Geometric Analysis Method Research Articles

A Novel Geometric Nonlinear Analysis Method for Planar Beam Structures Based on Co- Rotation and Substructure Method

Nonlinear behavior analysis of structures using finite element methods requires multiple iterative solutions. Therefore, improving computational efficiency while ensuring the accuracy of nonlinear calculations is crucial. In this paper, a new geometric nonlinear analysis method for planar beam structures is proposed, based on the co-spinning method and the substructure method, using a substructure containing two planar beam elements as an example. The co-spinning method accurately calculates small deformations by subtracting rigid body displacement from the large displacement of the structure. The substructure method condenses the degrees of freedom of internal nodes into boundary nodes, greatly reducing the order of the nonlinear equilibrium equation group of the structure. The two methods are combined, and a calculation program is developed using the arc length method, which has good performance in solving nonlinear equation groups. Two classic examples are used to verify the correctness of the proposed method by comparing the results with existing literature.

Shark mandible evolution reveals patterns of trophic and habitat-mediated diversification

Environmental controls of species diversity represent a central research focus in evolutionary biology. In the marine realm, sharks are widely distributed, occupying mainly higher trophic levels and varied dietary preferences, mirrored by several morphological traits and behaviours. Recent comparative phylogenetic studies revealed that sharks present a fairly uneven diversification across habitats, from reefs to deep-water. We show preliminary evidence that morphological diversification (disparity) in the feeding system (mandibles) follows these patterns, and we tested hypotheses linking these patterns to morphological specialisation. We conducted a 3D geometric morphometric analysis and phylogenetic comparative methods on 145 specimens representing 90 extant shark species using computed tomography models. We explored how rates of morphological evolution in the jaw correlate with habitat, size, diet, trophic level, and taxonomic order. Our findings show a relationship between disparity and environment, with higher rates of morphological evolution in reef and deep-water habitats. Deep-water species display highly divergent morphologies compared to other sharks. Strikingly, evolutionary rates of jaw disparity are associated with diversification in deep water, but not in reefs. The environmental heterogeneity of the offshore water column exposes the importance of this parameter as a driver of diversification at least in the early part of clade history.

Back to Almost Ricci Solitons

In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds in the class of complete almost Ricci solitons. Then, we examine compact almost Ricci solitons using the orthogonal expansion of the Ricci tensor, this allows us to substantiate the concept of almost Ricci solitons.

Image Denoising Method Based on Harmonic Filtering and Non-Subsample Shear Wave Block Matching in Wavelength Domain

<p>Efficient noise filtering is the difficulty of image denoising on the premise of preserving the edge and internal texture information of the image. Therefore, this paper focused on adaptive Gaussian variational model and block matching image denoising method in the wave domain from the non-local point of view. At first, a 3D block match harmonic filtering model was establish in that wavelet domain, 3D transform was use to represent that real signals in the match block group in a sparse form, then the shrinkage threshold was used to achieve the purpose of pre-denoising, and the wavelet transform was then used to extract the high frequency part of the predictor image for filtering. In order to avoid edge blurring, Laplace-Gaussian algorithm was used to construct a new operator into the diffusion model, and the wavelet coefficients were reconstructed to obtain the final approximation of the original image. Secondly, a block matching denoising model based on shear wave was proposed. In order to avoid ill-conditioned problem, The multi-scale geometric analysis method using shearlet transform can improve the edge protection ability, and a block matching denoising model based on shearlet is proposed. The new model predicts the scaling threshold according to the statistical characteristics of the histogram, performs hard threshold filtering on the high-frequency sub-band to obtain the processed sub-band coefficients, and performs block matching 3D filtering on the decomposed low-frequency sub-band coefficients to obtain the processed coefficients. All processed subband coefficients are inversely transformed and reconstructed to obtain a denoised image. The analysis and simulation results showed that the two new models can effectively suppress noise and improve the clarity, and the block matching denoising based on shear wave had more advantages.</p> <p> </p>

