Distribution Of Coefficients Research Articles

High-resolution physicochemical dataset of atmospheric aerosols over the Tibetan Plateau and its surroundings

Abstract. Atmospheric aerosol in the Tibetan Plateau (TP) and its surroundings has attracted significant scientific interest in recent decades due to its notable impacts on regional climatic and cryospheric changes, ecological and environmental security, and the hydrological cycle. However, our understanding of the atmospheric aerosol in this remote region is highly limited by the scarcity of available datasets owing to the extremely harsh natural conditions. This challenge has been mitigated in recent decades by establishing field observatories at typical sites within the TP and its surroundings. A continuous project initiated in 2015 aims to explore the properties and sources of atmospheric aerosols, as well as their regional differences, through multiple short-term intensive observations obtained across this vast region utilizing a suite of high-time-resolution online instruments. This paper presents a systematic and hourly scale dataset of aerosol physicochemical and optical properties at eight sites across the TP and its surroundings that is derived from the project. It includes size-resolved chemical compositions of submicron aerosols, high-resolution mass spectra and sources of organic aerosols, size distributions of particle number concentrations, particle light-scattering and light-absorption coefficients, particle light absorptions attributed to different carbonaceous substances including black carbon and brown carbon, and number concentrations of cloud condensation nuclei. In brief, atmospheric aerosols in these remote sites were all well mixed and highly aged, reflecting their dominant regional transport sources. However, the southern TP region exhibited high contributions of carbonaceous organic aerosols, neutralized bulk submicron aerosols, and a relatively high light-absorption capacity, whereas in the northern TP region, secondary inorganic species were the main contributors to the overall acidic submicron aerosols. Beyond providing insights into the regional differences in aerosol sources and properties across the TP and its surroundings, the datasets will also benefit simulations of aerosol radiative forcing and evaluations of interactions among different Earth system components in numerical models for this region. The datasets are accessible through the National Cryosphere Desert Data Center, Chinese Academy of Sciences (https://doi.org/10.12072/ncdc.NIEER.db2200.2022; Xu, 2022).

In Situ Imaging of Two-Dimensional Crystal Growth Using a Heat-Resistant Optical Microscope.

Revealing low-dimensional material growth dynamics is critical for crystal growth engineering. However, in a practical high-temperature growth system, the crystal growth process is a black box because of the lack of heat-resistant imaging tools. Here, we develop a heat-resistant optical microscope and embed it in a chemical vapor deposition (CVD) system to investigate two-dimensional (2D) crystal growth dynamics. This in situ optical imaging CVD system can tolerate temperatures of ≤900 °C with a spatial resolution of ∼1 μm. The growth of monolayer MoS2 crystals was studied as a model for 2D crystal growth. The nucleation and growth process have been imaged. Model analysis and simulation have revealed the growth rate, diffusion coefficient, and spatial distribution of the precursor. More importantly, a new vertex-kink-ledge model has been suggested for monolayer crystal growth. This work provides a new technique for in situ microscopic imaging at high temperatures and fundamental insight into 2D crystal growth.

Computational Fluid Dynamics Prediction of External Thermal Loads on Film-Cooled Gas Turbine Vanes: A Validation of Reynolds-Averaged Navier–Stokes Transition Models and Scale-Resolving Simulations for the VKI LS-94 Test Case

Given the increasing role of computational fluid dynamics (CFD) simulations in the aerothermal design of gas turbine vanes and blades, their rigorous validation is becoming more and more important. This article exploits an experimental database obtained by the von Karman Institute (VKI) for Fluid Dynamics for the LS-94 test case. This represents a film-cooled transonic turbine vane, investigated in a five-vane linear cascade configuration under engine-like conditions in terms of the Reynolds number and Mach number. The experimental characterization included inlet freestream turbulence measured with hot-wire anemometry, aerodynamic performance assessed with a three-hole pressure probe in the downstream section, and vane convective heat transfer coefficient distribution determined with thin-film thermometers. The test matrix included cases without any film-cooling injection, pressure-side injection, and suction-side injection. The CFD simulations were carried out in Ansys Fluent, considering the impact of mesh sizing and steady-state Reynolds-Averaged Navier-Stokes (RANS) transition modelling, as well as more accurate transient scale-resolving simulations. This work provides insight into the advantages and drawbacks of such approaches for gas turbine hot-gas path designers.

Three-dimensional nonlinear stress analysis of functionally graded shells subjected to displacement-dependent loads

The nonlinear geometrically exact (GeX) hybrid-mixed four-node solid-shell element under non-conservative loading, developed in the companion paper, is here extended to the stress analysis of functionally graded material (FGM) shells. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms can be taken exactly at element nodes. The FGM solid-shell element formulation is based on the choice of N sampling surfaces (SaS) parallel to the middle surface and located at Chebyshev polynomial nodes within the shell as well as on the outer surfaces, to introduce the displacements of these surfaces as basic unknowns. The use of Lagrange polynomials of degree N–1 in the distributions of displacements, strains, stresses, and elastic coefficients through the thickness of the shell leads to an efficient 3N-parameter shell formulation. To develop the FGM four-node solid-shell element based on the hybrid-mixed method, in which strains and stresses are utilized as primary variables, the Hu-Washizu variational principle is applied. Due to the analytical integration used to evaluate the tangent stiffness matrix, the developed FGM solid-shell element subjected to displacement-dependent loads shows superior performance in the case of coarse meshes and allows the use of only one load step in most of the considered benchmark problems. It has been established that the difference between the second Piola-Kirchhoff and Cauchy stress tensors in non-conservative problems for FGM shells undergoing moderately large strains can be significant.

