Numerical Method Research Articles

Static and dynamic response of pyramidal lattice sandwich plate with composite face sheets reinforced by graphene platelets

For the pursuit of lightweight structures with excellent mechanical performance, sandwich structures with lightweight cores and strengthened face sheets have become popular in the advanced engineering fields in recent years. In this paper, the nonlinear static and dynamic responses of the sandwich plate constructed with the aluminum pyramidal lattice core and functionally graded graphene platelets reinforced composite (FG-GPLRC) face layers are analyzed. The partial differential equations of the pyramidal lattice sandwich plate considering the geometric nonlinearity are achieved based on the Reddy’s third order shear deformation theory (TSDT), which are solved by the combination of finite element model, Raphson’s method and Newmark numerical integration method. Four different types of the impact loads including the step loading, triangular loading, half-sine loading and exponential loading with the same peak value and duration time are investigated. The influences of the thickness-to-truss radium ratio and the angle of the truss core, as well as the weight fraction and distribution patterns of graphene platelets (GPLs) over the face sheets under different impact loads and different boundary conditions are analyzed. According to the numerical results, it is concluded that the sandwich plate with higher weight fraction of GPLs, lower thickness-to-truss radium ratio, and higher angle of the truss core can exhibit better performance in both static and dynamic loading conditions. The FG-X distribution of GPLs presents the best dynamic performance as compared to the other GPL distributions. The combination of lightweight truss core with the advanced GPLRC face sheets is instructive for potential applications and further research.

Exploring tsunami generation and propagation: A case study of the 2018 Palu earthquake and tsunami

The tsunami disaster in Palu, Indonesia, on September 28, 2018, caused many casualties and damage along Palu Bay, Indonesia. Prior to the tsunami, an earthquake was recorded 25 km northeast of Donggala. The analysis suggests that the tsunami was triggered by a landslide beneath the waters of Palu Bay. The investigation then focused on the earthquake's impact on the tsunami. This study conducts simulations to discern the dominant causes of tsunamis, comparing the effects of landslides with earthquakes. Three distinct tsunami sources were identified: earthquake-only (T-E), earthquake and submarine landslide (T-EL), and submarine landslide-only (T-L). Interpretation of tsunami source parameters for underwater landslides is carried out accurately. A nesting grid numerical method was employed to increase resolution and accuracy in the simulations. This study accurately interprets tsunami source parameters using data from the Bathymetry National Data-Geospatial Information Agency (185 m resolution) and the field survey data from Baruna Jaya IV-BPPT Research Vessel Indonesia (25 m resolution), thereby contributing to the creation of a tsunami inundation model map. This map serves to inform preparedness efforts and guide recommendations for infrastructure development in the Palu Bay area. The tsunami inundation model map is verified with field data and estimated using tide gauge monitoring data. The characteristics of the tsunami waves on September 28, 2018, reflect a T-EL-type tsunami source, while the T-L type source produces tsunami waves with longer periods compared to earthquake-generated tsunamis (T-EL). The T-E type, located on land, had minimal influence in causing the tsunami, despite the destructive potential of the shallow-depth M7.5 earthquake.

Underwater implosion protection of a new concept composite structure for a deep-sea hollow ceramic sphere with CFRP shield

Carbon fiber–reinforced polymers (CFRP) and ceramics are lightweight, non-metallic materials with broad applications. However, their use in deep-sea engineering is limited owing to the potential risk of catastrophic implosions. This study introduces the concept of deep-sea ceramic-pressure-resistant hollow structures with CFRP shields for achieving a balance between safety and light weight. This research examines typical engineering cases, including the HROV Nereus and Titan accidents, and uses the Arbitrary Lagrangian–Eulerian method to investigate the fluid–structure interactions. First, the feasibility of the numerical method was verified, with the responses of the structure and flow field summarized. The advantages of ceramic hollow spheres with a CFRP shield were analyzed, leading to the development of a new implosion protection scheme with a composite structure. Furthermore, this study discusses the effects of the CFRP thickness, CFRP ratio, and trigger mode on implosion protection, with the results revealing that increasing the thickness and proportion of the CFRP shield considerably enhances the implosion suppression effect of the entire structure. These findings are valuable for designing pressure-resistant structures for practical engineering applications.

