Numerical Method Research Articles

High-Speed Surface Property Recognition with a 140 GHz Frequency

In the field of integrated sensing and communication, there is a growing need for advanced environmental perception. The terahertz (THz) frequency band, significant for ultra-high-speed data connections, shows promise in environmental sensing, particularly in detecting surface textures crucial for autonomous systems’ decision-making. However, traditional numerical methods for parameter estimation in these environments struggle with accuracy, speed, and stability, especially in high-speed scenarios like vehicle-to-everything communications. This study introduces a deep learning approach for identifying surface roughness using a 140-GHz setup tailored for such conditions. A high-speed data acquisition system was developed to mimic real-world scenarios, and a diverse set of rough surface samples was prepared for realistic high-speed datasets to train the models. The model was trained and validated in three challenging scenarios: random occlusions, sparse data, and narrow-angle observations. The results demonstrate the method’s effectiveness in high-speed conditions, suggesting terahertz frequencies’ potential in future sensing and communication applications.

Validation of the Physical and Mechanical Properties of Eucalyptus benthamii Maiden & Cambage Wood and Cross Laminated Timber Panels Using the Finite Element Method

Cross Laminated Timber (CLT) is a structurally complex panel that poses challenges in analysis due to the anisotropic nature of wood and the orthotropic characteristics of the composite. Numerical modeling using the Finite Element Method (FEM) offers a viable solution for analysis, particularly for addressing boundary value problems that are analytically challenging. Therefore, it is crucial to validate the experimental properties to ensure accurate results. The objective of this study was to validate the physical and mechanical properties for structural modeling using FEM, based on the characterization of Eucalyptus benthamii Maiden & Cambage wood and CLT panels. For wood characterization, the basic and apparent density were determined, and mechanical tests, including static bending, parallel-to-grain compression, and shear tests, were conducted. Utilizing the same batch of wood, three-layer CLT panels were manufactured and subjected to a non-destructive three-point bending test. This test was simulated in RFEM finite element software, employing Mindlin’s theory, and the displacements obtained were compared with the experimental method. The results from a Student’s t-test at a 5% significance level indicated no significant difference between the experimental and numerical methods, suggesting that the properties of the experimental E. benthamii CLT panel can be accurately represented by FEM.

Dual-Interface Solar Evaporator with Highly-Efficient Thermal Regulation via Suspended Multilayer Design.

Facing the increasing global shortage of freshwater resources, this study presents a suspended multilayer evaporator (SMLE), designed to tackle the principal issues plaguing current solar-driven interfacial evaporation technologies, specifically, substantial thermal losses and limited water production. This approach, through the implementation of a multilayer structural design, enables superior thermal regulation throughout the evaporation process. This evaporator consists of a radiation damping layer, a photothermal conversion layer, and a bottom layer that leverages radiation, wherein the bottom layer exhibits a notable infrared emissivity. The distinctive feature of the design effectively reduces radiative heat loss and facilitates dual-interface evaporation by heating the water surface through mid-infrared radiation. The refined design leads to a notable evaporation rate of 2.83kg m-2 h-1. Numerical simulations and practical performance evaluations validate the effectiveness of the multilayer evaporator in actual use scenarios. This energy-recycling and dual-interface evaporation multilayered approach propels the design of high-efficiency solar-driven interfacial evaporators forward, presenting new insights into developing effective water-energy transformation systems.

