Discontinuous Loading Research Articles

An improved higher-order explicit time integration method with momentum corrector for linear and nonlinear dynamics

An improved explicit time integration method is proposed for linear and nonlinear dynamics. Its calculation procedure is obtained with cubic B-spline interpolation approximation and weighted residual method. In the formulation, a momentum corrector is used to improve actual computation accuracy, especially for some special discontinuous loads. Analytical solutions of the local truncation errors, algorithmic damping and period elongation have been deduced to obtain the influence of algorithmic parameters on these basis algorithmic properties. The proposed method possesses at least second-order accuracy and can achieve at most third-order accuracy for no physical damping case. With free algorithmic parameters, the proposed method has controllable stability and numerical dissipation. Some demonstrative numerical examples are tested to confirm high efficiency of the proposed method for a variety of dynamic problems such as, dynamic response analysis of linear systems under various representative applied loads, finite element analysis (FEA) for dynamic response of engineering structures, and nonlinear dynamic analysis for strong nonlinear system.

Micro‐to‐macro interactions in complex bodies: Wavelet‐based post‐processing detection

We propose to couple finite element simulations and wavelet‐based post‐processing analysis to explore deeply the interaction degree of microscopic events on the gross behavior of complex bodies (which class includes metamaterials), above all around material or load discontinuities. After summarizing the theoretical structures our procedure refers to, as a sample case we select a special class of complex materials, namely, quasicrystals, and show how the proposed scheme works. As a result, we point out the effects of atomic rearrangements characterizing the quasicrystal structure on the stress field around a crack tip in static and dynamical setting. Our procedure can be also used for the analysis of dynamic experimental data. In this case, it allows us to detect discontinuities at least along directions selected within the body. In turn, our procedure can be used for monitoring purposes.

ИЗГИБ КОМБИНИРОВАННЫХ ПЛАСТИН КУСОЧНОПЕРЕМЕННОЙ ТОЛЩИНЫ. РЕШЕНИЯ В ФУНКЦИЯХ ЛЕЖАНДРА

Abstract. The work considers the problems of flexure of plates of circular form and consisting of separate parts with different laws of thickness variation. The each part of this plate has the form of a ring. The mentioned separate sections may be made from the same or from the different materials. The material of the piece-wise variable plate parts can be isotropic or orthotropic, homogeneous or nonhomogeneous. In the places of the separate parts conjugation the plate’s thickness can be continuous or discontinuous. The action of symmetric load on piece-wise variable plate is studied. The analytical approach is used, the solutions are obtained in the closed forms in terms of Legendre functions and Legendre polynomials. Rather wide set of plates’ profiles is determined. For the satisfaction of the conditions of the separate sections conjugation the special auxiliary functions are introduced. The computation of the plate, consisting of three sections and subjected to an action of discontinuous loads, is considered as an example.

Dislocation-mediated shear amorphization in boron carbide.

The failure of superhard materials is often associated with stress-induced amorphization. However, the underlying mechanisms of the structural evolution remain largely unknown. Here, we report the experimental measurements of the onset of shear amorphization in single-crystal boron carbide by nanoindentation and transmission electron microscopy. We verified that rate-dependent loading discontinuity, i.e., pop-in, in nanoindentation load-displacement curves results from the formation of nanosized amorphous bands via shear amorphization. Stochastic analysis of the pop-in events reveals an exceptionally small activation volume, slow nucleation rate, and lower activation energy of the shear amorphization, suggesting that the high-pressure structural transition is activated and initiated by dislocation nucleation. This dislocation-mediated amorphization has important implications in understanding the failure mechanisms of superhard materials at stresses far below their theoretical strengths.

Complex study of the Portevin-Le Chatelier effect by uniaxial tension of axisymmetric specimens with ring concentrators of various geometries

In order to assess the influence of the geometry of the concentrators on the spatio-temporal inhomogeneities of the plastic flow of aluminum-magnesium alloys, uniaxial tension tests of axisymmetric specimens with ring concentrators of various geometries were carried out. The test program includes 4 groups of concentrators: a groove with a radius of 5 mm, a groove with an angle of 157 ° and a nose radius of 5 mm, a groove with an angle of 140 ° and a nose radius of 5 mm, and a groove with an angle of 140 ° and a nose radius of 5 mm. It is of interest to detect the effect of intermittent flow, which manifests itself in the form of load discontinuities in the loading diagram. An increase in the sharpness of the annular concentrator, and, consequently, an increase in the degree of stress concentration, leads to an increase in the bearing capacity of the samples (maximum perceived load), but deformation reserves decrease (maximum deformation at the time of destruction), and also affects the manifestation of the Portevin-Le Chatelier effect.

