Shape Of Path Research Articles

A modified energy-based model for low-cycle fatigue life prediction under multiaxial irregular loading

This work provides a damage accumulation algorithm to calculate low cycle fatigue life under multiaxial irregular loading path, using an intuitively constructed energy-based parameter which combines both cyclic plastic work and non-proportional (NP) hardening effect. The cumulative fatigue damage is calculated according to actual shape of the loading path, which is different from the traditional damage accumulation models that consider block sequence effect. The effectiveness of this proposed damage accumulation algorithm has been validated by experimental results of 316L stainless steel under nine regular loading paths and nine irregular multiaxial loading paths.

Iterative Learning-Based Path Optimization for Repetitive Path Planning, With Application to 3-D Crosswind Flight of Airborne Wind Energy Systems

This paper presents an iterative learning approach for optimizing the course geometry in repetitive path following applications. In particular, we focus on airborne wind energy (AWE) systems. Our proposed algorithm consists of two key features. First, a recursive least squares (RLS) fit is used to construct an estimate of the behavior of the performance index. Second, an iteration-to-iteration path adaptation law is used to adjust the path shape in the direction of optimal performance. We propose two candidate update laws, both of which parallel the mathematical structure of common iterative learning control (ILC) update laws but replace the tracking-dependent terms with terms based on the performance index. We apply our formulation to the iterative crosswind path optimization of an AWE system, where the goal is to maximize the average power output over a figure-8 path. Using a physics-based AWE system model, we demonstrate that the proposed adaptation strategy successfully achieves convergence to near-optimal figure-8 paths for a variety of initial conditions under both constant and real wind profiles.

Collaborative design of fiber path and shape for complex composite shells based on isogeometric analysis

Composite shells with complex geometry are widely used in aerospace structures. Due to the complexity of geometry and curvilinear fiber path, the analysis and optimization based on finite element analysis (FEA) for complex variable-stiffness (VS) shells is extremely time-consuming. By comparing with FEA, isogeometric analysis (IGA) exhibits higher prediction efficiency of buckling load. In this work, the formula of geometric stiffness matrix for complex VS shells is derived for the first time based on degenerated shell method using IGA, which is the basis of performing linear buckling analysis. Then, a new variable curvature quasi-linear function (VCQLF) to describe curvilinear fiber path is proposed, which can further expand the design space of VS shells. After that, two frameworks for shape optimization of complex shells are put forward and then compared, and it is found that the one based on LOFT function can provide representative control variables of shape and effectively reduces the number of design variables for complex shells. Finally, a novel collaborative optimization framework of fiber path and shell shape using IGA is established. By comparison of traditional methods, it is demonstrated that the proposed framework can greatly improve the efficiency of optimization and fully explore the buckling load of complex VS shells.

Determining cooling rates from mica 40Ar/39Ar thermochronology data: Effect of cooling path shape

AbstractTectonic models are commonly underpinned by metamorphic cooling rates derived from diffusive‐loss thermochronology data. Such cooling ages are usually linked to temperature via Dodson's closure temperature (TC) formulation, which specifies a 1/time‐shaped cooling path (Contributions to Mineralogy and Petrology, 1973, 40, 259). Geologists, however, commonly discuss cooling rates as a linear temperature/time shape. We present the results of a series of simple finite‐difference diffusion models for Ar diffusion in muscovite and biotite that show that the difference in recorded age between 1/t and linear cooling paths increases significantly with hotter starting temperatures, slower cooling rates and smaller grain sizes. Our results show that it is essential to constrain the cooling path shape in order to make meaningful interpretations of the measured data.

On the material and material-adapted approaches to curve framing with applications in path estimation, shape reconstruction, and computer graphics

In this paper, we investigate an approach towards curve framing using material frames (MF). Motivated from the successful application of MF in shape sensing of rods in our previous work, we now present these frames as an alternative curve framing method. There are numerous instances of practical importance, where the dynamic system in consideration can be geometrically modeled by means of framed space curve. Unlike the Frenet-Serret and relatively parallel adapted frames (RPAF), the MF is conveniently defined in terms of the parameters associated with the system configuration.We detail the construction of the various material frames. We develop the relationships among the MF, Frenet frame, and the RPAF. We discuss the estimation of state space of the system from a limited set of material curvature and velocity data. In one of the approaches discussed, we obtain curvature-dependent shape functions to estimate the framed curve globally and discuss the errors associated with such estimations.We also describe the potential strengths of framed space curves in the reconstruction of slender structures, trajectory estimation of moving objects (like drone swarms), and in computer graphics. We do this by creating an analogy between the non-linear geometry of Cosserat beams and these applications.

