Geometric Relationship Research Articles

A Deep Learning-Based Ultrasonic Diffraction Data Analysis Method for Accurate Automatic Crack Sizing

The purpose of this paper is to automate the interpretation of data during ultrasonic diffraction using a non-destructive testing (NDT) technique to accurately size defects for assisting in decision-making. A convolutional neural network (CNN) architecture was developed to automatically measure the length of the defect. Using the architecture, the population of A-scan signals in the scanning path was classified. The defect region was extracted and its size in the scanning direction was obtained by the connected region solution algorithm based on the classification results. The arrival time of diffraction waves was accurately identified by the intelligent denoising framework proposed, combined with Hilbert transform, and then the height of defects was calculated by corresponding geometric relations. The estimation results demonstrate that the measurement method can be considered as a useful technique for crack sizing in industrial structures, even in the case of complex noise.

Study on Calculation Method of Bending Performance of Concrete Sandwich Composite Slab.

In order to explore the flexural behavior of a concrete sandwich panel under concentrated boundary conditions, based on Kirachhoff's elastic thin plate theory in this paper, the geometric deformation, physical conditions, and equilibrium relationship of a sandwich panel are deduced by constructing the layered analysis model of the sandwich panel, the basic differential equation of the flexural deformation of the concrete sandwich thin plate is obtained, and the mathematical expression of the internal force and displacement under the boundary condition of concentrated support is given. Combined with an engineering example, the proposed calculation method is verified. The results show that, in the arrangement of reliable connectors for concrete sandwich panels, the concrete wythes bear the load while the contribution of the core layer to the bending capacity of the structure can be ignored. When subjected to a laterally distributed load, the sandwich panel mainly experiences out-of-plane bending deformation, and the bending normal stress in the concrete panel layer shows a linear non-uniform distribution along the thickness direction of the panel. The bending deformation performance and bearing efficiency of a concrete sandwich slab with the change in concentrated support position have significant effects, and the load transfer efficiency can be improved by optimizing the arrangement of supports. Except for small local areas near the supports, the bending stress distribution and deformation behavior of the concrete sandwich panel can be accurately analyzed by the calculation method established in this paper.

Non-interference slow tool servo turning method for complex surfaces with large undulation changes

Complex curved surface parts are integral to the mechanical industry, demanding precise machining techniques. Multi-axis slow tool servo turning has emerged as an efficient method due to its high precision and quality. However, the challenge of severe tool flank interference arises, especially on surfaces with large undulation changes. Conventional methods, such as increasing tool clearance angles or adding extra tool axes, detrimentally affect machining precision and stability. To address this, a non-interference toolpath planning method is proposed for complex surfaces with large undulation changes. The approach begins with establishing geometric models of the single-point diamond turning tool and typical complex surfaces, followed by analyzing the mechanism and evolution of tool flank interference. By considering geometric parameters and vector relationships, the practical tool clearance angles are calculated. And then a criterion for subregion division is introduced and the non-cutting stroke is designed, accounting for the maximal acceleration of machine tool axis. Multi-pass toolpaths are generated to navigate different subregions while avoiding interference by transforming spindle rotation direction. Furthermore, a method is proposed to optimize toolpath stitching in practical machining regions, ensuring continuous and smooth transitions while maintaining machining precision and surface quality. Experimental validation, conducted on a hyperbolic paraboloid surface with large undulation changes, demonstrates a significant reduction in surface roughness (Sa) from 380.503 nm to 75.664 nm—a reduction of 80.115 %. The proposed method not only enhances machining precision and surface quality but also extends tool life and improves working conditions. This research offers vital guidance for non-interference toolpath planning in engineering practice.

Tangent lines that neither touch nor cross the curves at the points of tangency

Several studies on student's understanding of the concept of the tangent line agree that the difficulties students have when dealing with lines tangent to curves at inflection points or tangent lines that have more than one point in common with the curve are due to a misconception of tangency that is limited to the geometric relationship between line and circle. Here, we report difficulties Mexican high school students had when working on tangent lines in situations like those mentioned before. For our research, we designed Activities mostly carried out with dynamic geometry. Using the zoom-in provided by the software helped strengthen the student's mental image of the local geometric relationship between a curve and a line tangent. Several of the curves we designed for the investigation surprised the students when they zoomed in on the point of tangency. From the point of view of the tangency relation that is intuitively obtained from tangents to the circle or curves at inflection points, in several curves that we presented, the tangent lines neither touch nor cross the curves at the points of tangency. These are cases of curves and tangents that would be worth analyzing in Differential Calculus courses.

