Variable Curvature Research Articles

How Slab Age and Width Combine to Dictate the Dynamics and Evolution of Subduction Systems: A 3‐D Spherical Study

AbstractMany of the factors expected to control the dynamics and evolution of Earth's subduction zones are under‐explored in an Earth‐like spherical geometry. Here, we simulate multi‐material free‐subduction of a complex rheology slab in a 3‐D spherical shell domain, to investigate the effect of plate age (simulated by covarying plate thickness and density) and width on the evolution of subduction systems. We find that the first‐order predictions of our spherical cases are generally consistent with existing Cartesian studies: (a) as subducting plate age increases, slabs retreat more and subduct at a shallower dip angle, due to increased bending resistance and sinking rates; and (b) wider slabs can develop along‐strike variations in trench curvature due to toroidal flow at slab edges, trending toward a “W”‐shaped trench with increasing slab width. We find, however, that these along‐strike variations are restricted to older, stronger, retreating slabs: Younger slabs that drive minimal trench motion remain relatively straight along the length of the subduction zone. We summarize our results into a regime diagram, which highlights how slab age modulates the effect of slab width, and present examples of the evolutionary history of subduction zones that are consistent with our model predictions.

Design and analysis of a wheel-leg compound variable curvature ship hull cleaning robot

Underwater robotic cleaning devices are promising in ship hull maintenance for biofouling removal, but there are still some challenges for commercial application. Due to the complex surface of the ship hull, larger adsorptive force is needed for climbing robots to solve the problem of poor fitting between rigid structure and ship hull, which calls for more driving power. To mitigate the gap, this paper proposed a flexible wheel-leg composite moving mechanism for ship hull cleaning robots. The designed adjustable wheel leg, which is composed of three leg frames on the rotating shaft, eliminates the magnetic wheel's position constraints and expands the movement space. The relation equations of flip angle, pitching angle, turning angle, and hull curvature radius are generated and analyzed based on the robot's posture and steering motion. The mechanical properties of anti-slippage and anti-shedding under different motion states were studied so that the robot's critical point and limit adsorption force could be determined and verified. Simulation results show that the robot has good motion stability.

Велароидальные оболочки и оболочки велароидального типа

A group of velaroidal surfaces and surfaces of the velaroidal type belong to the class of "Translation Surfaces". In contrast to the direct translation surfaces, velaroidal surfaces are formed by curves of variable curvature so that the formed surface rests on straight lines of a flat rectangular contour. Only about a dozen velaroidal surfaces have been described and studied in the scientific and technical literature. Velaroidal surfaces are also formed by curves of variable curvature but supported by a flat oval or circular contour. A super ellipse can be taken as a flat contour. The contour may consist of fragments of two identical curves located symmetrically about the axis of symmetry. In Russia velaroidal surfaces are studied so far only in the Peoples' Friendship University of Russia (RUDN University), Moscow. They are popular with both research geometrists and students - architects and builders, who believe that these shapes can be used within parametric, nonlinear, evolutionary and generative architecture. The article provides information with reference to the extensive used bibliographic material on the geometry of known velaroidal surfaces and surfaces of the velaroidal type. Information on the construction and visualization of new velaroidal surfaces with an oval flat contour as a super ellipse, as well as with a frame and a guide super ellipse. The data on determination of the stress-strain state of thin shells with median surfaces in the form of the surfaces under consideration is given. The fields of practical application of velaroidal shells and velaroidal shells are indicated. As shown in the sources used, geometers and calculation engineers have solved almost all the issues related to the design of these shells. Architects use velaroidal shells rarely, mostly to cover industrial buildings. Enclosures of velaroidal type have been used only in draft designs and in diplom works of architecture students.

Proof-of-concept study of bolt connection status monitoring using fiber Bragg grating curvature sensor

For connection status monitoring of bolted joint groups, a novel method with fiber Bragg grating (FBG)-based curvature sensor is proposed. An FBG curvature sensor with an inextensible elastic matrix and an offset grating is adopted and clamped between a fixed support and the monitored bolt in a plane bending status. Based on the shape deformation of the FBG curvature sensor induced by the bolt loosening, the bending curvature change of the elastic matrix is measured by the FBG. By detecting the wavelength shift of the FBG induced by the matrix curvature variation, the relationship between the bolt loosening angle and the wavelength shift of FBG can be obtained, and hence the bolt connection status can be determined by the wavelength shift of FBG. Details of the proposed method are presented, and a surface-bonded FBG curvature sensor is designed, fabricated, and experimentally studied to verify the proposed method, and the parameters on sensing performance are also investigated. Experimental results show that the proposed method can monitor bolt loosening angle with high sensitivity and linear output by adjusting the parameters of the FBG curvature sensor. The looseness angle resolution of the proposed sensor can reach 0.0767°. This paper presents the first attempt to monitor bolt loosening angle using an FBG curvature sensor. With the advantages of high sensitivity and resolution, strong applicability, convenience and reusability for the maintenance of bolts, and ease of forming quasi-distributed sensor networks, the proposed method is able to provide a general solution for the on-line monitoring of bolt connection status for large-span distributed bolted-joint groups.

