spherical dust particle size distributions under different weather conditions in the Yinchuan area. [ABSTRACT FROM AUTHOR]

Astract This study examined the buckling of spherical caps with four different geometric imperfections: local inward dimple, increased-radius, force-induced dimple, and linear buckling mode. The influence of imperfection amplitude, meridional position, and meridional extent on cap buckling was numerically explored and partially validated using experiments. The numerical and experimental data were well consistent. Results indicated that, in the case of small-sized imperfections, the linear buckling mode-shaped imperfection presented a relatively conservative cap buckling prediction compared with those of the other three imperfections. This finding contradicts previous findings that the force-induced dimple imperfection is the most unstable imperfection. Highlights • Buckling of imperfect caps are numerically explored and experimentally validated. • Effect of imperfection amplitude, meridional position and extent on buckling is studied. • The linear buckling mode-shaped imperfection is relatively conservative. [ABSTRACT FROM AUTHOR]

Abstract General similitude requirements and the scaling laws for nonlinear buckling of stiffened orthotropic shallow spherical shells are presented by applying similitude transformation to the total energy of the structural system. In the absence of the experimental data, structural similitude is completed by numerical experiments. The predicted values of the prototype, obtained by substituting the model results into the scaling laws, are compared with those values of the prototype. In practical engineering, it may be hard to fulfill the complete similarity requirements. Thus, several cases of partial similitude are mainly investigated, including models distorted in material properties of ribs, in material properties and in material properties and geometry. By using specific formulas of stiffness parameters and the displacement scale factor, distorted models can predict geometric nonlinear buckling behavior of the prototypes of the stiffened orthotropic shallow spherical shell under external pressure with good accuracy. Highlights • We establish general similitude requirements and the scaling laws for nonlinear buckling of stiffened orthotropic shallow spherical shells are presented by energy approach. • By using specific formulas of stiffness parameters and the displacement scale factor, we establish the distorted models. • We investigate complete similitude and partial similitude for nonlinear buckling of stiffened orthotropic shallow spherical shells by numerical experiments. [ABSTRACT FROM AUTHOR]

With the development of sheet metal forming technology and the increase in the application of spherical shell parts, flexible male die drawing technology has become one of the research hotspots because of its merits on strong applicability and ability to significantly increase the forming limit of the sheet. As a new type of flexible male die drawing process, solid granule medium forming (SGMF) has been rapidly developed in recent years. During the granule medium drawing process, there is a significant reduction in the thickness of the sheet metal in the female die in addition to the flange deformation. Thus, the stress state and the required forming force during the sheet metal forming process are very different from those during the conventional drawing. Taking the deformation process of the spherical shell parts as research object, the stress state of the spherical shell and the pressure of the granule medium were studied between the single drawing deformation and the single bulging deformation. On this basis, the stress model, pressure model, and required forming force model of the spherical shell parts in the granule medium drawing process were established with the drawing weight and bulging weight. Theoretical analysis, experiments, and FEM-DEM numerical simulations were employed to study the deformation of the spherical shell parts. The results show that the mechanical model based on the weight function theory can accurately reflect the stress state of the spherical shell parts during SGMF and can fully reveal the sheet metal deformation mechanism during SGMF. In addition, the theoretical analysis model established in this paper provides necessary theoretical support for the selection of equipment for SGMF process in practical application. [ABSTRACT FROM AUTHOR]

The inverse dynamic model of a three-revolute–prismatic–spherical parallel robot based on Lagrange method is presented. This parallel robot presents a different configuration in the orientation of the actuators of the already reported in the literature. The dynamic model is validated by simulations obtained with a virtual prototype under MSC Automatic Dynamic Analysis of Mechanical Systems environment. For positioning the moving platform in a desired orientation, a proportional–integral–derivative-type controller is implemented for trajectory tracking using the dynamic of the actuators. In this dynamic, the load supported is unknown, that is, due to the inclination of the moving platform, the weight is not evenly distributed. Algebraic identification of parameters is implemented in order to know the load and improve the response in the orientation of the moving platform. Some simulations were performed with the virtual prototype in co-simulation environment under MSC Automatic Dynamic Analysis of Mechanical Systems/View and MATLAB/Simulink to verify the performance of the proportional–integral–derivative controller using the algebraic parameters identification. [ABSTRACT FROM AUTHOR]