Post-buckling behavior of variable-arc-length elastica pipe conveying fluid including effects of self-weight and pressure variation

This paper investigated the post-buckling behaviors of a variable-arc-length (VAL) elastica pipe caused by internal transporting fluid motion, accounting for the effects of the self-weight and variation of internal fluid pressure. Both weak-form and strong-form formulations of the VAL elastica pipe were developed. The weak-form formulation was derived by the virtual work principle, and later solved using the nonlinear finite element method (FEM). The strong-form formulation was derived using equilibrium of the force and moment equations, the geometrical relationship of the differential pipe segment, and the energy conservation of the transported fluid. Because of the large displacement analysis, the variation in the internal pressure inside the pipe was considered, which was taken into account by energy conservation based on the Bernoulli principle. Then, the set of nonlinear governing first-order differential equations, corresponding to the two-point boundary value problem, was conveniently solved using the shooting optimization method (SOM). The numerical results obtained from the presented FEM and SOM analyses independently verified each other, with good agreement between these two methods. The parametric study considered the effects of gravity load (pipe and fluid self-weights) and internal fluid pressure on the post-buckling characteristics of the VAL pipe. The numerical results showed that without the pipe and internal fluid weights, the transporting fluid exerted an axial compressive force on the pipe, causing post-buckling phenomena. Beyond the critical state, the support rotation and the length of the VAL pipe increased as the internal fluid velocity decreased. Finally, by including the effect of self-weight, the mode exchange of the odd buckling modes (1st and 3rd modes) was found from the load-displacement path.

Integrated attitude—orbit control of solar sail with single-axis gimbal mechanism

A new attitude control method for solar sails is proposed using a single-axis gimbal mechanism and three-axis reaction wheels. The gimbal angle is varied to change the geometrical relationship between the force due to solar radiation pressure (SRP) and the center of mass of the spacecraft, such that the disturbance torque is minimized during attitude maintenance for orbit control. Attitude maneuver and maintenance are performed by the reaction wheels based on the quaternion feedback control method. Even if angular momentum accumulates on the reaction wheels due to modelling error, it can also be unloaded by using the gimbal to produce suitable torque due to SRP. In this study, we analyzed the attitude motion under the reaction wheel control by linearizing the equations of motion around the equilibrium point. Further, we newly derived the propellent-free unloading method based on the analytical formulation. Finally, we constructed the integrated attitude-orbit control method, and its validity was verified in integrated attitude-orbit control simulations.

Diastolic Filling in Patients After Heart Transplantation Is Impaired Due to an Altered Geometrical Relationship Between the Left Atrium and Ventricle.

The geometrical relationship between atrial and ventricular short-axis cross-sectional area determines the hydraulic forces acting on intracardiac blood. This is important for diastolic filling. In patients undergoing heart transplantation (HTx), the left atrium is often enlarged as a result of the standard surgical technique. We hypothesized that diastolic filling in HTx patients is affected by the surgery altering the geometrical relationship between atrium and ventricle. This retrospective, cross-sectional study included 25 HTx patients (median age, 52 [range, 25-70] years), 15 patients with heart failure with reduced ejection fraction (median age, 63 [range, 52-75] years), 15 patients with heart failure with preserved ejection fraction (median age, 74 [range, 56-82] years), and 15 healthy controls (median age, 64 [range, 58-67] years) who underwent cardiac magnetic resonance imaging. Left ventricular, atrial, and total heart volumes (THV) were obtained. Atrioventricular area difference at end diastole and end systole was calculated as the largest ventricular short-axis area minus the largest atrial short-axis area. Left atrial minimum volume normalized for THV (LAmin/THV) was larger in HTx patients (median, 0.13 [range, 0.07-0.19]) compared with controls (median, 0.05 [range, 0.03-0.08], P <0.001), whereas left ventricular volume normalized for THV (left ventricular end-diastolic volume/THV) was similar between HTx and controls (median, 0.19 [range, 0.12-0.24] and median, 0.22 [range, 0.20-0.25], respectively). At end diastole, when atrioventricular area difference reached its largest positive value in controls, 11 HTx patients (44%) had a negative atrioventricular area difference, indicating impaired diastolic filling. Diastolic filling is impaired in HTx patients due to an altered geometrical relationship between the left atrium and ventricle. When performing cardiac transplantation, a surgical technique that creates a smaller left atrium may improve diastolic filling by aiding hydraulic forces.