Geometrical analysis of consecutive dynamic behaviors in process monitoring

Dynamic information plays an important role in developing monitoring models for industrial processes, and thus accurate evaluation of the dynamic behaviors within multiple consecutive process samples is of great significant. In this study, a geometrical analysis method is introduced to establish monitoring model for reflecting the operation status of the process system. By maximizing the volume of the obtained simplex, the source signals with least joint correlation are extracted from the archived process data. Based on the obtained signals, an offline model is developed with three monitoring statistics. Among them, two statistics are adopted to evaluate the static deviations of current sample, and the other one is used to reveal the dynamic behavior of the process system. After that, an online monitoring policy is designed for identifying the operation status of the industrial process based on the decisions of both static and dynamic statistics. Using the volume of simplex constructed by several consecutive samples, the dynamic behaviors of the process system can be better described and thus the detection sensitivity can be further improved. Besides, the normal shifts of operation conditions can also be distinguished from real process anomalies, so that the false alarms of the established model can be effectively reduced. Process data collected from a simulated process and a real industrial application is adopted to test the performance of the proposed method. Experimental results illustrate that the proposed method has better detection sensitivity for the faulty samples and can accurately identify varying operation condition.

Research on the Buckling Load of Clamped Spherical Caps Under External Pressure: Analyzed by the Fourier Series Model With Initial Geometric Imperfections

AbstractThe knockdown factor (KDF), which characterizes the difference between the actual buckling pressure and the classical theoretical pressure of clamped spherical caps under external pressure, is highly discrete. The mechanism that causes this discreteness is still not understood and has not been reproduced in numerical simulation. By scanning six clamped spherical caps, the geometric characteristics of the shells were analyzed, and a geometric model was established based on the Fourier series. The geometric model was simulated by the geometric and material double nonlinear buckling analysis method. The results were compared with the experimental data from this study and other references. 720 sets of clamped spherical caps under external pressure were simulated using the proposed Fourier series model and simulation method. The influence of the yield strength, geometrical parameter λ, dimensionless parameters radius-thickness ratio R/t, and the imperfection-thickness ratio e/t on KDF were studied, and the highly discrete characteristics of KDF were reproduced. The results showed that the proposed method has a better predictive effect on KDF, which is significantly improved over the “Eigemode imperfections” method. KDF is not only related to λ and e/t, but is also affected by the yield strength and R/t. The lower envelopes of KDF were obtained when e/t was less than 1.0 and 2.0. The NASA SP-8032 curve corresponds to the lower envelope of KDF when e/t is less than 8.0, and the curve is below the lower envelope of KDF when e/t is less than 1.0 and 2.0. As stipulated in the pressure vessel standard, the KDF obtained by NASA SP-8032 will be conservative for design conditions with e/t less than 1.0 or 2.0, and appropriate adjustment should be considered.

Review on Comparative Analysis of PSC Box Girder Bridge and PSC Precast I Girder Bridge Structure

Abstract: Bridge is the structure that provide passage over an obstacle. There are different types of bridge structure base on material & geometric parameters, from which prestress concrete I girder bridge and box girder bridge are widely used for medium to long span rang. Box girder bridge are the bridge where the main beam consist of girder in hollow shape, where as in I girder bridge main beam consist of I-shape girder are used as main girder beam. In this review article study about dynamic analysis of PSC precast I-girder bridge and PSC box girder bridge for different parametric variation and different span range have been studied by various researchers. The parameters are geometric parameters, span range, mending moment, shear force, displacement, base shear, base moment, time period, natural frequency, and method of analysis based on different codes. On the above parameters base reaction, base moment, time period, natural frequency, absolute displacement and girder forces of bridge is essential and major concern for the analysis of bridge structure

REFINEMENT OF THE FOUR-COMPONENT SYSTEM MgO – CaO – Al2O3 – Cr2O3 SUB-SOLIDUS STRUCTURE INCLUDING THE Сa6Al4Cr2O15 COMPOUND