Abstract Welded hollow spherical joints (WHSJs) are commonly used joints in reticulated shell structures. Corrosion that occurs on the surface of WHSJs can considerably reduce the compression capacity of WHSJs with randomly distributed corrosion. Randomly located corrosion is a typical corrosion type on steel structures. However, the influence of randomly located corrosion on the loading capacity of WHSJs has not yet been quantified. This work aims to construct a probabilistic distribution model of the compression capacity of WHSJs with randomly located corrosion and to establish the relationship between such model and the specified corrosion (including corroded thickness T c , corrosion diameter D c , and corrosion number n) and geometric parameters (including the thickness T and diameter D of the spherical body). The influences of the corrosion and geometric parameters on the random distribution of compression capacity were first analyzed. Then, the probabilistic distribution model of the compression capacity of WHSJs with randomly located corrosion was established. The analytical method presented in this study achieved high accuracy in predicting the probabilistic distribution model of compression capacity with specified T c /T , n , and D c. Highlights • The method to determine probabilistic model of reduction factor was proposed. • The formulae for predicting the variation of normal distribution was put forward by surface fitting technology. • The method to determine the probabilistic model of reduction factor corresponding to different D c was put forward. [ABSTRACT FROM AUTHOR]

Based on the applied theory of shells, an energy-consistent resolving system of equations is constructed, and a complex numerical method is developed which, within in the framework of an explicit variational-difference scheme, makes it possible to solve both quasi-static and dynamic problems of nonlinear nonaxisymmetric deformation and buckling of composite cylindrical shells. The quasi-static loading mode is simulated by setting an internal pressure in the form of a linearly increasing function reaching a steady-state value during three periods of vibration of a composite cylindrical shell at the lower form. The critical buckling load is determined by the characteristic kink on the maximum deflection–loading amplitude curve. The reliability of the method developed is substantiated by comparing calculation results with experimental data. The characteristic forms and critical buckling loads of GRP cylindrical shells as functions of the level of preloading by a quasi-static internal pressure and of the subsequent dynamic loading by an external pressure are analyzed for various reinforcement patterns in a wide range of loading rate. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the free vibration characteristics of uniform and stepped annular-spherical shells are investigated by using a semi-analytical approach with general boundary conditions. The theoretical model of annular-spherical shell is established by using Flügge's thin shell theory, and the annular-spherical shells are divided into their segments along the axial direction. The displacement functions of shell segments are consist of the Jacobi polynomials along the axial direction and the standard Fourier series along the circumferential direction. The boundary conditions at the ends of the shells and the continuity conditions at two adjacent segments were enforced by penalty method of spring stiffness technique. Then, the accurate solutions about the vibration characteristics of uniform and stepped annular-spherical shells were solved by method of Rayleigh–Ritz. The accuracy and reliability of the proposed method are verified with the results of FEM and published literatures. The results show that the present method has good convergence ability and excellent accuracy. In addition, some numerical results of uniform and stepped annular-spherical shells with various geometric parameters and boundary conditions are reported, which can be used as reference data for future researchers. Highlights • A generalized and unified Jacobi-Ritz formulation is proposed in this paper. • The paper generalizes the selection of admissible displacement functions. • The penalty method was used to deal with the boundary and continuity conditions. [ABSTRACT FROM AUTHOR]