A general fractional breast cancer model: Model graph energy, Caputo-Fabrizio derivative existence and uniqueness plus numerical simulation

In the study of epidemiology, mathematical modelling is crucial because it improves understanding of the underlying mechanisms that cause illnesses to spread and offers the possibility of developing preventative interventions. In this paper, we have discussed a fractional mathematical model. A set of fractional differential equations is used to build the model. We have applied a Caputo Fabrizio (CF) to describe the fractional breast cancer model. The model consists of five subpopulations that make up a population. They are disease-free (D), cardiotoxic (E), stages 1 and 2 (A), 3 (B), and 4 (C). We have used a digraph chart to present the breast cancer model. We have used some graph theory concepts to compute the energy of the breast cancer model corresponding digraph. We have demonstrated the existence, uniqueness, and positivity of the model solutions. The fixed point hypothesis demonstrates both the existence of a solution to the suggested fractional breast cancer model as well as the fact that this solution is one of a kind. Numerical simulations are a useful tool for explaining the suggested notion. We have presented a numerical method for simulating the problem. We have used an algorithm modelled after the Adams-Bashforth-Moulton method (ABMM) to solve the model. Numerical simulations of the model in various fractional orders illustrate the theoretical conclusions. We have used the Matlab application to calculate every solution. The results demonstrate the efficacy of the proposed fractional model from an epidemiological standpoint.

Nonlinear Vibration of Cracked Porous FG-GPL RC Cylindrical Panels Using a Phase-Field Crack Model

This study is concerned with the nonlinear free vibration of a cracked functionally graded porous cylindrical panel reinforced with graphene platelets by introducing a phase-field crack model. Conventional crack modeling by separating the grid nodes lying on the crack line is not only painstaking but also suffers from numerical instability. To overcome this problem, the internal crack is modeled by adopting the phase-field formulation and a virtual geometry rotation. The nonlinear numerical method is developed based on the first-order shear deformation theory incorporated with the von Kármán geometry nonlinearity in the framework of the 2-D extended natural element method, a recently introduced mesh-free method. The crack-induced singular field is represented by adopting the crack-tip singular functions, and the troublesome numerical locking is restrained by combining the MITC3+ shell concept and the shear stabilization factor. The curved shell surface is mapped to a 2-D rectangular NEM grid to avoid difficulty in defining the interpolation functions. The developed numerical method is verified through a comparison with the reference solutions, and the large-amplitude free vibration of porous cracked functionally graded grapheme platelet-reinforced cylindrical panels is profoundly examined by changing the major parameters.

A combined uncertainty and sensitivity analysis of melting in a cubical cavity, Part A: Model validation

Latent heat thermal energy storage systems exploit the solid–liquid phase transition of a material to store thermal energy almost isothermally with high energy density. Numerical methods are increasingly being used for the targeted design of these storage systems. The problem, however, is that the results obtained with these methods – despite a frequently shown near-perfect agreement between validation experiments and simulation results – are subject to large uncertainty. To illustrate the extent of this problem and to show approaches to solving it, a combined uncertainty and sensitivity analysis of the melting process of a paraffin (octadecane) in a cuboid heated from one side is carried out in this two-paper series. In part A, we present the model and validate it; in part B we use it to carry out the combined uncertainty and sensitivity analysis. The validation of the model is performed with the help of experimental results. For this purpose, we measure the liquid phase fraction, the position of the phase boundary, the velocity field in the liquid and the temperature inside the test capsule. We make sure that the experimental results are reproducible. Systematic deviations are discussed and, if possible, the results are corrected for their value. When measuring the velocity field using particle image velocimetry (PIV), the greatest systematic deviation is due to the inhomogeneous refractive index field in the liquid phase. Finally, it is shown that, in the present case, the influence is very low if constant material properties evaluated at the mean temperature are taken for each phase compared to a temperature-dependent implementation. An exception is the density. If the density change during melting is not taken into account the deviation of the melt fraction lies between 6 and 8%. In summary, the validation of the numerical model is very satisfactory and demonstrates the suitability of the model for performing the investigations of the part B paper.

A deep learning approach to explore the association of age-related macular degeneration polygenic risk score with retinal optical coherence tomography: A preliminary study.