Building a sustainable future: Exploring the nexus between climate awareness and thermal insulation choices in new home construction

Climate change is considered a major threat to the environment and society as a whole. Reducing building energy consumption through the use of thermal insulation is one way of combating climate change. This study examines the impact of climate change awareness on the pre-construction decision of Lebanese homeowners to use thermal insulation in their new homes. A model building consisting of a typical 160 m2 single-family home was used and its thermal loads were calculated in two cases: insulated and uninsulated case, in three different locations in Lebanon: Beirut, Chtaura, and Bcharre-Arz. The thermal loads were calculated using two methods: the degree-days empirical method, and the Hourly Analysis Program software numerical method. The computations showed energy reduction ranging between 23% in the coastal region to 52% in high mountains when thermal insulation of thickness 5 cm was used. The investment payback period ranged from 4.3 years in the coastal region to 1.5 years in the high mountains. A survey addressed to 100 respondents was used to understand how Lebanese homeowners’ decision to use thermal insulation was affected by knowledge of the obtained results. The survey results showed that climate change awareness has a high impact on this decision; however, the cost seems to play an important role in the owners’ final decision on whether or not to use thermal insulation. Spreading awareness about climate change and the payback periods of building thermal insulation will increase its use since the number of respondents refusing to use thermal insulation drastically decreased after being informed about its payback period.

Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures

This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

De-projecting the EFThedron

The space of Wilson coefficients of EFT that can be UV completed into consistent theories was recently shown to be described analytically by a positive geometry, termed the EFThedron. However, this geometry, as well as complementary numerical methods of semi-definite programming, have so far focused on the positivity of the partial wave expansion, which allows bounding only ratios of couplings. In this paper we describe how the unitarity upper bound of the partial waves can be incorporated. This new problem can be formulated in terms of the well known L-moment problem, which we generalize and solve from a geometrical perspective. We find the non-projective generalization of the EFThedron has an infinite number of non-linear facets, which in some cases have remarkably simple descriptions. We use these results to derive bounds on single couplings, finding that the leading derivative operators are bounded by unity, when normalized by the cut-off scale and loop factors. For general operators of mass dimension 2k we find the upper bound is heavily suppressed at large k, with an 1/k fall-off.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.

Numerical evaluation of low-head inverted cross-flow turbine design method: A comprehensive study

This study aimed to address the challenges of micro-hydropower generation in low-head environments to expand the proportion of hydropower in renewable energy and achieve a carbon neutrality policy. To achieve these goals, various factors affecting the micro-hydro systems, including geographical constraints, construction costs, and grid connectivity, were reviewed and assessed. The results concluded that a novel type of cross-flow turbine with inverted structures, improved the economic feasibility, productivity, and installability of micro-hydropower plants by reducing head losses in open channels or small streams. The parametric studies consisted of four steps: first, designing the initial inverted cross-flow turbine based on the traditional design rules; for the second and third steps, a parametric study for comparing the runner diameter ratio and the number of blades is conducted; and in the last step optimized turbine was designed. The best efficiency point of the optimized inverted cross-flow turbine was 72.92 % at a runner rotational speed of 170 RPM with a 0.75 runner diameter ratio and 35 blades. The optimized turbine was improved by 7.8 % in power and 7.35 % in efficiency, higher than the initial turbine. From the hill chart comparison between the initial and optimized turbine, operation range expansion was confirmed. Overall, this research demonstrates the potential of the inverted cross-flow turbine under low-head conditions.

Robustness of embedded fibre optic sensor mesh configurations for monitoring composite structures

Fibre optic sensors are attractive for monitoring of composite structures but the significant risk of damage to fibres where they enter the structure and within the structure itself can make their use unreliable. Mesh configurations of embedded fibre Bragg grating sensors with improved robustness are considered for monitoring composite structures. The configurations of single ended line, bidirectional line, loop, and a novel 2×2 mesh are analysed using a probabilistic model of the sensor system robustness. Numerical evaluation of these configurations has shown that the 2×2 mesh configuration provides the greatest robustness of all of the configurations across all inlet port failure probabilities. The probability of a sensor becoming isolated in a 2×2 mesh is approximately 3 times lower than for the bidirectional line configuration. Using a new matrix approach, the 2×2 mesh configuration is analysed in terms of disaggregation of individual sensor spectra for both fault free and faulty conditions. Simulation and experimental evaluation have demonstrated that successful recovery of individual grating spectra is possible with small spurious signals.