Design and analysis of a solid surface deployable antenna mechanism based on flasher rigid origami

This study proposes a mechanism for solid surface deployable antennas based on flasher rigid origami. The mechanism scheme design and degree-of-freedom analysis were conducted utilizing a Kirigami release constraint strategy. Subsequently, a spatial geometric model of the key points was established incorporating the folding and unfolding characteristics and geometric relationships within the mechanism. Furthermore, a comprehensive 3D model of the antenna was developed by determining the hinge locations, geometric parameters, and driving mechanism, followed by a kinematic simulation analysis. Finally, a prototype was constructed, and a microgravity deployment experiment was conducted to verify the feasibility of the mechanism.

Study on driving safety of vehicle-bridge interaction system based on ultra-high-dimensional point-selected extremum methods

ABSTRACT The driving safety indexes involve the geometric nonlinear contact relationship of the wheel and rail and the high-frequency vibration of the wheel-set. The calculation of their probability characteristic parameters requires very precise selection of random excitation samples. Track irregularity is an essential external excitation force in the vehicle-bridge interaction system (VBIS). Besides, many random phase angles must be considered when using the harmonic superposition method to simulate VBIS, leading to the ultra-high-dimensional random variables problem. Thus, this paper proposes a square power point method and a pseudo-random sequence (Sobol sequence) based on a number theoretic approach to model ultra-high dimensional random variables accurately. This strategy reduces the deviation between the representative track irregularity samples (TIS) and can be applied to fields of strongly nonlinear and high-frequency vibration. Then, by increasing the number of representative TIS, the deviation between response samples caused by non-linear factors can be significantly reduced. Finally, this paper proposes a threshold method for driving safety indexes that determines the service life of bridges, which can quickly obtain the threshold of its extreme value distribution through the cumulative distribution function, and establish the relationship between the threshold and the number of trains travelled. The above theories are verified by calculation examples, and some engineering suggestions are obtained.

Diastology of the Transplanted Heart: Is the Geometrical Relationship of the Left Atrium the Missing Link?

Diastology of the Transplanted Heart: Is the Geometrical Relationship of the Left Atrium the Missing Link?

Exact and efficient wall distance pre-classification overset grid assembly for unstructured grids

In this paper, we present a pre-classification overset grid assembly (OGA) based on the wall distance criterion. In contrast to the conventional OGA, where donor search is preceded by point classification, the proposed methodology first performs point classification based on the wall distance criterion, and then performs donor search on the reduced set of cells. To robustly profile the given grid components, a wall distance evaluation is performed exactly by considering the full geometry of the discretized surface while maintaining efficiency. The efficiency of the algorithm is achieved by redefining the methodology into a bounded form and establishing a conservative correlation between the vertex-based and element-based distances through a rigorous examination of geometric relations. From these observations, wall distance calculation, which requires a tremendous amount of computation, is divided into sequential steps of vertex-based approximate calculation and element-based exact calculation, dramatically reducing the computation load. To better adapt to parallel environments, load balancing is presented, and additionally, some voxelization techniques are developed to efficiently process the required geometric data. Numerous test cases are analyzed to demonstrate the efficiency and robustness of the proposed algorithm in various situations. The proposed algorithm consistently outperforms the conventional OGA, and also proves its robustness in the presence of high proximity objects, which highlights its suitability for large-scale multi-body problems.

GraM: Geometric Structure Embedding into Attention Mechanisms for 3D Point Cloud Registration

3D point cloud registration is a crucial technology for 3D scene reconstruction and has been successfully applied in various domains, such as smart healthcare and intelligent transportation. With theoretical analysis, we find that geometric structural relationships are essential for 3D point cloud registration. The 3D point cloud registration method achieves excellent performance only when fusing local and global features with geometric structure information. Based on these discoveries, we propose a 3D point cloud registration method based on geometric structure embedding into the attention mechanism (GraM), which can extract the local features of the non-critical point and global features of the corresponding point containing geometric structure information. According to the local and global features, the simple regression operation can obtain the transformation matrix of point cloud pairs, thereby eliminating the semantics that ignores the geometric structure relationship. GraM surpasses the state-of-the-art results by 0.548° and 0.915° regarding the relative rotation error on ModelNet40 and LowModelNet40, respectively.

Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport.

Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.