Age-related macular degeneration (AMD) is a complex eye disorder affecting millions worldwide. This article uses deep learning techniques to investigate the relationship between AMD, genetics and optical coherence tomography (OCT) scans. The cohort consisted of 332 patients, of which 235 were diagnosed with AMD and 97 were controls with no signs of AMD. The genome-wide association studies summary statistics utilized to establish the polygenic risk score (PRS) in relation to AMD were derived from the GERA European study. A PRS estimation based on OCT volumes for both eyes was performed using a proprietary convolutional neural network (CNN) model supported by machine learning models. The method's performance was assessed using numerical evaluation metrics, and the Grad-CAM technique was used to evaluate the results by visualizing the features learned by the model. The best results were obtained with the CNN and the Extra Tree regressor (MAE = 0.55, MSE = 0.49, RMSE = 0.70, R2 = 0.34). Extending the feature vector with additional information on AMD diagnosis, age and smoking history improved the results slightly, with mainly AMD diagnosis used by the model (MAE = 0.54, MSE = 0.44, RMSE = 0.66, R2 = 0.42). Grad-CAM heatmap evaluation showed that the model decisions rely on retinal morphology factors relevant to AMD diagnosis. The developed method allows an efficient PRS estimation from OCT images. A new technique for analysing the association of OCT images with PRS of AMD, using a deep learning approach, may provide an opportunity to discover new associations between genotype-based AMD risk and retinal morphology.

Observed Characterization of Multi‑level Retaining Structure for Deep Excavation of Subway Station

Traditional support structures cannot meet the complex conditions of different excavation depths and areas in underground transportation hubs. On the basis of fully considering the spatial position relationship of foundation pit groups, this article proposes a multilevel retaining system that meets the requirements of multilevel foundation pit excavation. The evolution law of the support structure during the excavation process of the inner pit was explored using on-site monitoring and numerical simulation methods. The results indicate that the excavation of the inner pit reduces the passive earth pressure, and the deformation of the outer support structure can be effectively suppressed by setting a retaining structure or a bottom slab in the bench zone. The excavation of the inner pit causes significant vertical deformation of the support structure adjacent to the foundation pit, while the impact on the structure far away from the foundation pit is relatively small. According to the contact force chain and soil pressure between the two rows of support structure, the soil in this area is divided into a “relaxation zone” and a “compression zone.” The evolution mechanism of earth pressure in the case of mutual-effect failure between two rows of piles is revealed. This paper addresses the deformation properties of multilevel support structures as well as the mechanism of earth pressure evolution between structures.

A Numerical Model to Predict the Relaxation Phenomena in Thermoset Polymers and Their Effects on Residual Stress during Curing-Part I: A Theoretical Formulation and Numerical Evaluation of Relaxation Phenomena.

This paper analyzes the effect of crosslinking reactions on a thermoset polymer's viscoelastic properties. In particular, a numerical model to predict the evolution of epoxy's mechanical properties during the curing process is proposed and implemented in an Ansys APDL environment. A linear viscoelastic behavior is assumed, and the scaling of viscoelastic properties in terms of the temperature and degree of conversion is modeled using a modified version of the TNM (Tool-Narayanaswamy-Mohynian) model. The effects of the degree of conversion and structural relaxation on epoxy's relaxation times are simultaneously examined for the first time. This formulation is based on the thermo-rheological and chemo-rheological simplicities hypothesis and can predict the evolution of epoxy's relaxation phenomena. The thermal-kinetic reactions of curing are implemented in a homemade routine written in APDL language, and the structural module of Ansys is used to predict the polymer's creep and stress relaxation curves at different temperatures and degrees of conversion.

Numerical method for the form finding and force analysis of non-prestressed cable-membrane structures with mechanism displacement

