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"Hoop"
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Some Properties of Hyper Ideals in Hyper Hoop‐Algebras
In this paper, we investigate the structural properties of hyper ideals in hyper hoop‐algebras, a generalization of hoop‐algebras under the framework of hyperstructures. Building upon foundational concepts in hyper group theory and hoop theory, the study introduces definitions for hyper ideals and weak hyper ideals, as well as their absorptive and implicative variants. Various properties, examples, and characterizations of these ideals are presented. Additionally, the paper explores quotient structures and homomorphisms in the context of hyper hoop‐algebras, and establishes connections between different classes of ideals through a series of theorems. These results extend classical ideal theory and provide new insights into the algebraic structure and logic of hyper hoop‐algebras.
Journal Article
The analysis of column hoop layout for steel formwork
In this paper, based on the code, the stress and arrangement of column forms under different widths are analyzed, and the arrangement of column hoop under different form widths is calculated by adjusting formula algorithm and parameter selection. The analysis shows that when the width of the template changes from 100 mm to 300mm, the maximum spacing of the column hoop decreases first, then increases and then decreases. When the steel grade of the template is different, multiple formulas should be used to compare the calculation, and the typical width cannot be used as the representative value. Increasing the thickness of the template and increasing the strength grade of the steel can optimize the spacing arrangement of the column hoop, and improving the strength grade of the steel can optimize the column hoop arrangement more effectively for wide form.
Journal Article
Effect of considering thermoplasticity of gun steel on thermomechanical coupling response of barrel
To explore the effect of considering thermoplasticity of gun steel on the thermomechanical coupling of the barrel during artillery firing, the thermoplastic coupling behavior of the barrel under transient thermal and mechanical loads is investigated. A thermomechanical coupling finite element model of the barrel was established. The transient temperature field and stress field of the barrel during the gun firing process were analyzed. By comparing the results of the thermoelastic model with that of thermoplasticity model, the effect of considering thermoplastic of gun steel on thermomechanical coupling response of barrel was investigated. The results show that the peak of Mises stress evolution considering thermoplasticity of material in the bore of the barrel is significantly reduced during the gun firing process, and the hoop stress evolution appears double-peak phenomenon. In addition, at the peak moment of bore pressure, the peak values that the hoop and Mises stress distributions along the radial direction at the midpoint of the land are reduced by 14.5 % and 20.9 %, respectively. This paper can provide a reference for the design of a large-caliber barrel.
Journal Article
Deep Neural Network-Based Inverse Identification of the Mechanical Behavior of Anisotropic Tubes
Tube hydroforming is a versatile forming process widely used in lightweight structural applications, where accurate characterization of the hoop mechanical behavior is crucial for reliable design and simulation. The ring hoop tensile test (RHTT) provides valuable experimental data for evaluating the elastoplastic response of anisotropic tubes in the hoop direction, but frictional effects often distort the measured force–displacement response. This study proposes a deep learning-based inverse identification framework to accurately recover the true hoop stress–strain behavior from RHTT data. Convolutional and recurrent neural network architectures, including CNN, long short term memory (LSTM), gated recurrent unit (GRU), bidirectional GRU (BiGRU), bidirectional LSTM (BiLSTM) and ConvLSTM, were trained using numerically generated datasets from finite element simulations. Data augmentation and hyperparameter tuning were applied to generalization. The hybrid ConvLSTM model achieved superior performance, with a minimum mean absolute error (MAE) of 0.08 and a coefficient of determination (R2) value of approximately 0.97, providing a close match to the Hill48 yield criterion. The proposed approach demonstrates the potential of deep neural networks as an efficient and accurate alternative to traditional inverse methods for characterizing anisotropic tubular materials.
Journal Article
Hoop Strain Measurement During a SiC/SiC Ceramic Composite Tube Burst Test by Digital Volume Correlation of X-Ray Computed Tomographs
Background
Silicon carbide-fibre/silicon carbide matrix (SiC/SiC) composites are candidate materials for accident tolerant fuel cladding in light water and advanced gas cooled nuclear fission reactors. The mechanical and damage behaviour of ceramic composites is sensitive to the composite geometry, the microstructure and the loading state. Reliable test methods are needed to investigate the subcritical damage that affects hermetic properties and strength, and this requires precise measurements under loading states that are representative of operating conditions.