Failure analysis and curvature-based failure criterion of super large cooling tower under strong equivalent static wind load

More and more super large cooling towers are used in recent years. However, investigations on them under strong wind are still insufficient and there is still not an agreement failure criterion. In this paper, we conducted the failure analysis of a super large cooling tower with 253 m height under the equivalent static wind load. The finite element analysis procedure incorporates the multi-layered shell element, the softened damage model of concrete and the two-level secant algorithm in one framework. The numerical results show that the nonlinear response of the tower can be divided into four stages, i.e., the initial linear stage, the nonlinear stage, the softening linear stage and the failure stage. The failure of the cooling tower is caused by the loss of material strengths, i.e., the cracking of the concrete and the following yield of the meridian rebar. Finally, a curvature-based failure criterion is proposed to evaluate the failure of the cooling tower, in which the structure fails when the global curvature variation ratio ϰ reaches some definite values. ϰ is defined as the ratio of the total curvature variation with the initial total curvature of the cooling tower geometry. It can evaluate the total curvature variation in a global view. It is recommended that ϰ can be used as an index in the design of the cooling tower, and 1.0% and 3.5% can be deemed as the nonlinear and failure index, respectively.

Water-Air Interface to Mimic In Vitro Tumoral Cell Migration in Complex Micro-Environments.

The long-known role of cell migration in physiological and pathological contexts still requires extensive research to be fully understood, mainly because of the intricate interaction between moving cells and their surroundings. While conventional assays fail to capture this complexity, recently developed 3D platforms better reproduce the cellular micro-environment, although often requiring expensive and time-consuming imaging approaches. To overcome these limitations, we developed a novel approach based on 2D micro-patterned substrates, compatible with conventional microscopy analysis and engineered to create micro-gaps with a length of 150 µm and a lateral size increasing from 2 to 8 µm, where a curved water–air interface is created on which cells can adhere, grow, and migrate. The resulting hydrophilic/hydrophobic interfaces, variable surface curvatures, spatial confinements, and size values mimic the complex micro-environment typical of the extracellular matrix in which aggressive cancer cells proliferate and migrate. The new approach was tested with two breast cancer cell lines with different invasive properties. We observed that invasive cells (MDA-MB-231) can align along the pattern and modify both their morphology and their migration rate according to the size of the water meniscus, while non-invasive cells (MCF-7) are only slightly respondent to the surrounding micro-environment. Moreover, the selected pattern highlighted a significative matrix deposition process connected to cell migration. Although requiring further optimizations, this approach represents a promising tool to investigate cell migration in complex environments.

Numerical Simulation of Entropy Optimization in Radiative Hybrid Nanofluid Flow in a Variable Features Darcy–Forchheimer Curved Surface

Studies associated with ethylene glycol (EG) have great significance in various engineering sectors because EG is more useful as a cooling agent in various engines. Furthermore, fluid inspection using two distinct nanoparticles has applications in mechanical systems, electronic devices, medical apparatus, and the diagnosis and treatment of disease. Therefore, present comminution explored the entropy production in magnetized hybrid nanomaterials flowing via Darcy–Forchheimer space with varying permeability. Hybrid nano liquid is synthesized by adding cobalt ferrite and gold nanoparticles to ethylene glycol and water. Effects of thermal radiation, Joule heating, heat sources, and an exponential heat source are considered in the energy expression. The assumed problem is modeled in the form of nonlinear PDEs. Such types of problems have mostly occurred in symmetrical phenomena and are applicable in engineering, physics, and applied mathematics. The obtained system is converted to ODEs using suitable substitution transformations. Resultant ODEs are numerically computed with the help of the NDSolve technique using Mathematica software. Their outcomes are displayed through figures and tables. Obtained results reveal that variable permeability and curvature parameters improve the velocity profile, while an exponential heat source (EHS) enhances the thermal effect. It is also observed that entropy optimization improves with the increment in magnetic parameter.

