Discontinuous Loading Research Articles

A permeability model considering the dynamic effect of stress on gas adsorption under discontinuous compression.

With the continuous advance of coal mining, the normal stress in front of coal seams will continue to increase, resulting in changes of internal structure and permeability of coal seams. During the continuous advance of mining face, the increase of vertical stress somewhere in front of coal seams may not be a transient process, but a gradual change process. Therefore, this paper carried out the seepage test of gas-containing coal under discontinuous loading axial stress. The stress, deformation and permeability of coal specimens were measured and recorded during the test, and the influence of discontinuous loading axial stress on the deformation, internal structure and seepage properties of coal specimens were discussed. On this basis, considering the influence of stress on the gas adsorption state, Klinkenberg effect and other factors, combined with Shi-Durucan permeability model, a new permeability model considering the dynamic adsorption state of coal specimens was developed.

Effect of continuous and discontinuous non-proportional loadings on formability of DX54 sheet material

Both continuous and discontinuous non-proportional loadings occur in multi-stage automotive stamping processes. Discontinuous loading is widely studied, but due to requiring sophisticated experimental procedures, continuous loading has been studied less. This study explores the impact of continuous loading on DX54 steel utilising an innovative experimental setup that enabled cruciform samples to undergo uniaxial to biaxial strain path change continuously without unloading. A similar two-stage discontinuous loading from uniaxial to biaxial with unloading in between was generated in DX54 to understand the differences in macro-strain, micro-strain, microstructure, and micro-texture evolution between the continuous and the discontinuous loadings. The stress state of the material during continuous loading was different to that during discontinuous loading. In this study, the occurrence of ‘pseudo-localisation’ was observed during continuous loading, and the observed rotation of high-strain bands differed between continuous and discontinuous loading. The discontinuous loading induced a higher strain, hardening rate, and increased elongation compared to the continuous loading. These results suggest the potential for higher formability during the discontinuous loading compared to the continuous loading.

Dynamic analysis of a hydraulic motor lifting auxiliary beam of monorail crane

Abstract Monorail crane that is an important class of auxiliary transportation equipment in coal mine. It works on a single hanging track fixed above the coal mine roadway to transport materials, machines, people, etc. Lifting auxiliary beam is the main part of the lifting beam which is used to complete the lifting and transport operations. In the application process, the lifting auxiliary beam is bore many types of loads such as discontinuous loading, frequent starting and braking etc. It complicates the dynamic performance that directly affects the safety and the lifting operation stability. By using finite element method, a dynamic model of the lifting auxiliary beam is established to study the variation laws of dynamic load, frequency, amplitude, etc. Furthermore, three loading conditions are defined in the model. They are static loading, slow loading and fast loading, considering the lifting operation time. The numerical simulation results show that the maximum displacement of the fast loading condition is 20% to 23% higher than that under the static loading condition. Moreover, under the fast loading condition, the largest displacement amplitude occurs in the middle part of the lifting auxiliary beam and it decreases gradually towards the ends.

Transient surrogate modeling of modally reduced structures with discontinuous loads and damping

In this work, a surrogate model for structural, transient and discontinuously excited finite element method simulations is developed. This allows to reduce the computational effort of repeated calculations of identical models under different load cases. The architecture of the surrogate combines fully connected neural network layers with long short-term memory layers. For the reproduction of different damping ratios, a categorical variable is added to the continuous input data. Based on a recursive flow of the predicted data back to the input layer, long-term dependencies do not vanish due to short-input sequences. The system dimension is reduced by applying the model-order reduction technique for modal decomposition. The high accuracy of the surrogate and the reduction of computational costs are shown on an academic example of a cantilever beam and a real-world example of a robot. The advantages of our approach are illustrated in comparison with state-of-the-art surrogates for transient finite element analysis. By using the surrogate proposed in this study, oscillations due to discontinuous excitation of mechanical structures can be reproduced. For this purpose, only short-input sequences are necessary since the excitation of the oscillations does not have to be part of the input sequence during the whole duration of the oscillations. Due to the categorical variable for the damping ratio, the surrogate can account for the influence of different damping in parameter studies.