The results of theoretical calculations of the subsolidus structure of the four-component system MgO – CaO – Al2O3 – Cr2O3 are presented, taking into account the three-component compound Сa6Al4Cr2O15. Thermodynamic and geometric topological analysis methods were used to establish stable conodes in the specified system. When dividing the concentration tetrahedron MgO – CaO – Al2O3 – Cr2O3 into elementary ones with the involvement of a geometro-topological analysis, it is possible to make an unambiguous closure to the elementary tetrahedron of faces with incident edges (connodes) through a common vertex. The use of this method allows to minimize the number of necessary thermodynamic calculations. The tetrahedra of the MgO – CaO – Al2O3 – Cr2O3 system, taking into account the stable phases, is caused by the presence of three "internal" conodes passing through the three-dimensional space of the concentration tetrahedron: Сa6Al4Cr2O15 – MgO; MgCa3Al4O10 – CaCr2O4, CaCr2O4 – MgAl2O4, which determine the presence of 14 elementary tetrahedra in the subsolidus region. The lengths of conodes and volumes of elementary tetrahedra were calculated taking into account barycentric coordinates and elements of Euclidean geometry. The phases included in the composition of the tetrahedron with the largest relative volume and the smallest asymmetry CaCr2O4 – СaAl2O4 –MgAl2O4 – MgO (185.6 ‰ and 2.55, respectively) have the highest probability of existence in the system, which will allow the development of a sustainable technology for creating composite materials based on calcium aluminochromite cement, with periclase as an aggregate, without special techniques dosage of initial components. At the same time, in the event of a violation of the technological process, magnesium aluminate spinel will be synthesized in the composition of the unformed material, which will not lead to deterioration of the performance characteristics of the composite used. It should be noted that elementary tetrahedra with a high degree of asymmetry, which require appropriate dosage accuracy when predicting the phase composition of synthesized composite materials, are located in areas of the system that are not technologically advantageous from the point of view of obtaining unformed refractories based on special binder materials, and are interest for materials scientists in the ceramic and refractory industries.

Experimental Study of the Thermally Grown Oxide and Interface of Thermal Barrier Coatings Using TEM In-Situ Heating.

Thermal barrier coating (TBC) materials play important roles in gas turbine engines to protect the Ni-based superalloys from high-temperature airflow damage. In this work, the nano-mechanism of TBC failure is analyzed. A scanning transmission electron microscopy-energy dispersive spectrometer (STEM-EDS)-based analysis method was used to study the influence of element migration on the deformation behavior of the bond-coat (BC) layer during heating. The content of elements in the same region varied greatly at different temperatures, which could prove the contribution of element migration to the deformation of the BC layer. TEM in-situ heating experiments were designed and carried out to study the deformation behavior near the ceramic topcoat (TC)/thermally grown oxide (TGO) and the TGO/BC interface. The TC/TGO interface was deformed violently during heating, and obvious deformation occurred at 100 °C, while the TGO/BC interface was relatively stable. A subset geometric phase analysis method was used for full field-strain measurement. The strain value near the TGO/BC interface was relatively small and did not change significantly at lower temperatures. The TC/TGO interface is more unstable and easier to deform than the TGO/BC interface. The stress and strain evolution in the internal region of TGO at high temperatures was quantitatively analyzed. The TGO layer has a tensile stress of GPa magnitude along the interface direction at the peak position, and the shear stress is small.

Geometric modeling analysis method for stacking assembly deviation of aero engine rotor

Purpose Assembly errors of aeroengine rotor must be controlled to improve the aeroengine efficiency. However, current method cannot truly reflect assembly errors of the rotor in working state owing to difficulties in error analysis. Therefore, the purpose of this study is to establish an optimization method for aeroengine rotor stacking assembly. Design/methodology/approach The assembly structure of aeroengine rotor is featured. Rotor eccentricity is optimized based on Jacobian–Torsor model. Then, an optimization method for assembly work is proposed. The assembly process of the high-pressure compressor rotor and the high-pressure turbine rotor as the rotor core assembly is mainly considered. Findings An aeroengine rotor is assembled to verify the method. The results show that the predicted eccentricity differed from the measured eccentricity by 6.1%, with a comprehensive error of 8.1%. Thus, the optimization method has certain significance for rotor assembly error analysis and assembly process optimization. Originality/value In view of the error analysis in the stacking assembly of aeroengine rotor, an innovative optimization method is proposed. The method provides a novel approach for the aeroengine rotor assembly optimization and is applicable for the assembly of high-pressure compressor rotor and high-pressure turbine rotor as the rotor core assembly.