Differential quadrature-based solution for non-classical Euler-Bernoulli beam theory

The non-classical theories have attracted the attention of many researchers due to their high potentiality in capturing the micro/nano scale structural behaviour. Unlike classical theories, numerical treatment of non-classical theories is complicated and involves the solution of higher order differential equation with accurate representation of classical and non-classical degrees of freedom and associated boundary conditions. In the present work, a beam element is developed with in the framework of differential quadrature method for bending, free-vibration and stability analysis of non-classical strain gradient Euler-Bernoulli beam theory. The element is formulated by combining the governing equation and stress resultant equations with Lagrange interpolations as test functions. Detailed mathematical formulation of the element and its numerical implementation is presented. The convergence, accuracy and efficiency of the proposed element is demonstrated through numerical examples for different loading and boundary conditions. Further, the generality of the element is verified through solving examples with geometry and load discontinuity. Lastly, the results are compared with the finite element solution obtained for gradient beams to asses the accuracy and convergence behaviour of the two methods.

Time-dependent microstructural evolution mechanisms of twisted carbon nanotube fibers under tension and relaxation

Carbon nanotube (CNT) fibers are inevitably subject to severe plastic deformation under complex loading conditions while applying in wearable electronics. In this work, we uncover the time-dependent structure evolution mechanism of twisted CNT fibers by a series of continuous and discontinuous loading experiments. The results reveal that the highly twisted CNT fibers are more sensitive to strain rate and have large stress attenuation during the relaxation process. The in-situ tensile test under scanning electron microscope (SEM) indicates that the twisting angles of CNT fiber decreased during the stretching and relaxation due to the slippage and rearrangement of CNTs. An unsteady ternary model is developed to describe the stress relaxation behavior of twisted CNT fibers taking strain rate effect and the time dependence of viscosity into account; then the constitutive equations are mathematically derived and analyzed. We believe that this work would provide beneficial guidance for designing twisted CNT fiber with high reliability and durability.

Calculation of three-layer composite beams using difference equations of successive approximation method

Beams are considered the most popular bending elements used in building structures. With the load-bearing capacity and production characteristics, it is possible to use many different materials to combine them into beams to receive high economic-technical efficiency. Besides, because of the development of structural material industry, the manufacturing and construction technology, the form of beams is as diverse as composite wood beams, foundation beams, force-sensitive composite beams prior to installation grafting, steel-concrete combination beams. So there are many researches about solving the problems of multi-layer structures in general and multi-layer beams in particular by different calculation methods. In this paper, based on the theory of multi-layer composite rods and plates of A.R Rzhanitsyn the solutions of calculation analysis of three-layer beams that is subjected to discontinuous loads using difference equations of successive approximation method (MSA) are presented. The obtained results with good convergence show high accuracy of the numerical method with the use of difference equations of successive approximation method.

Metaproteomics of microbiota involved in submerged culture production of alcohol wine vinegar: A first approach

Acetic acid bacteria form a complex microbiota that plays a fundamental role in the industrial production of vinegar through the incomplete oxidation reaction from ethanol to acetic acid. The organoleptic properties and the quality of vinegar are influenced by many factors, especially by the raw material used as acetification substrate, the microbial diversity and the technical methods employed in its production. The metaproteomics has been considered, among the new methods employed for the investigation of microbial communities, since it may provide information about the microbial biodiversity and behaviour by means of a protein content analysis. In this work, alcohol wine vinegar was produced through a submerged culture of acetic acid bacteria using a pilot acetator, operated in a semi-continuous mode, where the main system variables were monitored and the cycle profile throughout the acetification was obtained. Through a first approach, at qualitative level, of a metaproteomic analysis performed at relevant moments of the acetification cycle (end of fast and discontinuous loading phases and just prior to unloading phase), it is aimed to investigate the microbiota existent in alcohol wine vinegar as well as its changes during the cycle; to our knowledge, this is the first metaproteomics report carried out in this way on this system. A total of 1723 proteins from 30 different genera were identified; 1615 out of 1723 proteins (93.73%) belonged to the four most frequent (%) genera: Acetobacter, Gluconacetobacter, Gluconobacter and Komagataeibacter. Around 80% of identified proteins belonged to the species Komagataeibacter europaeus. In addition, GO Term enrichment analysis highlighted the important role of catalytic activity, organic cyclic compound binding, metabolic and biosynthesis processes throughout acetic acid fermentation. These findings provide the first step to obtain an AAB profile at omics level related to the environmental changes produced during the typical semi-continuous cycles used in this process and it would contribute to the optimization of operating conditions and improving the industrial production of vinegar.