Optimal declutching control of hinged multiple floating bodies

In deep seas, there is an increasing utilisation of multiple floating structures as devices for harnessing renewable energy, such as hybrid wind-wave energy systems and multi-body wave energy converters. The control strategies have a great influence on the motion characteristics and energy conversion efficiency of these systems. The control technology brings more benefits to the system's performance, yet also introduces more complex challenges. This paper aims to fill the research gap in the control of multiple floating bodies and to propose a novel optimal declutching control method. Declutching control enables discontinuous loading and releasing of the force from power take-off system between bodies. It was found that the feasibility of the proposed method is highly dependent on the choice of objective functions, iteration numbers, and wave frequencies. With appropriate parameters, the declutching control can achieve a variety of objectives for a hinged floating multibody system, such as reducing pitch motion, improving extracted wave power, increasing relative rotational speed, and enhancing power extraction. The control effects on the velocity and the force-velocity phase relationship and how they benefit the objectives are discussed. All objective functions show a better control effect (at least 7.76%) on their respective performance indices than others.

On a lack of stability of parametrized BV solutions to rate‐independent systems with nonconvex energies and discontinuous loads

AbstractWe consider a rate‐independent system with nonconvex energy under discontinuous external loading. The underlying space is finite‐dimensional and the loads are functions in . We investigate the stability of various solution concepts w.r.t. a sequence of loads converging weakly* in with a particular emphasis on the so‐called normalized, ‐parametrized balanced viscosity solutions. By means of three counterexamples, it is shown that common solution concepts are not stable w.r.t. weak* and even intermediate (or strict) convergence of loads in the sense that a limit of a sequence of solutions associated with these loads need not be a solution corresponding to the load in the limit. We moreover introduce a new solution concept, which is stable in this sense, but our examples show that this concept necessarily allows “solutions” that are physically meaningless.

Experimental study on fatigue failure properties of mudstone interlayers under discontinuous loading in salt cavern gas storage

During the operation of an underground salt cavern gas storage, Fatigue failure occurs in the surrounding rock of gas storage reservoirs under non-continuous gas injection and extraction loading. Due to the special layered salt rock structure in China, the mudstone interlayer is the weak part of the gas storage. It is necessary to study the effect of stress magnitude and interval time on the fatigue mechanical properties of mudstone. Graded upper stress limit interval fatigue (GUIF) test and graded lower stress limit interval fatigue (GLIF) test were carried out on mudstone respectively. And different interval times were set to investigate the effect of interval time on the mechanical properties of mudstone. With the increase in the interval time, the fatigue life and peak strain of the mudstone increased. Under the same interval time, the lower-limit interval test result showed a significantly higher fatigue life than the upper-limit interval test result. The stress–strain curve exhibited three stages: scattered–dense–scattered. During the unloading phase, the modulus of elasticity increased with increasing stress levels, indicating that the internal structure of the mudstone is extremely sensitive to the stress. In the (GUIF) test, the average residual strain increased with the increase in the interval time, and the residual strain during the cycle after the time interval under different grades was lower than the residual strain before the time interval; the results of the (GLIF) test showed the opposite trend. In the (GUIF) test, the average creep strain increased with increasing interval time under the same stress level, and the average creep strain was greater than the average residual strain, and the creep stage had a greater effect on mudstone damage than the fatigue stage. The post-fatigue creep strain was significantly greater than the pre-fatigue creep strain. The research results can be useful in ensuring the stable operation of gas storage in salt caverns.

Capacitance-based compression self-sensing effectiveness of cement paste with curing time

Capacitance-based self-sensing properties of cement pastes at different curing times were studied in this work. Cement paste samples that did not require any functional materials were tested at 7, 14 and 28 days. Continuous and discontinuous loading cycles (minimum load of 21 kPa and maximum load of 98 kPa) were applied to the cement pastes. It was found that capacitance-based self-sensing is superior to resistance-based self-sensing owing to its greater dependence on stress and reversibility. The capacitance change was found to be irreversible for the 7-day cement paste sample owing to irreversible deformation. Over time, capacitive self-sensing became more effective. The stress sensitivity (fractional increase in capacitance divided by stress) for the 28-day cement paste sample was 2.54 × 10−8/Pa. It was also found that, with an increase in hydration time, the capacitance decreased, indicating the strength increase in cement paste can also be sensed with capacitance measurements.