A bioinspired fishbone continuum robot with rigid-flexible-soft coupling structure

Rigid-flexible-soft coupled robots are an important development direction of robotics, which face many theoretical and technical challenges in their design, manufacture, and modeling. Inspired by fishbones, we propose a novel cable-driven single-backbone continuum robot which has a compact structure, is lightweight, and has high dexterity. In contrast to the existing single-backbone continuum robots, the middle backbone of the continuum robot is serially formed by multiple cross-arranged bioinspired fishbone units. The proposed bioinspired fishbone unit, having good one-dimensional bending properties, is a special rigid-flexible-soft structure mainly made by multi-material 3D printing technology. The unique design and manufacture of the middle backbone provide the continuum robot with excellent constant curvature characteristics and reduce the coupling between different motion dimensions, laying a foundation for the continuum robot to have a more accurate theoretical model as well as regular and controllable deformation. Moreover, we build the forward and inverse kinematics model based on the geometric analysis method, and analyze its workspace. Further, the comparison between the experimental and theoretical results shows that the prediction errors of the kinematics model are within the desired 0.5 mm. Also, we establish the relation between the cable driving force of the bioinspired fishbone unit and its bending angle, which can provide guidance for the optimization of the continuum robot in the future. The application demos prove that the continuum robot has good dexterity and compliance, and can perform tasks such as obstacle crossing locomotion and narrow space transportation. This work provides new ideas for the bioinspired design and high-precision modeling of continuum robots.

Experimental Study at the Phase Interface of a Single-Crystal Ni-Based Superalloy Using TEM.

The single-crystal Ni-based superalloys, which have excellent mechanical properties at high temperatures, are commonly used for turbine blades in a variety of aero engines and industrial gas turbines. Focusing on the phase interface of a second-generation single-crystal Ni-based superalloy, in-situ TEM observation was conducted at room temperature and high temperatures. Intensity ratio analysis was conducted for the measurement of two-phase interface width. The improved geometric phase analysis method, where the adaptive mask selection method is introduced, was used for the measurement of the strain field near the phase interface. The strained irregular transition region is consistent with the calculated interface width using intensity ratio analysis. An intensity ratio analysis and strain measurement near the interface can corroborate and complement each other, contributing to the interface structure evaluation. Using TEM in-situ heating and Fourier transform, the change of dislocation density in the γ phase near the two-phase interface of the single-crystal Ni-based superalloy was analyzed. The dislocation density decreases first with the increase in temperature, consistent with the characteristics of metal quenching, and increases sharply at 450 °C. The correlation between the variation of dislocation density at high temperatures and the intermediate temperature brittleness was also investigated.

A meshless method for geometric nonlinear analysis of arbitrary polygonal and circular stiffened plates

Based on the first-order shear deformation theory, a meshless Galerkin method for geometric nonlinear analysis of arbitrary polygonal and circular stiffened plates is proposed. The arbitrary polygonal and circular stiffened plates are modeled as composite structures that consist of flat plates and stiffeners. A series of points are used to discretize the flat plate and stiffeners to obtain the meshless model of the stiffened plates. The moving least-squares approximation is used to construct the shape functions and the displacement fields. The large deflection theory of von Karman is adopted for the geometric nonlinear analysis of the stiffened plates, and flexure and extensional properties of the stiffened plates are derived. The stiffeners are fitted to the flat plate by implementing displacement compatibility conditions between the flat plates and the stiffeners. The boundary conditions are enforced by the full transformation method. To demonstrate the convergence and accuracy of the proposed method, several numerical examples are employed. The solutions that are computed by the proposed method are compared with the finite element solutions that are given by ABAQUS and with the results of other research work. The results show that the agreement is good. Because no mesh is required in the model, the stiffeners can be placed anywhere on the flat plates, and changes to the positions of the stiffeners do not entail the remeshing of the plates.

