Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method.

In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method.

The present work's main objective is to investigate the natural vibrations of the thin (Kirchhoff-Love) plate resting on time-fractional viscoelastic supports in terms of the Stochastic Finite Element Method (SFEM). The behavior of the supports is described by the fractional order derivatives of the Riemann-Liouville type. The subspace iteration method, in conjunction with the continuation method, is used as a tool to solve the non-linear eigenproblem. A deterministic core for solving structural eigenvibrations is the Finite Element Method. The probabilistic analysis includes the Monte-Carlo simulation and the semi-analytical approach, as well as the iterative generalized stochastic perturbation method. Probabilistic structural response in the form of up to the second-order characteristics is investigated numerically in addition to the input uncertainty level. Finally, the probabilistic relative entropy and the safety measure are estimated. The presented investigations can be applied to the dynamics of foundation plates resting on viscoelastic soil.

Mechanical and Microstructural Properties of Thermally Sprayed Metallic Materials in Compression Tests over a Vast Range of Strain Rates.

This paper presents the mechanical behavior of thermally sprayed coatings produced using an arc wire coating material. The produced coatings were cut and subjected to strength resistance tests in static and in dynamic loading. The compressive behavior for the strain rates between 0.001 1/s and 2612 1/s was examined. The strain rate sensitivity of the material was recognized in the material during dynamic loading using the SHPB technique. Microstructural observations were made, and properties such as changes in porosity and the microhardness of the coatings tested were examined. A significant reduction in coating porosity was demonstrated after static loading (90%) and dynamic loading (86%). The result of porosity reduction is the strengthening of the coatings through an increase in the microhardness of these coatings after loading in the static test (160 HV 0.3/8) and the dynamic test (278 HV 0.3/8). As a result of the tests, the coatings retain their cohesion and remain consistent. At the same time, they can absorb a significant amount of mechanical energy due to plastic deformation and porosity reduction. The presented results concern a completely new coating material created from a core wire.

A Weibull process monitoring with AEWMA control chart: an application to breaking strength of the fibrous composite.

In recent times, there has been a growing focus among researchers on memory-based control charts. The Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts and the adaptive control charting approaches got the attention. Control charts are commonly employed to oversee processes, assuming the monitored variable follows a normal distribution. However, it's worth noting that this assumption does not hold true in many real-world situations. The use of the algebraic expression for normalization, which can be used for all kinds of skewed distributions with a closed-form distribution function, using the proposed continuous function to adapt a smoothing constant, motivates this study. In the present manuscript, we design an EWMA statistic-based adaptive control chart to monitor the irregular variations in the mean of two parametric Weibull distribution and use Hasting approximation for normalization. The adaptive control charts are used to update the smoothing constant according to the estimated shift. Here we use the proposed continuous function to adapt the smoothing constant. The average run length and standard deviation of run length are calculated under different parameter settings. The effectiveness of the proposed chart is argued in terms of ARLs over the considered EWMA chart through Monte-Carlo (MC) simulation method. The proposed chart is examined, followed by a real data set to demonstrate the design and application procedures.

Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs.

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.

Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake process.

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.

Self-Healing Mechanical Properties of Selected Roofing Felts.

In this work, roof felts are considered. Special attention is paid to the mechanical properties and self-healing (SH) phenomena under elevated temperatures. The results of the heating and strength tests for the entire range of material work, from the first load to sample breaking, are shown with respect to the angle of reinforcement relative to the longitudinal axis of the sample and different ways of breaking the continuity of the material. The influence that the material thickness and modifiers used for the production of the base material have on the obtained results was also pointed out. The meaningful SH strength is reported-from 5% up to 20% of the strength of the undamaged material-which, in perspective, can provide comprehensive knowledge of the optimal use of roofing felts and its proper mathematical modeling.

Developments on Constitutive Material Model for Architectural Soda-Lime Silicate (SLS) Glass and Evaluation of Key Modelling Parameters.

Architectural soda-lime silicate glass (SLS) is increasingly taking on complex shapes that require more detailed numerical analysis. Glass modeling is a thoroughly described topic with validated constitutive models. However, these models require a number of precise material parameters for SLS glass, and these are very sensitive to changes in glass composition. The currently available information is based on SLS glass tested in the late 1990s. As a result, most current publications are based on the above data. The object of this work was to analyze the available sources and update the information on selected key parameters for modeling. Using the currently utilized SLS glass in construction, the coefficient of thermal expansion (CTE), glass transition temperature, and the Young's modulus have been experimentally investigated. The updated material parameters will allow for more accurate modeling of the SLS glass currently used in construction, and in consequence will make the prototyping process for glass with complex geometries possible to be transferred from the production stage to the design stage, resulting in shorter production times.