An information theoretic metric for measurement vulnerability to data integrity attacks on smart grids

AbstractA novel metric that describes the vulnerability of the measurements in power systems to data integrity attacks is proposed. The new metric, coined vulnerability index (VuIx), leverages information theoretic measures to assess the attack effect in terms of the fundamental limits of the disruption and detection tradeoff. The result of computing the VuIx of the measurements in the system yields an ordering of their vulnerability based on the degree of exposure to data integrity attacks. This new framework is used to assess the measurement vulnerability of IEEE 9‐bus and 30‐bus test systems and it is observed that power injection measurements are significantly more vulnerable to data integrity attacks than power flow measurements. A detailed numerical evaluation of the VuIx values for IEEE test systems is provided.

Modal analysis and output characteristics of an ultrasonic motor with a square prismatic shell stator

Abstract A rotary traveling wave ultrasonic motor having a square prismatic shell stator is proposed. The stator contacts with the rotor through interference fit, and elastically deforms slightly, and then presses against the rotor. Then the pre-pressure is created by the initial deformation of the stator with simple structure. The in-plane modal problem of the stator is analyzed by numerical method as a folded beam and the results are compared with those from finite element method (FEM) and laser doppler measurement. The 3rd and 5th degenerate modes with repeat natural frequencies are selected as working modes, and the influence of actuating frequency and voltage on the no-load speed and stall torque is studied by multi-physics simulation for the operation of these two modes. A prototype is fabricated and the output characteristics were tested and compared with the simulated results. The 3rd working mode is found to have better performance and can reach a no-load speed of 205 rpm and maximum torque of 3.9 mN·m when the input is 28.0 kHz and 100V. The effect of the pre-pressure for the 3rd working mode is discussed further.

Research on the analysis and management measures of land subsidence caused by groundwater exploitation in Tianjin, China

Since the 20th century, there has been an increasing reliance on groundwater due to the rapid development of agriculture and industry. This has resulted in the exploitation of groundwater in large quantities, leading to global land subsidence problems. Tianjin is one of the cities where this problem first emerged, but few studies and surveys have been conducted. As a result, the lack of management of groundwater extraction has caused the issue of land subsidence to become more prominent in recent years. By investigating and collating global research on land subsidence problems caused by groundwater extraction, it is concluded that mathematical and numerical methods, global information systems, remote sensing, and other technologies can be utilized to monitor and predict groundwater levels. Regional management measures can then be developed based on simulation results. However, the application of such technology in Tianjin is insufficient, and there is a need to strengthen the connection between management measures and research data analysis results.

Normal form and Hopf bifurcation for the memory‐based reaction‐diffusion equation with nonlocal effect

In this paper, we provide the normal form for the Hopf bifurcation of a class of the reaction‐diffusion equation with memory‐based diffusion and nonlocal effect, where the delay is present in the differential term, similar to the chemotaxis model with time delay. The eigenvalue problems and the decomposition of the phase space are discussed in detail. Through a series of variable transformations, we obtain the third‐order truncated normal form of the model constrained on the central manifold and its equivalent equation in polar coordinates. Then, with the help of the dynamic analysis for the finite dimensional equations, the key parameters for determining the direction and stability of the Hopf bifurcation are given. These theoretical results are applied to the Bazykin's model, the stability, Turing bifurcation and Hopf bifurcation of the equilibrium are demonstrated through both theoretical and numerical methods.

An efficient high‐order two‐level explicit/implicit numerical scheme for two‐dimensional time fractional mobile/immobile advection‐dispersion model

AbstractThis article constructs a new two‐level explicit/implicit numerical scheme in an approximate solution for the two‐dimensional time fractional mobile/immobile advection‐dispersion problem. The stability and error estimates of the proposed technique are deeply analyzed in the ‐norm. The developed approach is less time consuming, fourth‐order in space and temporal accurate of order , where is the time step and denotes a positive parameter less than 1. This result shows that the two‐level explicit/implicit formulation is faster and more efficient than a large class of numerical schemes widely discussed in the literature for the considered problem. Numerical experiments are performed to verify the theoretical studies and to demonstrate the efficiency of the new numerical method.