Evaluating and Analyzing the Potential of the Gaofen-3 SAR Satellite for Landslide Monitoring

Gaofen-3 is the first Chinese spaceborne C-band SAR satellite with multiple polarizations. The Gaofen-3 satellite’s data has few applications for monitoring landslides at present, and its potential for use requires further investigation. Consequently, we must evaluate and analyze the landslide interference quality and displacement monitoring derived from the Gaofen-3 SAR satellite’s data, particularly in high and steep, mountainous regions. Based on the nine Gaofen-3 SAR datasets gathered in 2020–2021, this study used DInSAR technology to track landslide displacement in Mao County, Sichuan Province, utilizing data from Gaofen-3. Our findings were compared to SENTINEL-1 and ALOS-2 data for the same region. This study revealed that due to its large spatial baseline, Gaofen-3’s SAR data have a smaller interference effect and weaker coherence than the SENTINEL-1 and ALOS-2 SAR data. In addition, the displacement sensitivity of the Gaofen-3 and SENTINEL-1 data (C-band) is higher than that of the ALOS-2 data (L-band). Further, we conducted a study of observation applicability based on the geometric distortion distribution of the three forms of SAR data. Gaofen-3’s SAR data are very simple to make layover and have fewer shadow areas in hilly regions, and it theoretically has more suitable observation areas (71.3%). For its practical application in mountainous areas, we introduced the passive geometric distortion analysis method. Due to its short incidence angle (i.e., 25.8°), which is less than the other two satellites’ SAR data, only 39.6% of the Gaofen-3 SAR data in the study area is acceptable for suitable observation areas. This study evaluated and analyzed the ability of using Gaofen-3’s data to monitor landslides in mountainous regions based on the interference effect and observation applicability analysis, thereby providing a significant reference for the future use and design of Gaofen-3’s data for landslide monitoring.

Research on steering-tilting characteristics of an active tilting three-wheeled vehicle

Active tilting narrow vehicles can prevent rollover and improve riding stability through active tilting technology during steering, but it is difficult to obtain the turning radius and solve the optimal tilting angle. In this paper, based on the active tilting three-wheeled vehicle (ATTWV), the geometric analysis method of steering wheel’s alignment was proposed and used to calculate the specific formula of turning radius during steering and tilting, and the effect of tilting on the turning radius was studied. Based on the steering and tilting mathematical model of force equilibrium state, the ideal tilting angle was solved and the S-shaped curve steering test verification was carried out with the prototype vehicle. The results show that the lateral acceleration of the vehicle fluctuates within ±0.16 g during steering, realizing the equilibrium between the component of gravity and centrifugal force. The average error between the actual tilting angle and the calculated ideal tilting angle is 1.18°. Based on steering and tilting mathematical model of the rollover critical state of the ATTWV, the safe turning speed under the specific tilting angle can be solved, and the value range of the tilting strength coefficient can be obtained, which provides not only a reference for the control of ATTWVs but also a theoretical basis for the research on accurate self-driving control of the active tilting narrow vehicles in the future.

Nanoindentation investigation of incoherent twin boundary migration in Au nanocrystalline films

Incoherent twin boundary (ITB) evolution and migration induced by nanoindentation in Au nanocrystalline films were systematically investigated by Cs-corrected transmission electron microscopy (TEM). With a gradient stress distribution at various indentation depths, 9R/3R phase nucleation is greatly facilitated at the ITBs. The 9R/3R phase formation can be achieved by collective glide of triple partial dislocations with different Burgers vectors at two phase boundaries. With 9R/3R phase at ITBs, atoms on consecutive {111} planes shear in a helical manner, generating zero macroscopic strain during ITB migration. Dislocation interactions with ITBs were further analyzed by combining atomic-scale high-angle annular dark-field scanning TEM (HAADF-STEM) with geometric phase analysis method. ITBs can both absorb partial dislocations and emit partial dislocations from the junctions between coherent twin boundaries and ITBs, providing complementary mechanisms for ITB migration in Au nanocrystalline films under nanoindentation. These results suggest the critical role of 9R/3R phase nucleation in ITB migration and provide a deeper understanding of nanoindentation-induced deformation twinning in nanocrystalline films.

A class of spatial remote center-of-motion mechanisms and its forward kinematics

AbstractRobot-assisted minimally invasive surgery (MIS) has shown tremendous advances over the traditional technique. A crucial challenge for developing a MIS robot is the kinematic design of the remote center-of-motion (RCM) mechanism. In this paper, a class of spatial RCM mechanism is analyzed. They are obtained by generating virtual parallelograms. The main process is to construct a line that passes through a fixed point under the mechanical constraint. The axis of the surgical tool is then constrained to parallel with that line. Hence, due to the geometrical feature of the parallel lines, the axis of the surgical tool will always pass through a fixed point, i.e., the RCM point. Due to the specially designed structure, the fixed point does not need to be physically belonging to the mechanism. The geometrical analysis method is employed to obtain the closed-form solution of the forward kinematics of the proposed mechanisms. Due to the high load capacity of parallel mechanism, the robots based on the proposed RCM mechanisms have promising applications as an external positioner to be used in robotic single-port surgeries.