Review on Stress-Fractional Plasticity Models.

Fractional calculus plays an increasingly important role in mechanics research. This review investigates the progress of an interdisciplinary approach, fractional plasticity (FP), based on fractional derivative and classic plasticity since FP was proposed as an efficient alternative to modelling state-dependent nonassociativity without an additional plastic potential function. Firstly, the stress length scale (SLS) is defined to conduct fractional differential, which influences the direction and intensity of the nonassociated flow of geomaterials owing to the integral definition of the fractional operator. Based on the role of SLS, two branches of FP, respectively considering the past stress and future reference critical state can be developed. Merits and demerits of these approaches are then discussed, which leads to the definition of the third branch of FP, by considering the influences of both past and future stress states. In addition, some specific cases and potential applications of the third branch can be realised when specific SLS are adopted.

Identification of Aluminium Powder Properties for Modelling Free Air Explosions.

Aluminium is a component in many energetic formulations. Therefore, its combustion is one of the main thermochemical processes that govern the output from the energetics. Modelling aluminium combustion is a challenging task because the process is highly complex and difficult to measure. Here, tests of aluminium powder were conducted in an effort to isolate the burning of the aluminium and to determine an adequate representation of this process. Charges of 100 g and 500 g were tested, and the size of the Al/air cloud and the ratio of components in the Al/air mixture were determined, which has not been published previously. This information was used to assess the validity of the assumption that the detonation of the mixture was representative of the event. Parameters for the Jones-Wilkins-Lee equation of state for the explosive mixture and detonation products were defined. Simulations of the tests were performed, and the results were consistent with the field test data, indicating that detonation occurred when there was a mixture of 70-75% Al and 25-30% air by mass.

Fabrication and Mechanical Testing of the Uniaxial Graded Auxetic Damper.

Auxetic structures can be used as protective sacrificial solutions for impact protection with lightweight and excellent energy-dissipation characteristics. A recently published and patented shock-absorbing system, namely, Uniaxial Graded Auxetic Damper (UGAD), proved its efficiency through comprehensive analytical and computational analyses. However, the authors highlighted the necessity for experimental testing of this new damper. Hence, this paper aimed to fabricate the UGAD using a cost-effective method and determine its load-deformation properties and energy-absorption potential experimentally and computationally. The geometry of the UGAD, fabrication technique, experimental setup, and computational model are presented. A series of dog-bone samples were tested to determine the exact properties of aluminium alloy (AW-5754, T-111). A simplified (elastic, plastic with strain hardening) material model was proposed and validated for use in future computational simulations. Results showed that deformation pattern, progressive collapse, and force-displacement relationships of the manufactured UGAD are in excellent agreement with the computational predictions, thus validating the proposed computational and material models.

Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory.

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u 1 ( t ) , u 2 ( t ) and u 3 ( t ) , respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge-Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.

Experimental Analysis of Mechanical Anisotropy of Selected Roofing Felts.

In this work, four representatives of roofing felts are under consideration. Special attention is paid to the mechanical behaviour under the tensile load of the samples. The results of strength tests for the entire range of material work, from the first load to sample breaking, are shown with respect to a specific direction of sample cutting. Moreover, a unique study of the microstructure obtained with the scanning electron microscope and chemical composition determined by energy dispersive spectroscopy of the tested materials is presented. The significant mechanical material anisotropy is reported and moreover argued by microstructure characteristics. In perspective, the outcomes can give comprehensive knowledge on optimal usage of roofing felt and proper mathematical modelling.

Dynamics of Space-Fractional Euler-Bernoulli and Timoshenko Beams.

This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler-Bernoulli beam (s-FEBB) and space-Fractional Timoshenko beam (s-FTB) models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to a dynamic case. The study provides appropriate governing equations, numerical approximation, detailed analysis of free vibration, and experimental validation. The parametric study presents the influence of non-locality parameters on the frequencies and shape of modes delivering a depth insight into a dynamic response of small scale beams. The comparison of the s-FEBB and s-FTB models determines the applicability limit of s-FEBB and indicates that the model (also the classical one) without shear effect and rotational inertia can only be applied to beams significantly slender than in a static case. Furthermore, the validation has confirmed that the fractional beam model exhibits very good agreement with the experimental results existing in the literature-for both the static and the dynamic cases. Moreover, it has been proven that for fractional beams it is possible to establish constant parameters of non-locality related to the material and its microstructure, independent of beam geometry, the boundary conditions, and the type of analysis (with or without inertial forces).

Blast Test and Failure Mechanisms of Soft-Core Sandwich Panels for Storage Halls Applications.