Research on ultrasonic testing method of rotating component based on a 6-DOF robot

Some rotating components have the structural characteristics of variable thickness and variable curvature. The conventional ultrasonic testing is inappropriate for these components because of bad coupling and too many uncertainties. In order to meet the testing requirements of high-volume, high-efficiency and high-precision, the corresponding ultrasonic automatic detection program is proposed. A 6-DOF industrial robot is used to realize the precise control of the transducer position and posture, and combines the independent turntable to complete the spiral fast scan of the specimen. Based on the multi-Gaussian beam model and the internal flat-bottom hole flaw scattering model of specimen, the flaw ultrasonic measurement model is established. The system parameters, component material parameters and component surface parameters are all introduced to the ultrasonic measurement model to generate a series of flaw-sizing curves. An accurate flaw sizing method based on DGS(Distance-Gain-Size)curve predicted by regular reflector is proposed. The scanning experiment results of the reference specimen show that the minimum Ø 0.8mm artificial flat-bottom-hole flaw in the workpiece can be detected effectively, and the sizing error is less than Ø 0.3mm equivalent.

Scanning electron beam surface strengthening of column-faced 45 steel

• Columnar surface strengthening by scanning electron beam technology. • The effect of curvature on the microstructure of the fusion zone is investigated. • The relationship between microhardness distribution and curvature is established. • The carbon content of the sub-surface is higher than that of the near surface. To conquer the shortcomings that the column-faced 45 steel is susceptible to wear and failure, scanning electron beam was conducted to strengthen it, the microstructure and microhardness of the modified layer under variable workpiece curvature were investigated. The results revealed that the modified layer was composed of fusion zone and heat-affected zone, the depth of the modified layer manifested an ascend tendency as the increment of curvature. Martensite dominates the modified layer, and the carbon content of martensite for the sub-surface is higher than that of the near surface, moreover, the grain size of martensite first reduced and then increased with increasing of curvature. The position of the maximum microhardness along the direction of depth as the curvature increases, and the maximum microhardness of 1/20 curvature is 688.26 HV, which is about 3.13 times that of the matrix. This study demonstrated the potential of using scanning electron beam to reinforce column-faced 45 steel.

Research on time–frequency characteristics of contact force based on wavelet transform

When a train runs at high speed, affected by the structural characteristics of the catenary, the contact force changes periodically with span and dropper spacing. However, as the running speed of the train increases, the periodic signal of the contact force changes owing to the fluctuation of the catenary and the vibration of the pantograph, which directly affects the stable contact between the pantograph and catenary. Therefore, based on the simulation research method, this study uses the time–frequency transformation method to investigate the influence of changes in the catenary structure on the periodic signal of the contact force. First, the structural design of the catenary structure of the existing railway line is carried out by changing the length of the stitch wires and the dropper spacing, and the stiffness and stiffness curvature variation when the arrangement of the stitch wires and dropper varies are analysed. Then, the relationship between the stiffness, stiffness curvature variation, and contact force variation is analysed. Finally, the wavelet transform method is used to transform the contact force, and variations in the key amplitude component of the contact force are analysed when the structural parameters are changed, and the relationship between the period and the key amplitude component is obtained. By analysing the time–frequency characteristics of the contact force, technical support for improving the speed of the train can be provided.

Flamelet modeling of thermo-diffusively unstable hydrogen-air flames

In order to reduce CO2 emissions, hydrogen combustion has become increasingly relevant for technical applications. In this context, lean H2-air flames show promising features but, among other characteristics, they tend to exhibit thermo-diffusive instabilities. The formation of cellular structures associated with these instabilities leads to an increased flame surface area which further promotes the flame propagation speed, an important reference quantity for design, control, and safe operation of technical combustors. While many studies have addressed the physical phenomena of intrinsic flame instabilities in the past, there is also a demand to predict such flame characteristics with reduced-order models to allow computationally efficient simulations. In this work, a H2-air spherical expanding flame, which exhibits thermo-diffusive instabilities, is studied with flamelet-based modeling approaches both in a-priori and a-posteriori manner. A recently proposed Flamelet/Progress Variable (FPV) model, with a manifold based on unstretched planar flames, and a novel FPV approach, which takes into account a large curvature variation in the tabulated manifold, are compared to detailed chemistry (DC) calculations. Both flamelet approaches account for differential diffusion utilizing a coupling strategy which is based on the transport of major species instead of transporting the control variables of the manifold. First, both FPV approaches are assessed in terms of an a-priori test with the DC reference dataset. Thereafter, the a-posteriori assessment contains two parts: a linear stability analysis of perturbed planar flames and the simulation of the spherical expanding flame. Both FPV models are systematically analyzed considering global and local flame properties in comparison to the DC reference data. It is shown that the new FPV model, incorporating large curvature variations in the manifold, leads to improved predictions for the microstructure of the corrugated flame front and the formation of cellular structures, while global flame properties are reasonably well reproduced by both models.