Effects of Natural Aging and Discontinuous Cyclic Loading on High Cycle Fatigue Behavior of Steels

Metallic components may not be used immediately and are stored for several months or years after fabrication in some cases, which experience long-term natural aging. Moreover, the fatigue-beared components commonly suffer discontinuous cyclic loadings in service. In this paper, the effects of natural aging and discontinuous loading on high cycle fatigue life and failure mechanism were investigated through rotating bending fatigue tests. The long-term natural aging (e.g., more than 20,000 h) reduced the fatigue life of both 25CrMo4 and 30CrMnSiA steels, and this effect was irrespective of the roughness of the specimen surface. The effect of natural aging on the failure mechanism was related to the microstructure of materials. The natural aging promoted the probability of multi-site crack initiation for 25CrMo4 steel, but had no influence on the crack initiation mode of 30CrMnSiA steel. The discontinuous cyclic loading had no harmful influence on the fatigue life of 25CrMo4 steel, and it had no influence on the failure mechanism. The specimens under continuous and discontinuous cyclic loadings both failed from single-site crack initiation or multi-site crack initiation at the specimen surface.

On Enhanced Second-Order Explicit Integration Methods with Controllable Algorithmic Dissipation and Adjustable Sub-Step Size for Hyperbolic Problems

This paper constructs and analyzes a generalized composite two-sub-step explicit method to solve various dynamical problems effectively. Via the accuracy and dissipation analysis, the constructed explicit method is further developed into two novel members that achieve identical second-order accuracy, controllable algorithmic dissipation, and desired stability. Unlike all existing explicit schemes, the novel members employ two independent integration parameters ([Formula: see text] and [Formula: see text]) to control numerical features. The parameter [Formula: see text], denoting the splitting ratio of sub-step size, can determine the instant at which external loads are calculated, whereas another parameter [Formula: see text], denoting the spectral radius at the bifurcation point, can control numerical dissipation imposed. Independently adjusting the sub-step size is one significant advantage for solving dynamical problems triggered by discontinuous loads. This paper also provides two novel explicit members’ single-parameter versions for inexperienced users. Besides, the novel explicit members achieve a smaller local truncation error in acceleration, thus enhancing the solution accuracy in displacement and velocity. Numerical examples are solved to validate the significant superiority of the novel members in the solution accuracy.

Three-dimensional analytical elasticity solution for the mechanical analysis of arbitrarily-supported, cross and angle-ply composite plates under patch loads

Patch-type discontinuous loads lead to highly localized stresses which are three-dimensional (3D) in nature and can initiate failures. Their accurate characterization is of primal importance for composite and sandwich structures. The present contribution elaborates a 3D analytical elasticity solution for the mechanical analysis of cross and angle-ply composite plates under transverse patch loads and arbitrary support conditions. For the solution, the Reissner-type, mixed variational principle is used to derive the governing equations. Analytical solutions are obtained using the multiterm, extended Kantorovich method, by dividing the plate into loaded and unloaded parts. The present analytical solution exactly satisfies inter-segment, inter-layer continuity and edge support conditions, treating stresses and displacements as primal variables. Its accuracy is established by direct comparisons with existing analytical – where available – and 3D finite element results, both for cross-ply and angle-ply designs, for different boundary conditions. Extensive analysis is performed to quantify the effect of thickness, angle-ply and patch load position on the composite mechanical performance. Through thickness stress asymmetries are identified and quantified, along with angle-ply designs that can smoothen stress concentrations in the vicinity of patch loads. The methodology can be used as a reference solution in the design of multilayer anisotropic plates under discontinuous loads.

A stress-driven model incorporating surface energy effects for the bending analysis of functionally graded nanobeams with loading discontinuities

A stress-driven model incorporating surface energy effects for the bending analysis of functionally graded nanobeams with loading discontinuities

Boundary-integral analysis of a 3-d problem for a body with a periodic array of flexible inclusions

The static problem of discontinuous loading of an elastic body with a periodic array of flexible inclusions is considered. The problem is reduced to solving a 2-D boundary integral equation of the second kind of the Newton potential type with respect to an unknown inclusion opening function. With the help of solutions of the equation, the static stress intensity factors mode I are determined and their dependences on the distance between defects, the contrast between the rigidity of the matrix and the inclusion, and the filling of cracks with the injection material are analyzed.

