Elastic Rotation Research Articles

Experimental Study on the Seismic Performance of Confined High Walls of Autoclaved Aerated Concrete Panels Used in Subway Stations

This study addresses the unique challenge of the partition walls in subway stations, featuring high height, fire prevention, and located outside the main frames, by introducing a confined autoclaved aerated concrete (AAC) panel wall system. Different from studies on a main frame with infill walls, this study aimed to explore the seismic performance of partition walls, which were fabricated with confined high AAC panel walls and located outside the main frames. A custom-designed partition wall, measuring 6600 mm in height, 3400 mm in width, and 200 mm in thickness, underwent cyclic testing. A detailed analysis of specimen’s failure modes was conducted, focusing on seismic behavior such as hysteresis curves, envelope curves, ductility, stiffness degradation, and energy-dissipation capacity. Additionally, the study delved into shear deformation, relative slippage between AAC panels, and reinforcement strains within the specimen. Finally, the D-value method for calculating the initial stiffness of the confined high AAC panel walls and the weak sub-structural approach for determining the load-bearing capacity of confined high AAC panel walls were proposed and validated. The results indicate that the strength degradation factor of the confined high AAC panel walls ranges from 0.971 to 0.716. The drift of its upper portion accounts for 76.94–83.63% of the total drift, while the energy dissipation factor of its upper portion is 0.8–4.8% higher than that of the entire specimen. The yield and ultimate drift rotations of the entire confined high AAC panel wall and its upper portions satisfy the elastic and elastic-plastic inter-story drift rotation limits specified in the Chinese code. The calculated initial stiffness of the confining frame, obtained using the D-value method, closely aligns with experimental results, with a deviation of only 2.48%. Additionally, the load-bearing capacity calculated using the weak sub-structural approach deviates from the experimental average by just 4.30%.

Measurement of safety state of cross-jointed segmental lining based on system performance index

Measurement of safety state of cross-jointed segmental lining based on system performance index

An Analytical Solution for the Bending of Anisotropic Rectangular Thin Plates with Elastic Rotation Supports

The mechanical analysis of thin-plate structures is a major challenge in the field of structural engineering, especially when they have nonclassical boundary conditions, such as those encountered in cement concrete road slabs connected by transfer bars. Conventional analytical solutions are usually limited to classical boundary conditions—clamped support, simple support, and free edges—and cannot adequately describe many engineering scenarios. In this study, an analytical solution to the bending problem of an anisotropic thin plate subjected to a pair of edges with free opposing elastic rotational constraints is found using a two-dimensional augmented Fourier series solution method. In the derivation process, the thin-plate problem can be transformed into a problem of solving a system of linear algebraic equations by applying Stoke’s transform method, which greatly reduces the mathematical difficulty of solving the problem. Complex boundary conditions can be optimally handled without the need for large computational resources. The paper addresses the exact analytical solutions for bending problems with multiple combinations of boundary conditions, such as contralateral free–contralateral simple support (SFSF), contralateral free–contralateral solid support–simple support (CFSF), and contralateral free–contralateral clamped support (CFCF). These solutions are realized by employing the Stoke transformation and adjusting the spring parameters in the analyzed solutions. The results of this method are also compared with the finite element method and analytical solutions from the literature, and good agreement is obtained, demonstrating the effectiveness of the method. The significance of the study findings lies in the simplification of complex nonclassical boundary condition problems using a simple and reliable analytical method applicable to a wide range of engineering thin-plate structures.

A deep learning approach for automated segmentation of magnetic bright points in the solar photosphere

Context. Magnetic bright points (MBPs) are small, bright, and conspicuous magnetic structures observed in the solar photosphere and are widely recognized as tracers of magnetic flux tubes. Previous studies have underscored the significance of MBPs in elucidating the mechanisms of coronal heating. The continuous advancement of solar telescopes and observation techniques has significantly enhanced the resolution of solar images, enabling a more detailed examination of MBP structures. In light of the growing availability of MBP observation images, the implementation of large-scale automated and precise MBP segmentation methods holds tremendous potential to facilitate significant progress in solar physics research. Aims. The objective of this study is to propose a deep learning network called MBP-TransCNN that enables the automatic and precise pixel-level segmentation of MBPs in large quantities, even with limited annotated data. This network is designed to effectively handle MBPs of various shapes and backgrounds, including those with complex features. Methods. First, we normalized our sample of MBP images. We then followed this with elastic deformation and rotation translation to enhance the images and expand the dataset. Next, a dual-branch encoder was used to extract the features of the MBPs, and a Transformer-based global attention mechanism was used to extract global contextual information, while a convolutional neural network (CNN) was used to extract detailed local information. Afterwards, an edge aware module was proposed to extract detailed edge features of MBPs, which were used to optimize the segmentation results. Focal loss was used during the training process to address the problem of the small number of MBP samples. Results. The average values of precision, recall, F1, pixel accuracy, and intersection over union of the MBP-TransCNN are 0.976, 0.827, 0.893, 0.999, and 0.808, respectively. Experimental results show that the proposed MBP-TransCNN deep learning network can quickly and accurately segment the fine structure of MBPs.