Measuring the average shape of transition paths during the folding of a single biological molecule

Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈t(x)〉, or by averaging transitions of a given duration in the extension domain, 〈x(t|τ)〉 τ Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(t|τ)〉 τ had more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈t(x)〉 provided a less reliable representation of the path shape than 〈x(t|τ)〉 τ , because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations.

Measuring the Average Shape of Transition Paths during the Folding of a Single Biological Molecule

Measuring the Average Shape of Transition Paths during the Folding of a Single Biological Molecule

The flow path characteristics analysis for supercritical carbon dioxide gas turbines

Rising carbon dioxide concentration in the atmosphere is probably the main reason of global warming. The development of the oxy-fuel combustion cycles is a possible way to decrease the energy sector contribution in the emission process. However, an unusual composition and thermodynamic parameters of the working fluid cause the necessity of revision of the main equipment characteristics, especially for the supercritical carbon dioxide gas turbine. This study presents the method and the results of the flow path preliminary analysis for the new generation gas turbines working on carbon dioxide. The flow path shape with a constant root diameter of seven stages was chosen as the most reasonable due to cheap manufacturing. Influence of reaction degree of stages and velocity ratio on stage geometric parameters are revealed. It was found that the optimal reaction degree and velocity ratio are equal to 0.25 and 0.36 correspondingly. Thermal and constructive stages characteristics of the 350 MW turbine are determined.

A fast algorithm to racetrack filter multiaxial histories preserving load shape

A fast algorithm is presented to implement a multiaxial version of the racetrack amplitude filter, improved upon the authors’ previous works. The algorithm only requires a single user-defined scalar filter amplitude to eliminate noise and potentially non-damaging events from arbitrary non-proportional multiaxial stress or strain histories, while preserving all key features of the load path. It can be applied as a pre-processing step to both invariant-based and critical-plane multiaxial damage models, highly decreasing the computational cost in assessments involving oversampled or noisy data, much improving the usefulness of computationally-intensive multiaxial models. Since load path shape is well preserved (within the chosen filter resolution), peaks and valleys from subsequent candidate plane projections are not filtered out. Moreover, path-equivalent stress or strain calculations can still be applied after the filtering process, without precision loss beyond the filter resolution. The algorithm is synchronous and preserves load order, becoming suitable for strain-based multiaxial damage models involving plastic memory, as well as for mixed-mode crack propagation calculations. The filter efficiency is validated from oversampled tension-torsion experimental data in 316L stainless steel tubular specimens, following complex non-proportional histories. Finally, a fully-tested computer implementation of the algorithm is presented.

CALCULATED RESEARCH OF INFLUENCE OF HELICOPTER MAIN ROTORS GEOMETRY ON THE EFFICIENCY IN HOVER MODE BASED ON THE NONLINEAR VORTEX MODEL

The efficiency of the helicopter main rotor in the hover mode is very important, because this mode essentially determines the performance characteristics of the helicopter. A feature of the helicopter rotor aerodynamics is a significant inductive blade influence that highly defines its aerodynamic characteristics. The problem of the influence of the blade twist and spatial geometric layout of the main rotor on its aerodynamic characteristics in the hover mode for a fixed value of the rotor solidity has been considered in this article. As a criterion of efficiency of the rotor in the hover mode relative efficiency (FoM – Figure of Merit) is used. The results are obtained by numerical simulation based on the nonlinear vortex blade model of the rotor, developed at the Helicopter Design Chair of the MAI. The model allows taking into account a complicated spatial shape of the free vortex path of the rotor blades that determines their inductive interaction. As the example of a four-blade main rotor with rectangular blades in plan, the influence of the value of the blades twist on the efficiency in the hover mode is studied. For different values of the rotor thrust, the values and ranges of the blade twist angles are determined, providing the maximum positive effect of the efficiency increase in hovering. For a fixed value of the blade twist, the rotor solidity, and the same operating conditions, the effect of various schemes and configurations of rotor on its efficiency in hover mode is studied. A single rotor with a different number of blades (from 2 to 6), an X-shaped rotor, coaxial rotor and rotor with crossed blades type "synchropter" are considered. The values of the efficiency increase in hovering depending on the rotor layout in comparison with the two-blade rotor are obtained. The comparative analysis of inductive velocities and streamlines for the "synchropter" rotor scheme, coaxial rotor scheme and its equivalent single rotor scheme is presented. The obtained results can be useful at the stage of preliminary design of vertically taking-off aircraft when selecting the parameters of their main rotor system.