A series of multi-domain matched interface and boundary algorithms for dynamic and static responses of annular sectorial plates

A series of multi-domain matched interface and boundary (MDMIB) algorithms are proposed to analyze the free vibration and bending of annular sectorial thin plates. Through an in-depth understanding of the matched interface and boundary (MIB) method, six types of MDMIB algorithms are developed herein by using various domain decomposition techniques for handling bi-directional crossing interfaces due to non-homogeneous elastic foundations and discontinuous loads, which cannot be treated by the conventional MIB method. The rationale of the MDMIB method is to divide the entire computational domain into multiple subdomains that can be connected by using the interconnecting conditions between crossing interfaces and mesh lines. Annular sectorial plates, having non-uniform boundary conditions, partially supported elastic foundations, and patch loads, are all considered. Numerous examples are chosen to examine the computational performance of the MDMIB algorithms. For verification, the present results are checked against existing and finite element solutions. It is shown that the proposed MDMIB algorithms are highly effective to deal with the bi-directional interface problems.

Impact of loading rate during hybrid simulation on seismic response of steel structures

AbstractThis study investigates the influence of loading rates on the seismic response of steel structures. A series of coupon tests under typical earthquake‐induced loading rates are carried out. In addition to the conventional monotonic tension test, the specimens are also tested under a discontinuous loading protocol that is analogous to the ramp‐and‐hold scheme employed in the pseudo‐dynamic hybrid simulations. The test results are used to develop a uniaxial steel material model to account for the strain rate effect and stress relaxation. The material model facilitates the reuse of existing steel hysteresis models and can be used to model different structural components, such as columns, beams, braces, etc. The material model is then used for a parametric study to evaluate the impact of various loading rates on the global seismic response of a single degree of freedom structural system with different structural periods, and types and intensities of ground motions. It is found that the impact of loading rates is more significant for structures with a period of 0.5 s or less and it thus requires a fast control of the physical specimen in pseudo‐dynamic hybrid testing. In addition, the material model is applied to a five‐storey buckling restrained braced frame (BRBF) building with a structural period of 1.2 s. It is found that the earthquake‐induced loading rates have a minor impact on the global response of the structure.

Analytical elasticity solution for accurate prediction of localized stresses in laminated composites under patch loading

Discontinuous patch-type loads cause highly localized stresses which can initiate failures like crack and delamination, and thus must be predicted accurately for efficient design of structures. This paper presents an iterative analytical elasticity solution for accurate stress analysis of laminated composite beams with arbitrary support conditions under a transverse patch loading. The beam is divided into segments with and without the patch loading. The governing equations are derived in the mixed form by employing the Reissner-type mixed variational principle and solved analytically for each segment using the multiterm extended Kantorovich approach. As both displacements and stresses are primary variables, the solution ensures the point-wise satisfaction of inter-layer and inter-segment continuity and boundary conditions. The accuracy of the solution is established by comparing the present numerical results with exact elasticity solutions available in literature for simply-supported edge conditions and compared with finite element solutions of Abaqus for other boundary conditions. An extensive numerical study is performed, and benchmark results are provided for various composite and sandwich laminates, thickness ratios, and boundary conditions under different cases of distributed patch load. The behavior of laminated metal-composite beams is also studied for patch loading, which reveals that thin aluminum layers on the composite beam are highly efficient and effective in reducing the stress concentration in the vicinity of patch load. The presented benchmark results will be beneficial to assess the accuracy and efficacy of different beam theories and elasticity-based approximate models for the analysis of multilayered anisotropic beams subjected to discontinuous loads.

Nonlocal strain and stress gradient elasticity of Timoshenko nano-beams with loading discontinuities

A unified approach is applied for determining both strain- and stress-driven differential formulations of Timoshenko nano-beams in presence of loading discontinuities. The consequent models can simulate small scale effects with different types of constitutive laws (such as pure nonlocal, mixture of local and nonlocal phases, and nonlocal gradient). A specific novel feature of the proposed models is the ability to consider loading discontinuities, i.e. points of discontinuities for generalized internal forces occurring in presence of external supports, forces, or couples concentrated at internal points of the nano-beam. To this end, novel constitutive continuity conditions (CCCs) are imposed at the beam interior points of loading discontinuities. CCCs contain integral convolutions of generalized forces or displacements over suitable parts of the nano-beam; they represent a valid alternative to Dirac delta function and are different from the well-known constitutive boundary conditions (CBCs) imposed at the end-points of the nano-beam. Finally, the proposed models are applied for finding closed-form solutions to cases of practical interest.