Axial Tensile Ultimate Strength of an Unbonded Flexible Riser Based on a Numerical Method.

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed to different configurations to adapt to harsh marine environments, and is a key equipment in transporting oil and gas resources from Ultra Deep Waters (UDWs) to offshore platforms. The helical interlayer of an unbonded flexible riser makes the structural behavior difficult to predict. In this paper, the axial tensile behavior and the axial tensile ultimate strength of an unbonded flexible riser are studied based on a typical 2.5-inch eight-layer unbonded flexible riser model, and verified through a theoretical method considering the contact between adjacent layers. First, the balance equation of separate layers is deduced by a functional principle, and then the overall theoretical model of an unbonded flexible riser is established considering the geometric relationship between adjacent layers. Then, the numerical model considering the detailed geometric properties of an unbonded flexible riser is established to simulate the axial tensile behavior. Finally, after being verified through the experimental results, the axial tensile stiffness and axial tensile strength of an unboned flexible riser considering the elasticity of the tensile armor layer are studied using the proposed two methods. Additionally, the effect of frictional coefficients is conducted. The numerical and theoretical results show good agreement with the test results, and the friction between adjacent layers would increase the axial tensile stiffness of an unbonded flexible riser.

Nonlinear dynamics of cantilevered hyperelastic pipes conveying fluid: Comparative study of linearelasticity and hyperelasticity

In light of the softness and lightweight characteristics, hyperelastic pipes are prone to large deformation. Intending to provide accurate predictions of their large deformation vibrations, the present study aims to establish a rotation-angle-based geometrically exact model for cantilevered pipes conveying fluid composed of hyperelastic materials. Additionally, given the presence of nonlinear geometric relations, it is imperative to assess the role of hyperelasticity in the nonlinear dynamics of fluid-conveying pipes in comparison to linearelastic pipes. The modeling process integrates the Mooney-Rivlin hyperelastic model with a geometrically exact description of the pipe. And the final governing equation is developed through energy analysis and the extended Hamilton's principle. Subsequently, Galerkin's method and the finite difference method are employed to address the governing equation. Following the verification of the proposed model, parametric studies are conducted in the form of planar oscillation diagrams, time histories, phase trajectories, and bifurcation diagrams. The findings of the present study highlight three critical insights. Firstly, the hyperelastic model introduces numerous complicated nonlinear terms as function of the rotation angle with high-order nonlinearity. In the present study, at least fifth-order nonlinear terms should be preserved to adequately predict large deformation vibrations. Secondly, the Mooney-Rivlin hyperelastic model imparts a hardening effect in comparison to the linearelastic model, significantly reducing vibration amplitudes. Lastly, the third-order approximate model is demonstrated to be inadequate in predicting large deformation vibrations at high flow velocity, as it contains the approximation on not only the geometric description but the hyperelasticity-related terms.

A Signal Matching Method of In-Orbit Calibration of Altimeter in Tracking Mode Based on Transponder

In this paper, a matching method for altimeter and transponder signals in Sub-optimal Maximum Likelihood Estimate (SMLE) tracking mode is proposed. In the in-orbit calibration of the altimeter in SMLE tracking mode using the reconstructive transponder, it is necessary to separate the forwarding signal from the ground echo signal. At the same time, the fluctuations in the received signal of the altimeter, which are caused by the forwarding signal of the transponder, can be eliminated. The transponder generates a bias when measuring the arrival time of the transmitting signal from the altimeter and embeds this bias in both the transponder-recorded data and the altimeter-recorded data. Therefore, the two sets of data have one-to-one correspondence, and they are superimposed using the sliding sum method. Moreover, the distance between the altimeter and the transponder is a parabolic geometric relationship, and the outliers are eliminated by the fitting error minimization decision, and the transponder signal is separated from the ground echo. The final altimeter transmitting–receiving signal path is obtained. Furthermore, the principles underlying this method can be used for any transponder that can adjust the response signal delay during calibration.