Improving 3D printing process of lemon juice gel based on fluid flow numerical simulation

Food 3D printing has received attention as a novel field in recent years, bringing new ideas and opportunities for the development and transformation of food processing technology. This work investigated the moisture and rheological properties of lemon juice gels with different starches by experimental studies and simulated the effect of different material properties and process parameters (material viscosity and relaxation time, inlet volume flow rate and nozzle diameter) on the velocity, shear rate and pressure fields in the flow channel by the POLYFLOW software. Results showed that with the addition of different kinds of starches, the viscosity and mechanical properties of the lemon juice gel were varied. Adding potato starch altered fluidity with different relative degree of bound or immobilized water of lemon juice gel. According to the simulation study, in the same shape of the flow path, the velocity and shear velocity fields were determined by the inlet volume flow rate. The change of different process parameters was found to cause changes in pressure field in the flow channel to varying degrees, and the change of the nozzle diameter had the greatest influence on the pressure distribution. In addition, the extruded material exhibited swelling phenomenon.

Solutions for Gas-Air Flow Paths and Environmental Protection from Harmful Power-Plant Emissions in the Framework of the Scientific School Created by L. A. Rikhter [On the Centenary of the Birth of L. A. Rikhter

The paper considers the main scientific activities of the doctor of Technical Science, Professor Lev Aleksandrovich Rokhter, such as optimizing the shape of gas-air flow paths of thermal power plants, protecting the environment from harmful emissions, and identifying stack failures, which are currently being developed by his followers. For a systematic study of gas-air flow path components, L.A. Richter applied a technique based on the theory of complex variable and conformal mapping, which makes it possible to find optimal aerodynamic configuration of the gas-air flow path components. By means of the methodology developed by him, gas-air flow path research is currently carried out using Solid Works and Flow Vision application packages. Examples of optimizing the design of flue gas ducts with allowance for aerodynamic forces are given. The professor formulated the reasons and described the mechanism of structural collapse of reinforced concrete and brick stack constructions based on a theory of the occurrence of static pressures in the gas exhaust duct under certain conditions, which contribute to the penetration of aggressive substances of flue gas to the outer structural surface. In the last decade, works that additionally consider the flue gas mass transfer effect on the stack have become widespread. L.A. Richter proved that the problem of estimating the concentrations of impurities in TPP stack emissions is much more complicated under real conditions. This is due to the need to take into account the actual state of the atmosphere and its heterogeneous turbulent structure as well as the obligatory allowance for the rise of the stack plume over the stack mouth. Studies of his followers have shown that the scattering region of harmful substances is significantly reduced when a selfenvelopment phenomenon occurs under certain conditions. The professor’s contribution to the development of the methodology for finding economically optimal rates in various gas-air flow path components, as well as the creation of new structural components of electrostatic precipitators, which are currently widely used in practice, is also shown.

Forward dynamic optimization of handle path and muscle activity for handle based isokinetic wheelchair propulsion: A simulation study

Push-rim wheelchair propulsion is biomechanically inefficient and physiologically stressful to the musculoskeletal structure of human body. This study focuses to obtain a new, optimized propulsion shape for wheelchair users, which is within the ergonomic ranges of joint motion, thus reducing the probability of injuries. To identify the propulsion movement, forward dynamic optimization was performed on a 3D human musculoskeletal model linked to a handle based propulsion mechanism, having shape and muscle excitations as optimization variables. The optimization resulted in a handle path shape with a circularity ratio of 0.95, and produced a net propulsion power of 34.7 watts for an isokinetic propulsion cycle at 50 rpm. Compared to push-rim propulsion, the compact design of the new propulsion mechanism along with the ergonomically optimized propulsion shape may help to reduce the risk of injuries and thus improve the quality of life for wheelchair users.

Formation Control of Multiple Dubins Airplane System with Geometric Approach

Formation Control is very important for multi agent systems (Swarm). This paper analyses control formation on the Dubins airplane that consists of three airplanes, where an airplane as the leader and two other airplanes move to follow leader airplane’s track. First, Doing design of leader airplane’s controls by using the method of tracking error dynamics. Controls on the leader follow the trajectory tracking that desired. Desired path is in the form of parametric functions. Second, geometric approaches method is used to design two other airplanes, so the move follows path of the airplane as the leader with a certain distance. Simulation result shows that airplane leader can be controlled to the desired path crosses with good results. Therefore, error has been defined as the distance between leader airplane’s paths with the desired path while tracking also depends on the shape of path. The more difficult trajectory tracking of airplane also serves as a leader in passing through it. The result of the simulations also indicates that the value of the mean percentage error (MPE) of 26.93 percent. This suggests that the methods used in this study quite effective either used to control design leader or follower.

Optimal path shape for range-only underwater target localization using a Wave Glider

Underwater localization using acoustic signals is one of the main components in a navigation system for an autonomous underwater vehicle (AUV) as a more accurate alternative to dead-reckoning techniques. Although different methods based on the idea of multiple beacons have been studied, other approaches use only one beacon, which reduces the system’s costs and deployment complexity. The inverse approach for single-beacon navigation is to use this method for target localization by an underwater or surface vehicle. In this paper, a method of range-only target localization using a Wave Glider is presented, for which simulations and sea tests have been conducted to determine optimal parameters to minimize acoustic energy use and search time, and to maximize location accuracy and precision. Finally, a field mission is presented, where a Benthic Rover (an autonomous seafloor vehicle) is localized and tracked using minimal human intervention. This mission shows, as an example, the power of using autonomous vehicles in collaboration for oceanographic research.