Experimental Study on the Mechanical and Permeability Properties of Lining Concrete Under Different Complex Stress Paths

A promising large-scale energy storage is underground compressed air energy storage (CAES) in lined rock caverns. To ensure the safety and stability of storage caverns because of the influence of periodic injection during production, it is crucial to understand the mechanical behavior of lining concrete under different complex stress paths. In this study, three types of uniaxial compressive fatigue test and uniaxial creep test were conducted on concrete. The following conclusions were obtained from the results. 1) The irreversible deformation after the interval was larger than that before the interval in the discontinuous multi-step cyclic loading (DMCL) test. 2) Loading velocity significantly influenced concrete fatigue, and the irreversible deformation in the cycle of low loading velocity was greater than that in the cycle of high loading velocity. 3) The residual strain increased with an increase in stress level. 4) The creep strain increased with an increase in stress level during the multi-step creep loading test; the fractional derivative results were more consistent with the experimental results. 5) The permeability of concrete increased rapidly under the influence of an external force when the stress level exceeded 0.73.

Optimization study of blasting operations in Roşia Poieni open pit mine, Romania

Purpose. Drilling-blasting technology is one of the simplest and most often used techniques in open pit mining. This allows the excavation of a large volume of rock and useful mineral substance. The operation of blasting using the energy of explosives plays an important role in open pit exploitation, being also the key element of the blasting process through which a corresponding granulometry is obtained. This operation is a part of a series of interdependent operations, in the sense that each operation determines a certain result that will be an important element for the next operation that takes place in the working face. Consequently, the blasting operation with explosives should not be considered as an independent act. A global approach to the entire production technological process including blasting is required. Methods. In the optimization study, the basic method consisted in the analysis of the blasting operations performed at the drilling diameter of 250 mm (blasting technology used in Roşia Poieni open pit mining) and simulation of the excavation of the same rock volume, with the optimization of the explosive charge distribution at two other drilling diameters: 200 and 150 mm. Findings. The main problems when shooting 250 mm dia holes are caused by the length of the tamping in the mineralized rock that leads to the appearance of blocks with dimensions which are maximum allowed in the crusher tank (1.2-1.3 m). That is why discontinuous loads with intermediate tamping are used – the method that successfully limits their number. In order to obtain a granulometry corresponding to the primary crushing operation, which will allow to decrease the crushing costs, it is necessary to use smaller drilling diameters, but with productivity high enough to ensure the optimal development of the extraction process. Originality. Based on the performed study, it is recommended to use the discontinuous load, preserving the total length of the explosive charge. In the zones where the rocks have a Protodiakonov coefficient f > 6.5, it is recommended to apply an appropriate drilling diameter (150-200 mm) and use the intermediate tamping at 2-3 m length to limit the upper stemming area to a maximum of 7 m (to limit or eliminate the occurrence of oversized blocks). Practical implications. The research results will enhance the geometric and safety factors of the operation, limiting the explosion effect on the massif and the environment and reducing the total costs of the cutting operation. The cost of explosives and initiating materials can be reduced by using a smaller quantity of explosive gels in a dry environment (12-18 kg/hole), the difference in the explosive charge length being completed with AM 1.

A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

A completely new analytical method to solve the fourth-order governing partial differential equations with variable coefficients is proposed for the buckling of cylindrical shells subjected to distributed external pressure. Unlike the present energy method in literatures, pressure distribution needs not be assumed beforehand and be simple, which is arbitrary in this manuscript. The present novel method makes the buckling analysis for the complicated external pressure distributions (including discontinuous loads) possible. Furthermore, general buckling load formulas related to geometrical sizes of the shell and pressure distribution functions are obtained by the combined perturbation method and Fourier series expansion for the first time. The first and second order asymptotic terms of buckling loads are directly given for the purpose of engineering application. Based on the presented method, three types of external pressure loads (namely, linear liquid pressure, wind type pressure and discontinuous stepwise external pressure)are considered. Validity and accuracy are demonstrated by comparing with the results in published literatures for linear liquid pressure and wind type pressure, and it is also the first time to derive the buckling load for a shell under discontinuous stepwise external pressure. Parametric discussion is also performed to investigate the effects of load distribution types and parameters on buckling resistance capacity.