Focal adhesion and actin orientation regulated by cellular geometry determine stem cell differentiation via mechanotransduction

Tuning cell adhesion geometry can affect cytoskeleton organization and the distribution of cytoskeleton forces, which play critical roles in controlling cell functions. To elucidate the geometrical relationship with cytoskeleton force distribution, it is necessary to control cell morphology. In this study, a series of dextral vortex micropatterns were prepared to precisely control cell morphology for investigating the influence of the curvature degree of adhesion curves on intracellular force distribution and stem cell differentiation at a sub-cellular level. Peripherial actin filaments of micropatterned cells were assembled along the adhesion curves and showed different orientations, filament thicknesses and densities. Focal adhesion and cytoskeleton force distribution were dependent on the curvature degree. Intracellular force distribution was also regulated by adhesion curves. The cytoskeleton and force distribution affected the osteogenic differentiation of mesenchymal stem cells through a YAP/TAZ-mediated mechanotransduction process. Thus, regulation of cell adhesion curvature, especially at cytoskeletal filament level, is critical for cell function manipulation. Statement of significanceIn this study, a series of dextral micro-vortexes were prepared and used for the culture of human mesenchymal stem cells (hMSCs) to precisely control adhesive curvatures (0°, 30°, 60°, and 90°). The single MSCs on the micropatterns had the same size and shape but showed distinct focal adhesion (FA) and cytoskeleton orientations. Cellular nanomechanics were observed to be correlated with the curvature degrees, subsequently influencing nuclear morphological features. As a consequence, the localization of the mechanotransduction sensor and activator-YAP/TAZ was affected, influencing osteogenic differentiation. The results revealed the pivotal role of adhesive curvatures in the manipulation of stem cell differentiation via the machanotransduction process, which has rarely been investigated.

Optimal impact angle guidance law with barrier constraint

This paper presents an optimal guidance law for missile to achieve desired impact angles on a stationary target while accommodating the barrier constraint. The proposed guidance law consists of two parts: a baseline guidance command for intercepting the target with desired impact angles, and a bias command to prevent collision with the barrier. Specifically, the baseline guidance command is derived by solving a linearized optimal control problem, and its explicit trajectory solution is also obtained for collision estimation. The bias command is designed using a novel guidance error that is defined based on the geometrical relationship between the barrier and the proposed explicit trajectory solution. The new guidance law can be easily implemented to a variety of practical engagement geometries, resulting in successful collision avoidance and minimal control efforts. Its effectiveness and robustness are demonstrated via extensive numerical simulations.

Shoulder Movement-Centered Measurement and Estimation Scheme for Underarm-Throwing Motions.

Underarm throwing motions are crucial in various sports, including boccia. Unlike healthy players, people with profound weakness, spasticity, athetosis, or deformity in the upper limbs may struggle or find it difficult to control their hands to hold or release a ball using their fingers at the proper timing. To help them, our study aims to understand underarm throwing motions. We start by defining the throwing intention in terms of the launch angle of a ball, which goes hand-in-hand with the timing for releasing the ball. Then, an appropriate part of the body is determined in order to estimate ball-throwing intention based on the swinging motion. Furthermore, the geometric relationship between the movements of the body part and the release angle is investigated by involving multiple subjects. Based on the confirmed correlation, a calibration-and-estimation model that considers individual differences is proposed. The proposed model consists of calibration and estimation modules. To begin, as the calibration module is performed, individual prediction states for each subject are updated online. Then, in the estimation module, the throwing intention is estimated employing the updated prediction. To verify the effectiveness of the model, extensive experiments were conducted with seven subjects. In detail, two evaluation directions were set: (1) how many balls need to be thrown in advance to achieve sufficient accuracy; and (2) whether the model can reach sufficient accuracy despite individual differences. From the evaluation tests, by throwing 20 balls in advance, the model could account for individual differences in the throwing estimation. Consequently, the effectiveness of the model was confirmed when focusing on the movements of the shoulder in the human body during underarm throwing. In the near future, we expect the model to expand the means of supporting disabled people with ball-throwing disabilities.

Detection method for contact stress distribution of tapered roller bearings

The axle box of high-speed train adopts double row tapered roller bearings as transmission parts, and the reliability of bearings directly affects the safety of train operation. Tapered roller bearings can withstand axial and radial loads, their service life being closely related to the distribution of contact stress. The test object is the axle box bearing of high-speed train. According to bearing’s structural characteristics, based on the digital speckle correlation method (DSCM) and machine vision, the contact stress distribution detection devices for rollers and complete sets of bearings are developed respectively and an effective detection method is proposed. The contact stress data of the bearing which has reached the service life and the new bearing under the condition of no lubrication and grease lubrication are collected and normalized. Through the geometric relationship, based on the measured data of the selected detection points, the normal and tangential contact stress distribution of the roller and raceway under different contact conditions is obtained by data fitting. The test can be used as an evaluation basis for the effectiveness of bearing modification and provide reference for bearing design.