In this paper, an experimental investigation is presented for sandwich panels with various core layer materials (polyisocyanurate foam, mineral wool, and expanded polystyrene) when subjected to a justified blast load. The field tests simulated the case for when 5 kg of trinitrotoluene (TNT) is localized outside a building's facade with a 5150 mm stand-off distance. The size and distance of the blast load from the obstacle can be understood as the case of both accidental action and a real terroristic threat. The sandwich panels have a nominal thickness, with the core layer equal 100 mm and total exterior dimensions of 1180 mm × 3430 mm. Each sandwich panel was connected with two steel columns made of I140 PE section using three self-drilling fasteners per panel width, which is a standard number of fasteners suggested by the producers. The steel columns were attached to massive reinforced concrete blocks via wedge anchors. The conducted tests revealed that the weakest links of a single sandwich panel, subjected to a blast load, were both the fasteners and the strength of the core. Due to the shear failure of the fasteners, the integrity between the sandwich panel and the main structure is not provided. A comparison between the failure mechanisms for continuous (polyisocyanurate foam and expanded polystyrene) and non-continuous (mineral wool) core layer materials were conducted.

Improving the Blast Resistance of Large Steel Gates-Numerical Study.

Blast resistant gates/doors are essential for sensitive infrastructure, such as embassies, ministries, or parliaments. Lightweight gates equipped with 'energy absorbing systems' have better operational performance than the traditional costly and bulky design. Graded auxetic structures have not yet been used as potential passive damping systems in the supporting frame of blast resistant gates. Consequently, this study tries to test if a uniaxial graded auxetic damper (UGAD) proposed by the authors in a recent article, namely the development of a new shock absorbing UGAD, could maintain a 3000 × 4500 mm steel gate operable after high blast peak reflected overpressure of 6.6 MPa, from 100 kg TNT at 5 m stand-off distance. The blast-induced response of the gate was assessed, with and without the proposed UGAD, using Abaqus/Explicit solver. Results showed that the attachment of the proposed UGAD to the gate led to a dramatic decrease in permanent deformations (a critical factor for gate operability after a blast event). Hence, a lighter, more economical gate (with 50% reduction in mass) was required to satisfy the operability condition. In addition, 49% of peak reaction forces were diminished, that have a direct impact on the supporting frame. Moreover, the results revealed that, in the numerical model, 56% of the achieved plastic dissipation energy was from the UGADs, and 44% from the gate. The outcomes of this research may have a positive impact on other sectors beyond academia, such as industry, economy, and public safety.

The Development of a New Shock Absorbing Uniaxial Graded Auxetic Damper (UGAD).

Auxetic structures are efficient cellular materials that can absorb blast/impact energy through plastic deformation, thus protecting the structure. They are developing sacrificial solutions with light weight, high specific strength, high specific toughness and excellent energy dissipating properties, due to its negative Poison's ratio nature. The use of auxetic and non-auxetic panels in blast resistant structures had been relatively perceived by researchers. Nonetheless, implementation of those energy dissipaters, explicitly as a uni-axial passive damper is restrained to limited studies, which highlight the potential need for further explorations. The aim of this paper is the design of a new uniaxial graded auxetic damper (UGAD) that can be used as a blast/impact/shock absorber in different scales for different structural applications. First, the geometry, material, numerical model and loading are introduced. Then, a detailed parametric study is conducted to achieve the most efficient graded auxetic system. Moreover, the designed auxetic damper is numerically tested and its static and dynamic constitutive relations are derived and validated analytically. The selection of optimum parameters was based on the ratio of the reaction force to the applied load (RFd/P) and plastic dissipation energy (PDE). The final designed UGAD contains three auxetic cores that have the same geometry, material grade (6063-T4), size and number of layers equal to eight. The cell-wall thickness t of the three auxetic cores is 1.4 mm, 1.8 mm and 2.2 mm, respectively; composing a graded auxetic system. The performance of the three auxetic cores together have led to a wide plateau region (80% of total crushing strain) and variant strength range (1-10 MPa), which in return, can justify the superior performance of the UGAD under different blast levels. Finally, the 3D printed prototype of the UGAD is presented and the possible applications are covered.

Brain modelling in the framework of anisotropic hyperelasticity with time fractional damage evolution governed by the Caputo-Almeida fractional derivative.

In this paper the human brain tissue constitutive model for monotonic loading is developed. The model in this work is based on the anisotropic hyperelasticity assumption (the transversely isotropic case) together with modelling of the evolving load-carrying capacity (scalar damage) whose change is governed by the Caputo-Almeida fractional derivative. This allows the brain constitutive law to include the memory during progressive damage, due to the characteristic time length scale which is an inherent attribute of the fractional operator. Furthermore, the rate dependence of the overall brain tissue model is included as well. The theoretical model is finally calibrated and validated with a set of experimental data.