Exact closed-form solutions for nonlocal beams with loading discontinuities

A novel mathematical formulation is presented for the applications of the stress-driven nonlocal theory of elasticity to engineering nano-scale problems requiring longitudinal discretization. Specifically, a differential formulation accompanied with novel constitutive continuity conditions is provided for determining exact closed-form solutions of nonlocal Euler-Bernoulli beams with loading discontinuities, i.e. points of discontinuity for external loads and internal forces. Constitutive continuity conditions have to be satisfied in interior points where a loading discontinuity occurs and contain integral convolutions of the stress over suitable parts of the nonlocal beam. Several results show the effectiveness of the proposed method.

Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads

<p style='text-indent:20px;'>We study a rate-independent system with non-convex energy in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized <inline-formula><tex-math id="M1">\begin{document}$ BV $\end{document}</tex-math></inline-formula>-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.

Effect of mechanically induced structural rejuvenation on the deformation behaviour of CuZr based bulk metallic glass

Severe plastic deformation of bulk metallic glasses leads to rejuvenation of the amorphous structure. Here we present results demonstrating an improved plasticity for a Cu45Zr45Al5Ag5 bulk metallic glass alloy rejuvenated by severe plastic deformation via high-pressure torsion (HPT). Nanoindentation as well as atomic force microscopy measurements performed on the cross-section of HPT samples provide evidence for the enhancement in plasticity. A robust algorithm developed to reliably detect and quantify the discontinuities (pop-ins) in the nanoindentation load–displacement curves is applied to a large dataset. The results related to the rejuvenated structure demonstrate (i) a reduction of the number of detectable pop-ins as well as (ii) a reduction of their displacement offset. Furthermore, (iii) a pronounced increase in the total creep value is observed and correlates with a plasticity criterion as well as a reduced hardness and Young’s modulus that are heterogeneously distributed across the samples due to localized strain softening during HPT. Finally, (iv) atomic force microscopy topographies obtained from selected indents support the findings, showing less pronounced steps in the plastic pile-up. The experimental results indicate that rejuvenation by HPT processing leads to structural and dynamical heterogeneities, increased atomic mobility and an improved plastic deformation response.

A novel weak form quadrature element for gradient elastic beam theories

• A quadrature element is proposed for non-classical Euler–Bernoulli beam theories. • The element is formulated using variational principles and employs Hermite interpolation. • GLL points are used as element nodes and also used for numerical integration of matrices • All classical and nonclassical boundary conditions are represented accurately and with ease. • Numerical examples demonstrate the efficiency, accuracy and generality of the element. A novel weak form quadrature element is proposed for non-classical strain gradient Euler–Bernoulli beam theories. The element is formulated with the aid of variational principles and has displacement as the only degree of freedom in the element domain and displacement, slope and curvature at the boundaries. All the classical and non-classical support conditions associated with the gradient beam theory are represented accurately. The Gauss–Lobatto–Legendre quadrature points are considered as element nodes and also used for numerical integration of the element matrices. Numerical examples on bending, free vibration and stability analysis of gradient beams are presented to demonstrate the efficiency and accuracy of the proposed element. To substantiate the generality of the element, beams with discontinuity in loading and geometry are examined.

Study on oil pilot circuit of adaptive hydraulic drive of tool advance in mobile drilling machine

Introduction.An adaptive hydraulic drive of the tool advance in a mobile drilling machine is studied on the example of the URB-2.5 installation. A typical technological cycle of the mobile drilling machine is considered; the performance criteria are defined. An original design of the adaptive hydraulic drive is proposed on the basis of the analysis. Adaptation of the hydraulic drive of the tool advance is carried out using an adjustable volumetric hydraulic motor with a hydraulic control circuit under discontinuous loads on the tool during the drilling process.Materials and Methods. Through a preliminary computational experiment in the Matlab Simulink program, the following parameters of the control loop devices were determined: a hydromechanical sensor and a hydraulically controlled valve, on the basis of which the experimental setup was implemented. The performed multifactor experiment allowed identifying the processes in the original hydraulic control circuit of the hydraulic motor under various modes of tool loading.Research Results.The kinematic and power characteristics of the hydromechanical system of a mobile drilling rig, the hydraulic control effect on the settings of the hydraulic control circuit devices were obtained and determined. The results enabled to specify the rational ranges of the hydromechanical system operation for a typical work cycle.Discussion and Conclusions.The results obtained can be used to create hydraulic systems of new drilling machines with various characteristics. The application of the developed techniques of research and processing of their results will reduce the time and costs involved in designing adaptive hydraulic systems for mobile technological machines, creating prototypes and conducting commissioning procedures.