A synergistic approach to optimizing the performance of a concentrating solar segmented variable area leg thermoelectric generator using numerical methods and neural networks

AbstractThis study presents an optimized design for segmented variable area leg thermoelectric modules using finite element methods and Bayesian regularized neural networks. We explored the impact of geometry and thermal parameters on module performance using ANSYS software, identifying optimal parameters for power output and efficiency. Key findings revealed the higher influence of geometric parameters and confirmed the advantages of segmented thermoelectric generators for high-temperature applications like concentrated solar systems. With this optimization, power output and efficiency of the module increased by 875% and 165%, respectively, under 25 Suns. To refine the optimization process, a Bayesian regularized neural network was utilized, proving effective in predicting module performance with a low mean squared error and high coefficient of determination. This research provides important insights into high-performance thermoelectric modules for sustainable energy applications, demonstrating the significant role of advanced computational methods in energy solutions.

Assessment of structural mechanical effects related to torsional deformations of propellers

AbstractLifting propellers are of increasing interest for Advanced Air Mobility. All propellers and rotors are initially twisted beams, showing significant extension–twist coupling and centrifugal twisting. Torsional deformations severely impact aerodynamic performance. This paper presents a novel approach to assess different reasons for torsional deformations. A reduced-order model runs large parameter sweeps with algebraic formulations and numerical solution procedures. Generic beams represent three different propeller types for General Aviation, Commercial Aviation, and Advanced Air Mobility. Simulations include solid and hollow cross-sections made of aluminum, steel, and carbon fiber-reinforced polymer. The investigation shows that centrifugal twisting moments depend on both the elastic and initial twist. The determination of the centrifugal twisting moment solely based on the initial twist suffers from errors exceeding 5% in some cases. The nonlinear parts of the torsional rigidity do not significantly impact the overall torsional rigidity for the investigated propeller types. The extension–twist coupling related to the initial and elastic twist in combination with tension forces significantly impacts the net cross-sectional torsional loads. While the increase in torsional stiffness due to initial twist contributes to the overall stiffness for General and Commercial Aviation propellers, its contribution to the lift propeller’s stiffness is limited. The paper closes with the presentation of approximations for each effect identified as significant. Numerical evaluations are necessary to determine each effect for inhomogeneous cross-sections made of anisotropic material.

Semi-empirical cross-section formulas for electron-impact ionization and rate coefficient calculations

We propose a semi-empirical formula for the cross section of ionization by electron impact. The formula involves adjustable parameters which are determined by comparison with measured or numerically calculated cross sections. In the latter case, the ions are perturbed by their environment which is a high-density plasma. As a consequence, the cross section is significantly modified. We investigate Be-like carbon, nitrogen and oxygen as well as aluminum ions. We also show that the formula is well-suited for interpolation and extrapolation. Knowing the cross section, we calculate the rate coefficient within the Boltzmann and Fermi–Dirac statistics. In the first case, the rate can be calculated analytically. In the second one, it can be expressed in terms of special functions, but the numerical evaluation is more convenient while providing accurate results. Our results are compared to experiment and to other calculations.

Numerical Simulation of the Density Effect on the Macroscopic Transport Process of Tracer in the Ruhrstahl–Heraeus (RH) Vacuum Degasser

Silicon steel (electrical steel) has been used in electric motors that are important components in sustainable new energy Electrical Vehicles (EVs). The Ruhrstahl–Heraeus process is commonly used in the refining process of silicon steel. The refining effect inside the RH degasser is closely related to the flow and mixing of molten steel. In this study, a 260 t RH was used as the prototype, and the transport process of the passive scalar tracer (virtual tracer) and salt tracer (considering density effect) was studied using numerical simulation and water model research methods. The results indicate that the tracer transports from the up snorkel of the down snorkel to the bottom of the ladle, and then upwards from the bottom of the ladle to the top of the ladle. Density and gravity, respectively, play a promoting and hindering role in these two stages. In different areas of the ladle, density and gravity play a different degree of promotion and obstruction. Moreover, in different regions of the ladle, the different circulation strength leads to the different promotion degrees and obstruction degrees of the density. This results in the difference between the concentration growth rate of the salt tracer and the passive scalar in different regions of the ladle top. From the perspective of mixing time, density and gravity have no effect on the mixing time at the bottom of the ladle, and the difference between the passive scalar and NaCl solution tracer is within the range of 1–5%. For a larger dosage of tracer case, the difference range is reduced. However, at the top of the ladle, the average mixing time for the NaCl solution case is significantly longer than that of the passive scalar case, within the range of 3–14.7%. For a larger dosage of tracer case, the difference range is increased to 17.4–41.1%. It indicates that density and gravity delay the mixing of substances at the top area of the ladle, and this should be paid more attention when adding denser alloys in RH degasser.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials

Abstract Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This paper also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pre-trained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pre-training.