The non-prestressed cable-membrane structures exhibit significant nonlinear characteristics such as mechanism displacement and large deformation under external loads. Analyzing such structural behaviors using traditional finite element analysis methods is challenging due to the singularity of the stiffness matrix and the non-convergence of the iterations. In this study, a numerical method based on the vector form intrinsic finite element (VFIFE) method for form finding and force analysis of non-prestressed cable-membrane structures with mechanism displacement is introduced. First, the basic principle and calculation process for analyzing the deformation and internal force of cable-membrane structures are introduced. Second, the applicability of the present method is demonstrated by four numerical examples, including static analysis of the double parabolic inflated membrane and the hemispherical inflated cable-membrane, mechanism motion simulation of the cloth, and large deformation calculation for the flexible curtain. Finally, a spatial non-prestressed cable-membrane model experiment is performed. The effectiveness of VFIFE method is further validated by comparing the measured displacement and internal force to the numerical results. It is shown that the numerical method proposed in this study can effectively simulate the morphological evolution and internal force distribution for the flexible cable-membrane structures with large mechanism displacement, providing a reference for analyzing such practical engineering problems involving strongly nonlinear characteristics.

Numerical analysis of optimal control problems governed by fourth‐order linear elliptic equations using the Hessian discretization method

AbstractThis article focuses on the optimal control problems governed by fourth‐order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretization method (HDM). The HDM is an abstract framework that enables the convergence analysis of several numerical methods such as the conforming finite element methods, the Adini and Morley nonconforming finite element methods (ncFEMs), the method based on gradient recovery (GR) operators, and the finite volume methods (FVMs). Basic error estimates and superconvergence results are established for the state, adjoint, and control variables. A companion operator for the GR method with specific property is designed. The article concludes with numerical results that illustrate the theoretical convergence rates for GR method, Adini ncFEM, and FVM.

In Silico Evaluation of In Vivo Degradation Kinetics of Poly(Lactic Acid) Vascular Stent Devices.

Biodegradable vascular stents (BVS) are deemed as great potential alternatives for overcoming the inherent limitations of permanent metallic stents in the treatment of coronary artery diseases. The current study aimed to comprehensively compare the mechanical behaviors of four poly(lactic acid) (PLA) BVS designs with varying geometries via numerical methods and to clarify the optimal BVS selection. Four PLA BVS (i.e., Absorb, DESolve, Igaki-Tamai, and Fantom) were first constructed. A degradation model was refined by simply including the fatigue effect induced by pulsatile blood pressures, and an explicit solver was employed to simulate the crimping and degradation behaviors of the four PLA BVS. The degradation dynamics here were characterized by four indices. The results indicated that the stent designs affected crimping and degradation behaviors. Compared to the other three stents, the DESolve stent had the greatest radial stiffness in the crimping simulation and the best diameter maintenance ability despite its faster degradation; moreover, the stent was considered to perform better according to a pilot scoring system. The current work provides a theoretical method for studying and understanding the degradation dynamics of the PLA BVS, and it could be helpful for the design of next-generation BVS.

Nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation

This paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin’s method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester.

Investigation of Non-Uniform Inflow Effects on Impeller Forces in Axial-Flow Pumps Operating as Turbines

Due to the existence of an inlet elbow, transmission shaft, and other structural components, the inflow of axial-flow pumps as turbines (PATs) becomes non-uniform, resulting in the complexity of internal flow and adverse effects such as structural vibration. In this paper, numerical methods were employed to explore the non-uniform inflow effects on impeller forces and internal flow field characteristics within an axial-flow PAT. The study results indicated that non-uniform inflow caused uneven pressure distribution inside the impeller, which leads to an imbalance in radial forces and offsetting the center of radial forces. With an increasing flow rate, the asymmetry of radial forces as well as the amplitude of their fluctuations increased. Non-uniform inflow was found to induce unstable flow structures inside the impeller, leading to low-frequency, high-amplitude pressure fluctuations near the hub. Using the enstrophy transport equation, it was shown that the relative vortex generation term played a major part in the spatiotemporal evolution of vortices, with minimal viscous effects.