Fluid flow through male rotor housing clearances of dry running screw machines using dimensionless numbers

The efficiency of positive displacement machines is strongly influenced by clearance flows. The prediction of the mass flow rate is a challenging task since it depends on thermodynamic and operating boundary conditions as well as the shape of the clearance path. When simulating positive displacement machines using chamber models, clearance flow is commonly estimated by using simplified approaches, such as equations for isentropic nozzle flow combined with a flow coefficient. Knowledge of these flow coefficients is important for an accurate simulation of the machine. For this reason one of the goals of the European Union funded project “MOTOR” (Multi-ObjecTive design Optimization of fluid eneRgy machines) is the determination of the flow coefficient for different clearance shapes. This paper deals with the simulation of the two-dimensional fluid flow in the housing clearance of twin-screw machines using the finite volume method for air as ideal gas. Dimensionless numbers are varied to show their individual influence on the mass flow. Results are compared with experimental data from reports in the literature and show good accordance. The primary factors affecting the results are Reynolds number and the moving boundary in the low Reynolds number region.

First-Principles Investigation on the Tribological Properties of h-BN Bilayer Under Variable Load

Using first-principles method, for h-BN bilayer, we successfully probe the major factors of different low-friction paths in the three-dimensional potential energy surface (3D-PES) under variable loads. By means of the static PES and charge density difference analysis, we demonstrate how electrostatic interactions, with regard for van der Waals contributions at 0 nN, progressively impact the shape of 3D-PES and low-friction paths with increasing the normal load. Herein, the sliding properties of h-BN bilayers have a distinct relative orientation. Especially, the load-induced 3D-PES with variable shape is assigned to the band gap and repulsive van der Waals force. It is noted that the low friction not only is obtained for the commensurate layers under low loads, but also high ones.

How price path characteristics shape investment behavior

Price paths are often the only graphical representation of financial products investors receive before making an investment decision. We argue that price paths serve as ”graphical” frames that influence the perceived attractiveness of an asset by highlighting specific asset characteristics. In a controlled lab experiment we find that price paths have an impact on investment decisions. In a regression we test a simple model relating the perception of price path shapes to several heuristics. These heuristics are: focusing on more recent outcomes, deriving implicit reference prices from focal prices, focusing on losses, and estimating risk from the amplitude of the path. We conclude that investment decisions are systematically biased due to the shape of an asset’s price path.

Path Following in Non-Visual Conditions

Path-following tasks have been investigated mostly under visual conditions, that is when subjects are able to see both the path and the tool, or limb, used for navigation. Moreover, only basic path shapes are usually adopted. In the present experiment, participants must rely exclusively on continuous, non-speech, and ecological auditory and vibrotactile cues to follow a path on a flat surface. Two different, asymmetric path shapes were tested. Participants navigated by moving their index finger over a surface sensing position and force. Results show that the different non-visual feedback modes did not affect the task's accuracy, yet they affected its speed, with vibrotactile feedback causing the slowest gestures. Also, vibrotactile feedback caused participants to exert more force over the surface. Finally, the shape of the path was relevant to the accuracy, and participants tended to prefer audio over vibrotactile and audio-tactile feedback.

A planar neuro-musculoskeletal arm model in post-stroke patients

Mathematical modeling of the neuro-musculoskeletal system in healthy subjects has been pursued extensively. In post-stroke patients, however, such models are very primitive. Besides improving our general understanding of how stroke affects the limb motions, they can be used to evaluate rehabilitation strategies by computer simulations before clinical evaluations. A planar neuro-musculoskeletal arm model for post-stroke patients is developed. The main idea is to use a set of new coefficients, Muscle Significance Factors (MSF), to incorporate the effects of stroke in the muscle control performance. The model uses the optimal control theory to mimic the performance of the CNS and a two-link skeletal model with six muscles for the biomechanical part. The model was developed and evaluated using experimental data from six post-stroke patients with Brunnstrom levels of 4-6. The results show that MSFs are relatively distinct and independent from the arm motion which is used to determine their values. Its variation is in the range of 0-2.58% and decreases in higher Brunnstrom levels. The mean error of the model in predicting the path of motion varies from 0.9% in level 6 to 5.58% in level 4 subjects which can be considered a promising level of accuracy. Using the proposed model and the MSF to customize the model for each individual stroke patient seems a promising approach. It shows a reasonable level of robustness, i.e., independence from the type of motions and correlated with the severity of stroke, and accuracy in predicting the shape of the motion path.