Identification of moving loads using a local linear embedding algorithm

A new approach for identifying moving loads is proposed in which one can identify continuous or discontinuous loads from the response data by using a local linear embedding algorithm. This approach is especially well suited for moving loads that are difficult to measure directly and it does not depend on modeling the structures. Four simulated examples are conducted on a 5-m beam with four types of moving loads and the results verify the usefulness of our approach, but there is a small amount of distortion at some stages. The robustness of the approach is further verified by contaminating the response data with white noise of different levels, and the results show that the approach mentioned in this paper has good robustness. This identification approach for moving loads can be applied to aerospace engineering applications.

Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities

This paper introduces a local multilevel mesh refinement strategy that automatically stops relating to a user-defined tolerance even in case of local singular solutions. Refinement levels are automatically generated thanks to a criterion based on the direct comparison of the a posteriori error estimate with the local prescribed error. Singular solutions locally increase with the mesh step (e.g. load discontinuities, point load or geometric induced singularities) and are hence characterized by locally large element-wise error whatever the mesh refinement. Then, the refinement criterion may not be self-sufficient to stop the refinement process. Additional stopping criteria are required if no physical-designed estimator wants to be used. Two original geometry-based stopping criteria are proposed that consist in automatically determining the critical region for which the mesh refinement becomes inefficient. Numerical examples show the efficiency of the methodology for stress tensor approximation in $$L^2$$ -relative or $$L^\infty $$ -absolute norms.

Methodology for analysis and calculation the discontinuous loading and transport systems in preparation the technical documentation using the RPMGlobal - Talpac software

Methodology for analysis and calculation the discontinuous loading and transport systems in preparation the technical documentation using the RPMGlobal - Talpac software

Microstrip Leaky-Wave Antennas With Nonuniform Periodical Loading of Shorting Pins for Enhanced Frequency Sensitivity

This paper investigates on an effective approach to enhance frequency sensitivity of the classic wideband EH1-mode microstrip leaky-wave antenna (MLWA). Nonuniform loadings of shorting pins are installed into the traditional EH1-mode microstrip line, which provide a unique discontinuity affecting the mutual intersection of the passband and stopband, thus generating a newly created stopband within the continuous EH1-mode fast-wave region. After broadening the stopband, the slope of normalized phase constant is remarkably raised up and the original wide bandwidth of the operating region is effectively reduced, resulting in a dramatically enhanced frequency sensitivity. An equivalent-circuit model of the proposed EH1-mode MLWA with nonuniform loading is built up at first, then its nonuniform loading discontinuity effect on dispersion transformation between passband and stopband is further explicated. Moreover, full-wave numerical extraction is also conducted to accurately demonstrate the modified phase constant under varied lateral pins’ loading positions and strip widths. After thorough discussion, one set of optimized parameters are selected into antenna design. Compared with the conventional counterpart, the proposed EH1-mode MLWA with nonuniform loading of shorting pins notably increases the frequency sensitivity from 0.038°/MHz to 0.135°/MHz.

General analysis of stressed beams on elastic foundation subjected to discontinuous loads

Analytical solutions describing the static and dynamic behaviour of axially loaded beams with elastic end restrains resting on two parameter foundation subjected to multiple discontinuous lateral loads have been obtained using the Adomian decomposition method (ADM). Fourier expansion (FE) is used to transform discontinuous loads to continuous loading functions. The effects of the truncation index of both the ADM and FE on the accuracy of the obtained solutions are studied to assess the validity of the given solutions. The influences of end restraints, foundation stiffness, loading type, axial stressing and excitation frequency on the beam deflection and straining actions are investigated. It has been concluded that as the foundation stiffness increases relative to the beam stiffness, the effects of the end conditions on the beam behaviour decrease.

Effectiveness of the Sliding Mode Control in a Two Coupled Discontinuous Dynamical Systems with Dry Friction

Numerical modeling and a tracking control of angular velocity of a rotor measured in the assumed sliding contact bearing subject to a discontinuous dynamical loading has been performed in this contribution. A contact interface in the direct current motor’s sleeve bearing has been treated as a dynamical system with dry friction, including a few sources of the stick-slip and creep-slip effects. The object of control is subject to an irregularly changing torque generated by another discontinuous dynamical system with friction. The loading comes from a block-on-belt model of a conveyer system with intensification of friction force, which has been elastically coupled with the direct current rotor’s shaft by means of the transmission belt. Therefore, the dynamic loading of the DC motor changes because of time-varying linear velocity of two belts. If such additional torque oscillates while the rotational velocity of the motor’s shaft is small due to a requirement, then it significantly affects the entire system’s dynamics producing stronger nonlinear response of the motor’s speed.