Bearing capacity evaluation of embedded circular footing considering presence of an overload adjacent

The bearing capacity of axially loaded embedded foundations has been widely studied using analytical and numerical methods. However, there are many discrepancies in the literature results regarding the bearing capacity factors and depth factors of circular embedded footings proposed by different authors. Terzaghi's hypothesis has been used to assess the bearing capacity of shallow foundations and several analytical solutions have been proposed for computing bearing capacity factors, even though a superposition of individual contributions may lead to some error in the computed bearing capacity. This assumption has sometimes been criticized as being more conservative. This article aims to study two problems; The first part is focuses on the numerical evaluation of the superposition hypothesis in the calculation of the bearing capacity for rough circular foundations embedded in sand. In this section, the bearing capacity factors contributing to the conventional solution have been evaluated and superposition errors are indicated and compared with those found by different authors. The latter part of the work is devoted to studying the depth effect on the estimation of the bearing capacity of a rough circular footing embedded in the sand considering presence of an overload adjacent. For both analyses, the finite-difference code Flac2d (FLAC 2007) was used to reach the bearing capacity for embedded circular footings, the ground friction angles are between 25° and 40° and a depth ratio Df/D varies from 0.1 to 2. The calculation results are presented in tables and graphs and compared to previously published results available in the literature.

Impact Response Features and Penetration Mechanism of UHMWPE Subjected to Handgun Bullet.

Ensuring military and police personnel protection is vital for urban security. However, the impact response mechanism of the UHMWPE laminate used in ballistic helmets and vests remains unclear, making it hard to effectively protect the head, chest, and abdomen. This study utilized 3D-DIC technology to analyze UHMWPE laminate's response to 9 mm lead-core pistol bullets traveling at 334.93 m/s. Damage mode and response characteristics were revealed, and an effective numerical calculation method was established that could reveal the energy conversion process. The bullet penetrated by 1.03 mm, causing noticeable fiber traction, resulting in cross-shaped failure due to fiber compression and aggregation. Bulge transitioned from circular to square, initially increasing rapidly, then slowing. Maximum in-plane shear strain occurred at ±45°, with values of 0.0904 and -0.0928. Model accuracy was confirmed by comparing strain distributions. The investigation focused on bullet-laminate interaction and energy conversion. Bullet's kinetic energy is converted into laminate's kinetic and internal energy, with the majority of erosion energy occurring in the first four equivalent sublaminates and the primary energy change in the system occurring at 75 μs in the fourth equivalent sublayer. The results show the damage mode and energy conversion of the laminate, providing theoretical support for understanding the impact response mechanism and improving the efficiency of protective energy absorption.

A Review on Submarine Geological Risks and Secondary Disaster Issues during Natural Gas Hydrate Depressurization Production

The safe and efficient production of marine natural gas hydrates faces the challenges of seabed geological risk issues. Geological risk issues can be categorized from weak to strong threats in four aspects: sand production, wellbore instability, seafloor subsidence, and submarine landslides, with the potential risk of natural gas leakage, and the geological risk problems that can cause secondary disasters dominated by gas eruptions and seawater intrusion. If the gas in a reservoir is not discharged in a smooth and timely manner during production, it can build up inside the formation to form super pore pressure leading to a sudden gas eruption when the overburden is damaged. There is a high risk of overburden destabilization around production wells, and reservoirs are prone to forming a connection with the seafloor resulting in seawater intrusion under osmotic pressure. This paper summarizes the application of field observation, experimental research, and numerical simulation methods in evaluating the stability problem of the seafloor surface. The theoretical model of multi-field coupling can be used to describe and evaluate the seafloor geologic risk issues during depressurization production, and the controlling equations accurately describing the characteristics of the reservoir are the key theoretical basis for evaluating the stability of the seafloor geomechanics. It is necessary to seek a balance between submarine formation stability and reservoir production efficiency in order to assess the optimal production and predict the region of plastic damage in the reservoir. Prediction and assessment allow measures to be taken at fixed points to improve reservoir mechanical stability with the numerical simulation method. Hydrate reservoirs need to be filled with gravel to enhance mechanical strength and permeability, and overburden need to be grouted to reinforce stability.