This paper presents the design methodology for a single-mobility, large surface-deployable mechanism using irregularly shaped triangular prismoid units. First, we demonstrate that the spherical shell, as the deployed profile of the large deployable mechanism, cannot be filled with identical regular-shaped triangular prismoids (truncated pyramid) without gaps, which makes the design challenging because a large set of nonidentical modules should be moved synchronously. Second, we discuss the design of a novel deployable mechanism that can be deployed onto irregularly shaped triangular prismoids, which will be used as the basic module to fill the spherical shell. Owing to high stiffness and ease of actuation, a planar scissor-shape deployable mechanism is applied. Third, we study the mobile assemblies of irregularly shaped modules in large surface-deployable mechanisms. We discover that hyper kinematic redundant constraints exist in a multiloop mechanism, making the design even more difficult. In order to address this issue, a methodology for reducing these redundant constraints is also discussed. Finally, a physical prototype is fabricated to demonstrate the feasibility of the proposed design methodology. [ABSTRACT FROM AUTHOR]

Both the tangent modulus theory and the double modulus theory are classical theories which can be applied to the elastic-plastic stability analysis of columns. In the traditional tangent modulus theory, numerous iterations are required to calculate the critical buckling stress and this makes the method very time-consuming. In this paper, an explicit formula for establishing a direct correlation between the critical stress and the Euler stress has been proposed to reduce trial calculations. This formula can be applied to spherical shells by simplifying their stiffened plates to the form of beams on elastic foundations. The explicit expressions of both modulus theories can be used to calculate the ultimate strength of a spherical shell under pressure. The results from the proposed expression are compared with experimental results and other numerical results. [ABSTRACT FROM AUTHOR]

Abstract The suggested before energy barrier criterion for design buckling pressure is extended to the case of clamped shallow spherical caps. It is developed for shells with geometrical imperfections and a new adjusted formula is obtained for design buckling load of imperfect structures. The method is applied to shells with elastic-perfectly plastic material. It is validated by experimental data and proved by numerical analysis based on finite element method. Calculation results were obtained and analysed for different values of shell geometrical parameter. A simple formula for design buckling pressure is suggested and validated. [ABSTRACT FROM AUTHOR]

Highlights • Ideal MHD turbulence contains an intrinsic dynamo mechanism (broken ergodicity). • Real MHD turbulence forced at mid-wavenumber k behaves like ideal MHD at low k. • Periodic box (Fourier) simulations are surrogates for spherical shell simulations. • Quasi-stationary or slowly translating largest-scale magnetic structures appear. • If Fourier methods are good surrogates, then Geodynamo – MHD turbulence. Abstract Ideal magnetohydrodynamic (MHD) turbulence contains an intrinsic statistical mechanism called 'broken ergodicity' for producing an energetic, large-scale, quasi-stationary coherent structure. Since MHD turbulence occurs in the Earth's liquid outer core, the implication is that the Earth's dipole magnetic field may be due to MHD turbulence, per se. The purpose of this work is to examine how ideal MHD results apply to the real (i.e. , dissipative) MHD turbulence found in the outer core. Prior theoretical and computational results will be briefly reviewed, after which new results will be presented. The significant effects caused by variations in the time-dependence of the forcing will be discussed. It will be also shown that dissipative MHD turbulence driven with isotropic forcing produces large-scale, coherent structures similar to those appearing in ideal MHD turbulence. A connection between spherical harmonic degree and turbulence wave number will be made, allowing for a qualitative comparison of numerical magnetic energy spectra with the International Geomagnetic Reference Field. In addition, a mechanism for explaining the dominance of the Earth's axial dipole component over its azimuthal ones will also be described. These results indicate that MHD turbulence, per se, may underlie the geodynamo. [ABSTRACT FROM AUTHOR]

Thin steel shells in the form of spherical segments, loaded by external pressure, have a tendency to sudden buckling under a lower pressure than their plastic resistance. The buckling phenomenon of spherical shells was the subject of research done by many authors and the previous results of theoretical and experimental research were used in the European Design Recommendations published in 2008 by European Convention for Constructional Steelwork. This article presents experimental research done on a specially designed and manufactured stand. Specimens were manufactured with a metal spinning technique from steel sheets usually used for deep drawing and stamping of metal objects. The actual shape of every specimen was determined with the three-dimensional scanning technique. Material research was also done on the steel sheets. Pressure was exerted with an air compressor and displacement was measured with the optical measurement system ARAMIS. The deformation modes of the whole specimen were registered precisely at every step of pressure exertion till the final postbuckling stage. All the data measured were registered automatically by two computers. The result of every experiment is presented in the form of an equilibrium path as the relationship of the pressure p as a function of a chosen displacement parameter. This article also presents a comparison between the critical pressures obtained during the experiments and the results obtained from the numerical simulations done with COSMOS/M. The experimental and the numerical results were also compared with the buckling resistances proposed by Rotter and Schmidt and Błażejewski and Marcinowski. [ABSTRACT FROM AUTHOR]