Paraxial equivalent of the gradient-index lens of the human eye

The lens of the eye has a refractive index gradient that changes as the lens grows throughout life. These changes play a key role in the optics of the eye. Yet, the lens is generally simulated using a homogeneous model with an equivalent index that does not accurately represent the gradient. We present an analytical paraxial model of the gradient lens of the eye that gives the direct relation between refractive index distribution and paraxial characteristics. The model accurately simulates the changes in lens power with age and accommodation. It predicts that a decrease in equivalent index with age is associated with a flattening of the axial refractive index profile and that changes in lens power with accommodation are due primarily to changes in the axial variation of the iso-indicial curvature, consistent with Gullstrand's intracapsular theory of accommodation. The iso-indicial curvature gradient causes a shift of the principal planes compared to the homogeneous equivalent model. This shift introduces a clinically significant error in eye models that implement a homogenous lens. Our gradient lens model can be used in eye models to better predict the optics of the eye and the changes with age and accommodation.

RBF network-based adaptive sliding mode control strategy for the tendon-sheath driven joint of a prosthetic hand.

The complex in-hand manipulation puts forward higher requirements for the dexterity and joint control accuracy of the prosthetic hand. The tendon-sheath drive has important application potential in the fields of prosthetic hand to obtain higher dexterity. However, the existing control methods of tendon-sheath driven joint are mainly open-loop compensation based on friction model, which makes it difficult to achieve high-precision joint control. The purpose of this work is to improve the position control accuracy of the tendon-sheath driven joint for the prosthetic hand. The structure of the prosthetic hand is introduced, and the encoder and potentiometer are mounted on the driving motor and joint respectively. Then, the transfer function of the joint is established based on the dynamic model. The adaptive sliding mode control strategy based on RBF network is applied to realize the closed-loop feedback position control of the prosthetic hand joint. The stability of the system is demonstrated by Lyapunov theorem. Under the condition of constant and variable sheath curvature, the effectiveness of the controller is demonstrated by simulation and joint motion experiments, respectively. The results show that the closed-loop control has better position tracking ability than the open-loop control, and the designed controller can reduce the tracking error more obviously than the traditional algorithm. The high-precision position control can be realized by designing the controller based on the joint angle feedback. The research content has certain theoretical and practical significance for the development of joint high-precision control of tendon-sheath driven prosthetic hand. This is beneficial to the implementation of complex in-hand manipulation for prosthetic hand.

Establishment and Extension of a Fast Descriptor for Point Cloud Registration

Point cloud registration (PCR) is a vital problem in remote sensing and computer vision, which has various important applications, such as 3D reconstruction, object recognition, and simultaneous localization and mapping (SLAM). Although scholars have investigated a variety of methods for PCR, the applications have been limited by low accuracy, high memory footprint, and slow speed, especially for dealing with a large number of point cloud data. To solve these problems, a novel local descriptor is proposed for efficient PCR. We formed a comprehensive description of local geometries with their statistical properties on a normal angle, dot product of query point normal and vector from the point to its neighborhood point, the distance between the query point and its neighborhood point, and curvature variation. Sub-features in descriptors were low-dimensional and computationally efficient. Moreover, we applied the optimized sample consensus (OSAC) algorithm to iteratively estimate the optimum transformation from point correspondences. OSAC is robust and practical for matching highly self-similar features. Experiments and comparisons with the commonly used descriptor were conducted on several synthetic datasets and our real scanned bridge data. The result of the simulation experiments showed that the rotation angle error was below 0.025° and the translation error was below 0.0035 m. The real dataset was terrestrial laser scanning (TLS) data of Sujiaba Bridge in Chongqing, China. The results showed the proposed descriptor successfully registered the practical TLS data with the smallest errors. The experiments demonstrate that the proposed method is fast with high alignment accuracy and achieves a better performance than previous commonly used methods.