A finite rotation, small strain 2D elastic head model, with applications in mild traumatic brain injury

A finite rotation, small strain 2D elastic head model, with applications in mild traumatic brain injury

Динамика плоского движения космического крана-манипулятора типа руки с учетом изгиба звеньев

The paper considers the plane motion dynamics of a three-link crane-manipulator consisting of two rods elastic in bending and a massive solid body attached to them at their end (load capture). All links are interconnected by hinge joints with the given (controlled) relative rotation angles. The first link is also connected to the mobile base. The system mathematical model was developed to calculate its non-stationary oscillations and dynamic loading of links at arbitrary in time and large relative angles of the links rotation as the solid bodies. The rods bending deformations (elastic transverse displacements and rotation angles of the axes) were considered to be insignificant (linear). Each rod ending was represented by the Ritz method using two given shape functions with the unknown coefficients, which were taken as the generalized coordinates. In this case, the “cantilever” bending forms of each rod with the given transverse displacement and angle of rotation at their ends were used. A simplified version was considered: each rod bending was represented by only one given form of its bending by a single moment applied at the end. System oscillation equations were obtained based on the principle of probable displacements in the generalized coordinates (four equations or two in a simplified form). Since rotation angles at the ends of the elastic rods were added to the given rotation angles of the non-deformable rods, total angles were left under the signs of sines and cosines without linearization for convenience of calculations and increasing accuracy. As a result, such equations of non-stationary oscillations remained non-linear. They were integrated by numerical methods using standard programs in one of the computer algebra systems. Examples are provided with the comparative results estimates obtained in the two-term and one-term approximations of the function in regard to the bending form of the system bending rod joints.

A NiCrAlTi coating combining the tough nano-grained matrix and the soft nano-precipitate with outstanding cavitation-resistant performance

A NiCrAlTi coating combining the tough nano-grained matrix and the soft nano-precipitate with outstanding cavitation-resistant performance

Measurement of the pattern shifts for HR-EBSD with larger lattice rotations

High-resolution electron backscattering diffraction (HR-EBSD) was used to measure rotations and elastic strains by matching diffraction patterns based on cross-correlation. However, the subset-based phase correlation algorithm was unable to determine pattern shifts accurately when large rotations occurred. In this paper, a new matching algorithm was proposed to measure pattern shifts and recover the elastic strain and lattice rotation with finite deformation theory. The algorithm was implemented in two steps: (a) Integral pixel matching: The pixel-related information of the Kikuchi patterns was mapped to the original three-dimensional sphere to obtain the image projected in parallel by using the feature points as the pattern center through the transformation of its spatial coordinates. The correlation between the images projected in parallel before and after deformation was then obtained. The locations of the integral pixels were determined by the peaks of the surface of correlation obtained by traversing all pixels in the search area. (b) subpixel refinement: the locations of subpixels were obtained by FAGN with an appropriate shape function involving rotation and translation. The algorithm was applied to dynamic simulated test sets, and its results were compared with those of the first-pass cross-correlation and the second-pass cross-correlation method with remapping. The proposed method was more robust in the case of rotation and solved the problem that displacement vectors could not be accurately measured when a larger lattice rotation occurred. The mean errors of the measured displacement, rotation, and strain components were 0.02pixel, 0.5×10-4rad, and 1×10-4, respectively. Compared with the second-pass cross-correlation method, the angle of rotation was more precisely extracted.

Characterization of a nanopipe dislocation in GaN by means of HR-EBSD and field dislocation mechanics analysis

A nanopipe threading screw dislocation in a GaN layer is studied. A recently developed high-angular resolution electron backscatter diffraction technique, relying on a global image registration of Kikuchi patterns, is used to assess elastic strain and rotation fields in the defected area. The characterization is complemented with predictions from a piezoelectric field dislocation mechanics model of a threading screw dislocation line. In plane elastic fields are obtained at the free surface, which arise from the cancellation of the dislocation bulk shear stress field. The experimental and simulated long range fields agree qualitatively well and correspond to a screw dislocation with Burgers vector magnitude 3c = 1.56 nm.