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitude-frequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates. [ABSTRACT FROM AUTHOR]

This paper considers a dense imploding spherical shell, where perturbations on the inner surface grow due to hydrodynamic instabilities, geometric convergence and compression. A low-convergence implosion with a single spherical harmonic mode perturbation with mode numbers in the range from ℓ = 5 to ℓ = 100 and at three different amplitudes is considered. The linear theory of Epstein [1] is extended to incorporate reshock, making it applicable to the full implosion process (while perturbations are linear). Linear theory is employed to choose modes such that quantified geometric convergence and compression effects contribute significantly to perturbation growth at the lower mode number, while at the higher mode number the contribution from Rayleigh–Taylor instability dominates. Simulation results from four independent simulation codes (FLASH, HYDRA, Miranda and Flamenco) are presented. The simulation predictions are validated against linear theory pre-reshock and employed to validate the extended theory across the reshock. The simulations continue to substantially non-linear perturbation amplitudes, beyond the limits of the analytical approach, and the presented perturbation amplitudes can inform future non-linear modeling. The simulated perturbation amplitudes agree to within approximately 10% for most cases, with isolated cases having differences of greater than 50% from the simulated ensemble-mean. This occurs in the case of a low mode number perturbation with a very small amplitude, where the growth of secondary small-scale instabilities leads to substantial differences between the codes after re-shock. [ABSTRACT FROM AUTHOR]

Stars similar to the Sun demonstrate super-flares, which are considerably more powerful than solar flares. It is believed that the magneticfield energies of these stars are much higher than that of the Sun. The present study attempts to explain such an anomalously high magnetic energy by resonance phenomena related to the stellar dynamo, which involve significant changes in the behavior of the solutions subject to certain external effects and satisfy certain parametric relationships. These resonance phenomena are studied using low-mode models for a dynamo occurring in two or one spherical shells. It is shown that resonance effects arising in these models can result in increases of the magnetic energies by one and a half orders of magnitude compared with nonresonance cases. It is also shown that resonance dynamo conditions can differ considerably from the simple resonance conditions used for oscillating systems. This can probably be explained by the fact that the excitation and propagation of magnetic waves in dynamo problems are closely connected with each other, so that the resonance equations remain nonlinear even when they are maximally simplified. [ABSTRACT FROM AUTHOR]

Based on a previously observed analogy between electromagnetic and non-inertial effects, we investigate the competition between magnetic field and rotation in the quantum motion of an electron constrained to the surface of a sphere. We solve numerically the Schrödinger equation of the problem for the energy eigenvalues and the eigenfunctions and compare the effects of the magnetic field and rotation. We obtain that, for a weak magnetic field, an electron can not distinguish between magnetic field and rotation, since they lead to equivalent behavior. But this is no longer true for strong magnetic fields. However, surprisingly, even though the rotation and magnetic fields play different roles in the electronic properties of the system, when together, each influence of the magnetic field on the energy levels can be separately balanced by rotation. We also show that no matter the intensity of the magnetic field, it is always possible to destroy the Landau levels in the sphere by rotation. [ABSTRACT FROM AUTHOR]

Radiation efficiencies of modal current densities distributed on a spherical shell are evaluated in terms of dissipation factor. The presented approach is rigorous, yet simple and straightforward, leading to closed-form expressions. The same approach is utilized for a two-layered shell and the results are compared with other models existing in the literature. Discrepancies in this comparison are reported and reasons are analyzed. Finally, it is demonstrated that radiation efficiency potentially benefits from the use of internal volume, which contrasts with the case of the radiation $Q$ -factor. [ABSTRACT FROM AUTHOR]