Distributed Hybrid Electric Propulsion Aircraft Design Based on Convex Optimized Power Allocation Management

In order to ensure that aircraft have medium and long-range flights, enhanced aerodynamic performance, and reduced fuel consumption, this paper presents an original Distributed Hybrid Electric Propulsion Aircraft (DHEPA) design scheme and proposes a novel power allocation management method based on convex optimization. Firstly, by taking the Tecnam P2006T general-purpose aircraft as a reference, key components of DHEPA are selected and modeled. Then, a power allocation management method for DHEPA is proposed on the basis of convex optimization, which takes the minimum fuel consumption as the performance index to realize the reasonable power allocation of the battery and engine, while avoiding sliding into the local optimum of allocation. Finally, momentum theory and numerical simulation methods are used to analyze the aerodynamic enhancement effect of the propeller on the wing in the DHEPA, and a dynamics method is utilized to calculate the dynamics performance of the aircraft at several important stages. The results show that, compared with the reference aircraft, the lift of the DHEPA is increased by 46%. Under typical sectors, the DHEPA has a higher rate of climb and maximum leveling off speed at cruise, and a significantly lower fuel consumption.

Comparison of numerical calculations and ALOHA modeling in consequence assessment of chlorine gas emissions from ethylene dichloride reactors.

Incidents involving chemical storage tanks in the petrochemical industry are significant events with severe consequences. Within the petrochemical industry, EDC is a sector that produces ethylene dichloride through the reaction of chlorine and ethylene. The present research was conducted to evaluate the consequences of chlorine gas released from the EDC reactor in a petrochemical industry in southern Iran. Data regarding reactor specifications were obtained from the factory's technical office, while climatic data was acquired from the Meteorological Organization. The consequences of chlorine gas release from the reactor were assessed in four predefined scenarios using numerical calculation methods and modeling with the ALOHA software. The numerical calculation method involved thermodynamic fluid path analysis, discharge coefficient calculations, and wind speed impact analysis. The hazard radius was determined based on the ERPG1-2-3 index. Results showed that in the scenario of chlorine gas release from EDC reactors, according to the ALOHA model, an increase in wind speed from 3 to 7m/h led to an expanded dispersion radius. At a radius of 700m from the reactor, the maximum outdoor concentration reached 3.12ppm, decreasing to 2.27ppm at 800m and further to 1.53ppm at 1000m. The comparison of numerical calculations and modeling using the ALOHA software indicates the desirable conformity of the results with each other. The R2 coefficient for evaluating the conformity of the results was 0.9964, indicating the desired efficiency of the model in evaluating the consequences of the release of toxic gasses from the EDC tank. The results of this research can be useful in designing the site and emergency response plan.

Numerical Investigation of Rotor and Stator Matching Mode on the Complex Flow Field and Pressure Pulsation of a Vaned Centrifugal Pump

The match of rotor and stator blades significantly affects the flow field structure and flow-induced pressure pulsation characteristics inside the pump. In order to study the effects of the rotor and stator matching mode on the complex flow field and pressure pulsation of a centrifugal pump with a vaned diffuser, this paper designs three different vaned diffusers (DY5, DY8 and DY9) and uses the DDES (Delayed Detached Eddy Simulation) numerical method combined with structured grids to simulate the unsteady flow phenomena of the model pump under rated conditions. The results show that, under different rotor and stator matching modes, the pressure pulsation spectrum is dominated by the blade passing frequency and its harmonics. The matching mode of the rotor and stator significantly affects the time–frequency domain characteristics of the pressure pulsation inside the pump, and it is observed that the pressure pulsation energy of vaned diffusers with more blades is significantly smaller than that of fewer-blade vaned diffusers in comparison to the energy of the pressure pulsation at the blade passing frequency and within the 10–1500 Hz frequency band. Combined with the distribution characteristics of the complex flow field inside the pump, it can be found that increasing the number of vaned diffuser blades can reduce the energy of flow-induced pressure pulsation, improve the distribution of high-energy vortices in the interaction zone and stabilize the flow inside the centrifugal pump effectively.