Search Results (6)

Concrete structures such as bridge decks and road pavements are subjected to repetitive loading and are susceptible to fatigue failure. A simplified stress–strain analysis method that can simulate concrete behavior with a sound physical basis, acceptable prediction precision, and reasonable computation cost is urgently needed to address the critical issue of high-cycle fatigue in structural engineering. An equivalent fatigue constitutive model at discrete loading cycles incorporated into the concrete damaged plasticity model (CDPM) in Abaqus is proposed based on fatigue damage evolution. A damage variable is constructed from maximum fatigue strains, and fatigue damage evolution is described by a general equation whose parameters’ physical meaning and value range are identified. With the descending branch of the monotonic stress–strain curve as the envelope of fatigue residual strength and fatigue damage evolution equation as shape function, fatigue residual strength, residual stiffness, and residual strain are calculated. The equivalent fatigue constitutive model is validated through comparison with experimental data, where satisfactory simulation results were obtained for axial compression and flexural tension fatigue. The model’s novelty lies in integrating the fatigue damage evolution equation with CDPM, explicitly explaining performance degradation caused by fatigue damage. The proposed model could accommodate various forms of concrete constitution and fatigue stress states and has a broad application prospect for fatigue analysis of concrete structures. Full article

In order to resolve the issues of low efficiency and poor precision in the traditional finishing process of hardened internal gears, a method is proposed for calculating the profile curves of a drum-shaped grinding tool suitable for mass finishing of hardened internal gears. Additionally, the impact of drum-shaped grinding tool installation errors on the tooth surface deviation of internal gears is analyzed. Firstly, the processing principle for the generation grinding of internal gears by the drum-shaped grinding tool is introduced. Based on differential geometry, meshing theory, and two-degree-of-freedom enveloping method, a mathematical model is developed for the generation grinding of internal gears. Profile curves of the drum-shaped grinding tool are obtained by solving the meshing equation between the drum-shaped grinding tool and the internal gear. Then, the tooth surface equation for the internal gear is derived in the presence of drum-shaped grinding tool installation errors. By discretizing the error tooth surface of the internal gear, the average normal deviation of the tooth surface is calculated. In the end, the distribution of normal deviation on the tooth surface of the internal gear with different drum-shaped grinding tool installation errors is acquired, and the influence of four kinds of installation errors on the tooth surface of the internal gear is analyzed. The sensitive direction is identified for drum-shaped grinding tool installation errors on the tooth surface of the internal gear. Consequently, this research provides a calculation method for the drum-shaped grinding tool fit for high-precision and high-efficiency finishing of mass-produced hardened internal gear and offers a reference for correcting deviation in the tooth surface of internal gear with installation errors of the drum-shaped grinding tool. Full article

This paper employs the discrete element method (DEM) to study the mechanical properties of artificial crushed stone. Different grain shapes and gradations are considered, and three types of 3D artificial stone models are generated based on the statistical conclusions in the relevant literature and the observed data. Concurrently, the 3D models of the artificial stones are divided into three groups by their shape parameters (elongation index and flatness index). Furthermore, three types of gradation with different Cu (coefficient of uniformity) and Cc (coefficient of curvature) are also considered. Then, several 3D triaxial compression tests are conducted with the numerical methods to determine the relationship between the grain shapes and their mechanical characteristics. The test results showed that there was a positive correlation between a particles’ angularities and the maximum deviatoric stress in the triaxial compression tests when there were obvious distinctions between the particles. In addition, gradations had a conspicuous impact on the stiffness of the sample. The stress–strain curve possessed a larger slope when the coefficient of curvature was bigger. In terms of shear strength, the results in this paper align well with the traditional shear strength envelope which are convincing for the dependability of the methods used in this paper. The radial deformation capacity and volume strain of the specimen during the triaxial compression tests are also examined. It is believed that there were great differences in deformability between different samples. At the mesoscopic level, the change in coordination number is identified as the fundamental reason for the change in volume strain trend. Full article

This paper presents a method for obtaining the shape and area of a sofa. The proposed approach is based on a discrete solution to the equation, which states the necessary conditions for the existence of envelopes. Based on provided examples, it was proved that the method can be used for deriving the solutions of the posed problem. The method offers an area calculation accuracy of $1.5\times {10}^{-8}$. Full article

This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT. Full article

Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the ${\mathbb{R}}^{2,1}$ Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in ${\mathbb{R}}^{2,1}$ that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently. Full article