Testing the Bordes method on handaxes: A geometric morphometric approach

Bordes’ typology has been in use for many years and is widely applied in studies of Early and Middle Palaeolithic stone tools, especially in vocabulary and typological classification in shaping artefacts (mainly flake tools and handaxes). However, over the years, this method has received different critiques, especially regarding the arbitrariness and subjectivism in the definition and classification of some artefacts. The application of geometric morphometric methods (2D or 3D) on the study of stone tools is starting to become widespread. These methodological approaches are highly suitable for measuring patterns in shape change between artefact groups, which would be impossible to establish with more “traditional” methods. This paper aims to analyse the accuracy and reliability of the main types of handaxes established by Bordes, by performing different methods of Geometric Morphometric Analysis. The evidence from this study suggests that a large percentage of the handaxe types noted by Bordes is reliable and correlates with statistically significant changes in shape and only a small percentage of forms have no geometric morphometric significance. Likewise, these findings support the suitability of Geometric Morphometric Analysis on lithic artefact assemblages focusing on the measurement and classification by shape changes.

The Influence of Buckling Mode and Buckling Stability Coefficient of Rigid-Frame Bridge during Construction in Cold Region

The study aims to further standardize the construction process, improve the construction quality, and ensure the stability of infrastructure construction. The continuous rigid-frame bridge is taken as the research object, the finite element model of the bridge body is established by using the beam element, and the overall stability of the rigid-frame bridge is analyzed in the construction and completion stages. Moreover, the stability coefficient and buckling mode are established under different working conditions in each stage, the linear stability variation law is summarized, and the geometric nonlinear stability analysis method is established through the specific data. The nonlinear stability safety factor and buckling mode are obtained, and the influence of wind load and initial defects on the stability of continuous rigid-frame bridge is further explored. The results show that with the increase of the bridge height, the overall stability factor of the bridge is decreasing, and the safety factor of the single-limb thin-walled hollow pier is relatively larger than that of the double-limb thin-walled hollow pier. During the construction, the asymmetric self-weight load caused by the asynchronous load and cantilever pouring has the greatest impact on the stability of the bridge. The stability safety factor of the geometric nonlinear stability analysis method constructed is 0.3% and 1.27% lower than the ideal state, respectively. The stability safety factor of the wind load and the initial defect is 12.65% lower than the ideal state, and the stability safety factor is greatly reduced. The results have important reference significance to ensure the construction safety and overall stability of the bridge.

Morphometric analysis for the sex determination of the skull of the Deltari Ilir dog (Canis lupus familiaris) of Kosovo.

This study aimed to explain the sex determination of the autochthonous dog Deltari Ilir with both morphometric and geometric analysis methods. For this purpose, 24 Deltari Ilir dog skulls (12 females and 12 males) were used in the study. The difference between males and females at 6 values was statistically significant. The most statistically significant difference was seen in the measurement of the greatest breadth of the occipital condyles (p < 0.000). This measurement was higher in male skulls. The next most significant difference was seen in the greatest inner height of the orbit measurement (p < 0.002). This measurement was also higher than for females. In general, the skull length measurements of male dogs were higher than that of females. Male dog skulls had greater skull length and skull height. The lateral view was used for geometric analysis and 14 landmarks were determined. As a result of principal component analysis, 22 PC values were obtained. PC1 accounted for 23.73% of the total variance. As a result of canonical variants analysis, it was observed that males and females were completely separated from each other. The caudal part of the males was wider than the females in geometric analysis. As a result of the study, sex-determining characteristics were revealed for the Deltari Ilir dog. It was seen that gender analysis could be done with both morphometric and geometric analysis methods. In addition, it was seen that morphometric results and geometric analysis results supported each other. Moreover, the results of the study will be useful in the function of comparative anatomy, in veterinary clinical practice, in zooarchaeology but why not also in the veterinary forensic investigation.