Objective
The objective was a novel methodology to measure the deformation of an internally pressurised ceramic composite tube.
Methods
A burst test of an internally ground SiC/SiC (filament wound and braided) ceramic composite tube, pressurized by radial expansion of a compressed elastomer insert, was observed in situ by high resolution (synchrotron) X-ray tomography. The full field three-dimensional displacements were measured by digital volume correlation, with a precise rotation correction applied to obtain the relative radial and circumferential displacements of the tube wall for the first time.
Results
The hoop strain, and its spatial variations, were determined as a function of the applied hoop stress and showed ovalisation and barreling of the tube. The quantity of subcritical matrix cracking increased with the tensile hoop strain, but the critical crack that caused rupture was not at the location of maximum tensile strain.
Conclusion
Precise measurements of the deformation during the burst test found non-uniform hoop strains that caused a non-uniform distribution of subcritical cracking, which could influence the hermetic properties and strength.
Journal Article
Fuzzy sub-hoops based on fuzzy points
Using the belongs to relation (e) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (e, e)-fuzzy sub-hoop, an (e, ev q)-fuzzy sub-hoop and a (q, ev q) -fuzzy sub-hoop are introduced, and several properties are investigated. Characterizations of an (e, e)-fuzzy sub-hoop and an (e, ev q)-fuzzy sub-hoop are displayed. Relations between an (e, e)-fuzzy sub-hoop, an (e, ev q)-fuzzy sub-hoop and a (q, ev q)-fuzzy sub-hoop are discussed. Conditions for a fuzzy set to be a (q, e vq)-fuzzy sub-hoop are considered, and condition for an (e, ev q)-fuzzy sub-hoop to be a (q, ev q)-fuzzy sub-hoop are provided.
Journal Article
Involutive filters of pseudo-hoops
In this paper, we introduce the notion of involutive filters of pseudo-hoops, and we emphasize their role in the probability theory on these structures. Characterizations of involutive pseudo-hoops are given, and their properties are investigated. We give a characterization of involutive filters of a good pseudo-hoop, and we prove that in the case of good pseudo-hoops, the sets of fantastic and involutive filters are equal. One of the main results consists of proving that a normal filter
F
of a bounded pseudo-hoop
A
is involutive if and only if
A
/
F
is an involutive pseudo-hoop. It is also proved that any implicative filter of a bounded pseudo-hoop is involutive and that any Boolean filter of a bounded Wajsberg pseudo-hoop is involutive. The notions of state operators and state-morphism operators on pseudo-hoops are introduced, and the relationship between these operators is investigated. For a bounded Wajsberg pseudo-hoop, we prove that the kernel of any state operator is an involutive filter.
Journal Article
Experimental Investigation on Effect of Hoop Thickness on Performance of Hooped Pelton Wheel
A recent improvement in Pelton runner design, the hooped runner, is based on a redistribution of behaviour among the buckets and hoops and which allows stresses to be minimized and efficiency is nearly equivalent to conventional Pelton Runner apart from low nozzle opening of 40% and 60%. This advanced design having a couple of superiority from the mechanical orientation as well as from the assembly point of view without any different difficulty from the hydraulic orientation that establishes the significance of this unique concept. In the present work, an actual laboratory-scale hooped Pelton runner is developed. The thickness of its hoop is varied as 2 mm, 3 mm and 4 mm and to prove the competence of this advanced design and the influence of hoop thickness on the hydraulic performance of the Pelton wheel, detailed experimental studies have been performed. From the results it has been concluded that the power output and efficiency of hooped Pelton runner are nearly the same as the conventional Pelton runner at all nozzle opening.
Journal Article
State hoops
In this paper, we define the notions of a state ⊔-hoop and a state-morphism ⊔-hoop extending the language of hoop by adding a unary operator and investigate some properties of them. Also, we extend state ⊔-hoop to state hoop and study the relation between state hoops and state BL-algebras, MV-algebras and BCK-algebras.
Journal Article