Based on the plane geometry and stereo geometry theory and the light refraction law, the output laser axial deviation angle is calculated in theory after passing through the spherical shell. Considering the detection and the launch system with different wavelength, the error between the detection and the launch is analyzed and the relationship is calculated. The calculated results show that the optical axis error must be considered when the wavelength is different between detection and the launch system. At the same time, the optical axis error should be compensated in the electro-optical system to achieve accurate detection and target tracking. [ABSTRACT FROM AUTHOR]

A semi analytical approach is employed to analyze the free vibration characteristics of uniform and stepped combined paraboloidal, cylindrical and spherical shells subject to arbitrary boundary conditions. The analytical model is established on the base of multi-segment partitioning strategy and Flügge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of uniform and stepped combined paraboloidal, cylindrical and spherical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of proposed method, convergence study and numerical verifications for combined paraboloidal, cylindrical and spherical shell with different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with FEM. In addition, some interesting results about the geometric dimensions are investigated. [ABSTRACT FROM AUTHOR]

Abstract: Today, robots are expected to be used for the inspection of infrastructures such as bridges. One important task in bridge inspection is to acquire clear images of its various parts for further damage evaluation. However, this task has not yet been completely realized because of the complexity of bridge structures. For this situation, a UAV with a passive rotating spherical shell (PRSS) that can easily maneuver while protecting itself is introduced. In this paper, we explain the development of the PRSS unmanned aerial vehicle (UAV) based on the design strategy. We then analyze its performance through simulated bridge inspection. Finally, we discuss the results of actual bridge experiments. The spherical shell has a size ( D = 0.95 m) and structure (fullerene) that is well‐suited for bridge inspection applications. It can also handle an impact equivalent to 2 m/s, which is more than the UAV's maximum flight speed. Test flight experiment also validated the characteristic of PRSS that shows a stable flight during disturbances. The image test also shows that the visual system can provide a full overhead view of the bridge. Likewise, it can detect a 0.1‐mm wide line that replicates the damage (e.g., a crack) from a position 0.5 m away and while the camera moves at 0.3 m/s. These characteristics have yielded a system that can acquire inspection images from critical parts of the bridge. An evaluation by third parties confirmed the effectiveness of the system. Further, the system satisfies the mandatory requirements of the Next Generation Robots for Social Infrastructure (NGRSI) program. [ABSTRACT FROM AUTHOR]

This manuscript studies the impact of non-integer dimensional (NID) space on cloaking and magnification introduced through polarly radially anisotropic (PRA) cylindrical shell/spherically radially anisotropic (SRA) spherical shell. By selecting appropriate value of ratio, between components of tensor permittivity, these structures in ordinary space ( α = 3 ) can yield cloaking and magnification under the quasi-static limit. In case of NID space ( α ≠ 3 ), PRA cylindrical shell can only yield cloaking. It has been shown that bound on anisotropy ratio get effected by the NID parameter in case of PRA shell. It has also been noted that magnification cannot be achieved using PRA shell in NID space. Further, cloaking and magnification of SRA shell remains independent of parameter describing NID space. [ABSTRACT FROM AUTHOR]

This paper focuses on two opening reinforcement methods of spherical shells under uniform external pressure. To reduce the local weakening and buckling effects of openings in spherical shells, designs comprising the wall reinforcement and the combination of a wall and thick plate reinforcement were employed to minimize buckling instability. In addition, the equal-proportion models of two kinds of reinforcement methods were manufactured and tested. The geometry, thickness, buckling load, and final collapsed mode were measured for each spherical shell with opening reinforcement. The paper contains a comparison between theoretical predictions, numerical analysis results and experimental data for two reinforced spherical shells. The theoretical and numerical results were in good agreement. The numerical solution result, obtained by considering the real defect, was consistent with the experimental result, and the failure mode was consistent with the location of the defect. [ABSTRACT FROM AUTHOR]