Investigation on ultrasonic-assisted embossing process of micro-features with variable curvature as functional surface using ultra-thin sheet of 5052 aluminum alloy

Investigation on ultrasonic-assisted embossing process of micro-features with variable curvature as functional surface using ultra-thin sheet of 5052 aluminum alloy

Investigating The Failure of Leaf Springs in Automobile Suspension on Ghana Road

This study investigates the failure of leaf springs used in the suspension system of heavy-duty vehicles in Ghana. Primary and secondary data were collected using both open and closed-ended questionnaires. Welders and fabricators of Sarkyoyo enterprise at the Suame Spare parts dealership area in Kumasi were engaged in the survey. The elastic strain and stress mathematical models were used to determine the stress points in a loaded leaf spring with the aid of ANSYS. The factors considered in the analysis were the leaf spring SAE design specification, the recommended Ghana Highway Authority load limit for heavy-duty vehicles, and the terrain. Analysis was done for both the standard and variable curvature leaf springs. The mode of failure was found to be fatigue loading. The causes of failure were determined to be loaded beyond the recommended 43 tons per wheel limit, bad roads, and reckless driving. It was also observed that loading causes the edges of the leaf spring to bend outwardly from the top, making the edges more prone to failure. Results further showed that the leaf spring with variable curvature recorded strain energy 2.5 times higher than the standards leaf spring.

Elite Chaotic Manta Ray Algorithm Integrated with Chaotic Initialization and Opposition-Based Learning

The manta ray foraging optimizer (MRFO) is a novel nature-inspired optimization algorithm that simulates the foraging strategy and behavior of manta ray groups, i.e., chain, spiral, and somersault foraging. Although the native MRFO has revealed good competitive capability with popular meta-heuristic algorithms, it still falls into local optima and slows the convergence rate in dealing with some complex problems. In order to ameliorate these deficiencies of the MRFO, a new elite chaotic MRFO, termed the CMRFO algorithm, integrated with chaotic initialization of population and an opposition-based learning strategy, is developed in this paper. Fourteen kinds of chaotic maps with different properties are used to initialize the population. Thereby, the chaotic map with the best effect is selected; meanwhile, the sensitivity analysis of an elite selection ratio in an elite chaotic searching strategy to the CMRFO is discussed. These strategies collaborate to enhance the MRFO in accelerating overall performance. In addition, the superiority of the presented CMRFO is comprehensively demonstrated by comparing it with a native MRFO, a modified MRFO, and several state-of-the-art algorithms using (1) 23 benchmark test functions, (2) the well-known IEEE CEC 2020 test suite, and (3) three optimization problems in the engineering field, respectively. Furthermore, the practicability of the CMRFO is illustrated by solving a real-world application of shape optimization of cubic generalized Ball (CG-Ball) curves. By minimizing the curvature variation in these curves, the shape optimization model of CG-Ball ones is established. Then, the CMRFO algorithm is applied to handle the established model compared with some advanced meta-heuristic algorithms. The experimental results demonstrate that the CMRFO is a powerful and attractive alternative for solving engineering optimization problems.

Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds

We study Poincaré inequalities and long-time behavior for diffusion processes on Rn under a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estimates on the rate of convergence to equilibrium in L1 optimal transport distance, as well as bounds on the constant in the Poincaré inequality in several situations of interest, including some where curvature may be negative. In particular, we prove a self-improvement of the Bakry-Emery estimate for Poincaré inequalities when curvature is positive but not constant.

A new multiobjective optimization adaptive layering algorithm for 3D printing based on demand-oriented

PurposeAdaptive slicing is a key step in 3D printing as it is closely related to the building time and the surface quality. This study aims to develop an adaptive layering algorithm that can coordinate the optimization of printing quality and efficiency to meet different printing needs.Design/methodology/approachA multiobjective optimization model is established for printing quality, printing time and layer height based on the variation of surface features, profile slope and curvature of the model. The optimal solution is found by an improved method combining Newton's method and gradient method and adapts to different printing requirements by adjusting the parameter thresholds.FindingsSeveral benchmarks are applied to verify this new method. The proposed method has also been compared with the uniform layering method, it reduces the volume error by 46.4% and shortens the printing time by 28.1% and is compared with five existing adaptive layering methods to demonstrate its superior performance.Originality/valueCompared with other methods with only one layered result, this method is a demand-oriented algorithm that can obtain different results according to different needs and it can reach a trade-off between the building time and the surface quality.

The influence of the Gaussian curvature sign of the compound shell structure’s middle surface on local and overall buckling under combined loading

The buckling problem of an elastic compound shell structure with a variable Gaussian curvature of the middle surface, especially the middle surface meridian curvature sign, under the action of external pressure and axial loading is considered. In continuation of the previous research of the authors, this paper is devoted, in particular, to examining the influence of the negative Gaussian curvature sign of one of its compartments on stability. The solution is based on using the method of finite differences for basic stability equations of each compartment in the case when one of them can have a negative curvature of the meridian, taking into account the discreteness of the intermediate rib location and their rigidity from the initial curvature plane as well. The obtained solution allows visualizing the buckling modes under various combinations of external loading and identifying rational, according to overall buckling modes, geometric and rigidity parameters of the system being investigated.