A multinode superelement in the generalized strain formulation

Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes.This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called “full approach” gives more accurate results than the so-called “corotational approach” but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.

Three-Dimensional Modeling of Soil-Structure Interaction for a Bridge Founded on Caissons under Seismic Conditions

In recent years, the urgent need to increase the safety standards of viaducts and bridges—under static and dynamic loading conditions—has required the development of advanced modeling approaches able to accurately predict the expected behavior of such infrastructures in a reliable manner. This paper presents a comparison between the adoption of a simplified modeling approach, widely used in the current practice, where the response of the structural system neglects the effects of the soil-structure interaction (SSI) phenomenon (considering the base of the structure fixed at the ground surface) and a rigorous modeling approach that considers the full 3D problem with all the components of the system (superstructure, foundation, and soil), through a finite element model. The pier of a real-world viaduct in central Italy was considered, with the aim of starting from a specific case study with foundation characteristics that are frequently found in viaducts in Italy, to obtain results that can be generalized to a wide range of similar types. Its behavior was evaluated both in the dynamic range of small oscillations and in the field of the seismic response to low and strong motion events. The results show that, in terms of seismic demand, the fixed-based model appears more conservative, but it significantly underestimates both elastic and residual displacements and rotations

Characterization of complex fluvial-deltaic deposits in Northeast India using Poisson impedance inversion and non-parametric statistical technique

Characterizing complex fluvial-deltaic deposits is a challenging task for finding hydrocarbon discoveries. We described a methodology for predicting the hydrocarbon zones from complex well-log and prestack seismic data. In this current study, data analysis involves an integrated framework based on Simultaneous prestack seismic inversion (SPSI), target correlation coefficient analysis (TCCA), Poisson impedance inversion, and non-parametric statistical analysis, and Bayesian classification. First, seismic elastic attributes from prestack seismic data were estimated. They can provide the spatial distribution of petrophysical properties of seismic data. Then target correlation coefficient analysis (TCCA) was estimated roration factor “c” from well-log data. Using the seismic elastic attributes and rotation factor “c”, Poisson impedance inversion was performed to predict the Poisson impedance volume. Finally, Bayesian classification integrated the Poisson impedance volume with non-parametric probabilistic density functions (PDFs) to estimate the spatial distribution of lithofacies. Despite complex characteristics in the elastic properties, the current study successfully delineated the complex fluvial-details deposits. These results were verified with conventional findings through numerical analysis.

Improving the Mechanical Properties of Liquid Hydrocarbon Storage Tank Materials

Methods for effective modules evaluation of materials with nanoinclusions of different shapes have been developed. The strength and dynamic characteristics of tanks and structures of fuel tanks and cisterns were determined by solving hydroelastic interaction issues. Especially important are the researches of the structures strength under the impulse, shock and seismic loads conditions. The crucial issue of ensuring the reliability and trouble-free operation of liquid hydrocarbon storage systems today has been remain actual. The aim of the paper is to improve the mechanical properties of liquid hydrocarbon storage tank materials.The refined mathematical model has been proposed to clarify the frequencies and shapes of free tank oscillations of the partially filled by liquid due to the internal partitions presence taking into account the surface tension of the aggregate on the dynamic characteristics of liquid hydrocarbon storage tank at low gravity. The method for studying free and forced oscillations of the elastic rotation shell with the arbitrary meridian partially filled with the ideal incompressible fluid has been developed. To research the free and forced oscillations of shell structures with compartments containing liquid, the method of given shapes has been developed.Nanocomposites with aluminum matrix with steel spherical inclusions and with steel and carbon inclusions-fibers have been considered. The effective modules of these composites have been estimated. The calculations results demonstrate the obtained composite materials strengthening in the while density reducing. The method to specify the static and dynamic characteristics of shell structures made of different composite materials and partially filled with liquid has been developed. Numerical analysis of static and dynamic characteristics for the liquid hydrocarbon storage tank model has been performed.

Computation of Burgers vectors from elastic strain and lattice rotation data.

A theoretical framework for computation of Burgers vectors from strain and lattice rotation data in materials with low dislocation density is presented, as well as implementation into a computer program to automate the process. The efficacy of the method is verified using simulated data of dislocations with known results. A three-dimensional dataset retrieved from Bragg coherent diffraction imaging (BCDI) and a two-dimensional dataset from high-resolution transmission Kikuchi diffraction (HR-TKD) are used as inputs to demonstrate the reliable identification of dislocation positions and accurate determination of Burgers vectors from experimental data. For BCDI data, the results found using our approach show very close agreement to those expected from empirical methods. For the HR-TKD data, the predicted dislocation position and the computed Burgers vector showed fair agreement with the expected result, which is promising considering the substantial experimental uncertainties in this dataset. The method reported in this paper provides a general and robust framework for determining dislocation position and associated Burgers vector, and can be readily applied to data from different experimental techniques.

Confirmation of the physic unification by the ether elasticity theory

We precise the concept of ether by proving that its points can only rotate elastically on themselves, the ether volumetric density remains then constant, and an ether wave is the propagation of elastic ether point rotations. We prove that: a particle is constituted by ether point rotations, i.e., when a particle moves, only elastic ether rotations change their emplacements, but not those of the ether points; a particle is generally constituted by a sum of monochromatic ether waves that becomes only one of them when it is confined to move around a nucleus; the changes in the ether created by a particle but out of it, is the field that it created; two ether waves associated each to an electron moving in opposite sense around the nuclei can form by interference a stationary wave of very small energy. An atom of which all the electron ether waves are coupled, is said “noble”. A single electron ether wave can also propagate around the nucleus without falling on the nucleus, this happens when this ether wave superpose itself adequately at each round, this case is an “oxidation”. We prove that there is a “strong gravitation” between two protons even in a repulsive electromagnetic field when they are sufficiently close one to the other, this is explained by the General Relativity and the ether concept. We present then the ether elasticity interpretation of the “chemical” reaction and of the “nuclear” reaction and prove that two very close protons are submitted to a very strong gravitation that overcome their electrical repulsion as for example: two H nuclei form a He nucleus, on the contrary to the fact that in heavy nuclei, there are protons that cannot get close and therefore are submitted to repulsive forces that can cause their disintegration.

Analytical model of the in-plane torsion test

In research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination.

Investigation on behavior and seismic performance of reduced beam sections

Engineers prefer reduced beam section (RBS) connections in steel moment frames built in earthquake zones due to their many benefits. The RBS shape design significantly affects joint behavior. This paper examines the effect of RBS geometry on joint behavior and seismic performance using ANSYS finite element analysis software. RBS connections are investigated using European profiles and steel grades due to the limited number of studies using European profiles in the literature. The simulation study is carried out in three stages. In the first stage, an experimental study in the literature is simulated, and the reliability of the created finite element model is checked. In the second stage, geometric changes are made to the verified numerical model, and the obtained new models are examined under monotonic loading to observe the effect of RBS geometry on moment-rotation behavior. In the third stage, the effect of the change in the RBS geometry on the seismic performance is investigated under cyclic loading. As a result of the study, the effects of various changes made in the RBS geometry on the joint behavior and seismic performance are presented graphically. By using the results of the analysis under monotonic loading, the regression analysis is carried out, and the formulas giving the elastic-plastic stiffness, elastic moment capacity, and elastic rotation angle of the support are derived. Besides, simulation models show that the RBS joints' seismic performance met the minimum criteria specified in the earthquake code (AISC/ANSI 341-16) when European steel profiles and quality are applied.

Organic abrasive machining system for optical fabrication with 0.1-mm spatial resolution.

High-precision optics for short-wavelength regions, such as x rays and extreme ultraviolet light, generally require nanometer-level figure accuracy on their surfaces. Such optics are finished via a numerically controlled figure correction process in which the dwelling time of the machining tool on the workpiece is controlled. Due to the limitation of the machined spot size, it is difficult to remove mid-spatial-frequency (1 to 10mm-1) errors on an optical surface. To realize a high-spatial-resolution figure correction process for high-precision optics, we have been developing the organic abrasive machining (OAM) technique, which can generate a 100 µm machined spot using a small elastic rotation tool in a slurry that includes acrylic particles. In this study, an OAM apparatus that can measure the machining load was constructed. The effects of the machining and slurry conditions were investigated and high-spatial-resolution machining on a flat glass substrate was demonstrated. The root-mean-square roughness of the surface after OAM processing was below 0.2nm. Patterns with a minimum line and space size of 100 µm were successfully fabricated.

A duality‐based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

AbstractHigh‐rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement‐based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality‐based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf‐sup‐based skew‐symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high‐order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement‐rotation‐phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty‐based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different.