Effect of Floating Support Parameters on the Load-Sharing Performance of EDPGS Based on Mathematical Statistical Methods

The encased differential planetary gear system (EDPGS) allows power to be distributed among multiple output paths, enhancing efficiency and reducing weight. Uniform load distribution ensures stable system operation and prolongs service life. However, stochastic manufacturing errors leading to uneven load distribution pose challenges in engineering practice. To investigate the impact of floating support parameters on the load-sharing performance within an acceptable tolerance band, a dynamic model of the EDPGS considering time-varying meshing stiffness and random errors is established using the Monte Carlo method. This study employs the orthogonal experimental design method to analyze the effects of floating support stiffness and clearance on the load-sharing characteristics. The findings indicate that a larger sample size leads to a probability distribution of load-sharing coefficients closer to the Gaussian distribution, with minimal influence on the expectation and variance. Furthermore, this study highlights the significant influence of floating structure parameters on load-sharing characteristics in the encased stage systems compared to the differential stage. Decreasing floating support stiffness or increasing floating clearance proves beneficial in enhancing the load-sharing performance of the system.

Comprehensive evaluation of natural ventilation potential of buildings in urban areas under the influence of multiple environment-related factors

Realistic natural ventilation potential estimation is critical for energy-efficient building design. For buildings in urban areas, evaluations using design expectations tend to overestimate potential. This study presents a comprehensive framework and corresponding method to predict the natural ventilation potential of buildings, integrating multiple key environmental factors of climate features, local wind status, and air pollution level. It addresses their complex interplay. Climate impacts are evaluated through simulating using a pre-set natural ventilation rate. Computational fluid dynamics models typical neighbourhood wind fields, giving empirical wind pressure coefficient distributions by layout and wind direction to enable real-time ventilation rate calculation. Substituting real-time for pre-set rates, the natural ventilation potential considering the community layout can be obtained. Based on the data-driven rapid pollutant prediction model established in the previous study, the predictions of the temporal and spatial distributions of particulate matter can be obtained. Filtering excessive pollution periods yields air quality-integrated potentials. Natural ventilation potentials are compared under different analysis scenarios for a case-study building. Hotter climates and more frequent heatwaves lower the potential. Morphology-based potentials are significantly lower than design expectations using constant ventilation rates. Deteriorating urban air quality also directly limits ventilation use, substantially decreasing potentials when filtering for poor conditions. By capturing complex environmental interactions, this research provides a robust platform to reveal localization potentials and limitations.

On the Fidelity of RANS-Based Turbulence Models in Modeling the Laminar Separation Bubble and Ice-Induced Separation Bubble at Low Reynolds Numbers on Unmanned Aerial Vehicle Airfoil

The operational regime of Unmanned Aerial Vehicles (UAVs) is distinguished by the dominance of laminar flow and the flow field is characterized by the appearance of Laminar Separation Bubbles (LSBs). Ice accretion on the leading side of the airfoil leads to the formation of an Ice-induced Separation Bubble (ISB). These separation bubbles have a considerable influence on the pressure, heat flux, and shear stress distribution on the surface of airfoils and can affect the prediction of aerodynamic coefficients. Therefore, it is necessary to capture these separation bubbles in the numerical simulations. Previous studies have shown that these bubbles can be modeled successfully using the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) but are computationally costly. Also, for numerical modeling of ice accretion, the flow field needs to be recomputed at specific intervals, thus making LES and DNS unsuitable for ice accretion simulations. Thus, it is necessary to come up with a Reynolds-Averaged Navier–Stokes (RANS) equation-based model that can predict the LSBs and ISBs as accurately as possible. Numerical studies were performed to assess the fidelity of various RANS turbulence models in predicting LSBs and ISBs. The findings are compared with the experimental and LES data available in the literature. The structure of these bubbles is only studied from a pressure coefficient perspective, so an attempt is made in these studies to explain it using the skin friction coefficient distribution. The results indicate the importance of the use of transition-based models when dealing with low-Reynolds-number applications that involve LSB. ISB can be predicted by conventional RANS models but are subjected to high levels of uncertainty. Possible recommendations were made with respect to turbulence models when dealing with flows involving LSBs and ISBs, especially for ice accretion simulations.

Numerical study on lead–bismuth cross-flow induced vibration in the elastic tube bundle

The physical properties of liquid lead–bismuth eutectic fluid are quite different from that of water or air. It needs to be verified whether the cross-flow vibration mechanism and the empirical prediction model of fluidelastic instability in conventional media are applicable to lead–bismuth. In this work, for an in-line elastic tube bundle with pitch ratio P/D = 1.5, the flow excitation of lead–bismuth at 200 °C is studied and compared with that of water in uncoupled flow field. Then, two cases of lead–bismuth flow-induced vibration with different mass-damping parameters are simulated and studied by fully coupled numerical simulation considering fluid viscous damping. The tube bundle experiences the process from turbulence-induced vibration in low flow velocity to fluidelastic instability in high velocity. The results of flow excitation show that the pressure coefficient distribution of the front row tube in lead–bismuth is basically consistent with that in water, while the inconsistency of the pressure coefficient distribution for the back row tube is caused by the bi-stable deflective flow. The results of lead–bismuth flow-induced vibration show that, in fluidelastic instability, the vibration of tube bundle and the vortex shed from tube bundle are dominated by the frequency close to the first wet modal frequency of tube bundle. The different deflective directions of lead–bismuth and water, caused by bi-stable characters, have less effect on the onset of fluidelastic instability. The instability points of lead–bismuth agree with the experimental results of other media and the Connors prediction model considering fluid viscous damping. The prediction model is suggested to predict the onset of fluidelastic instability induced by lead–bismuth cross-flow in the tube bundle.

SCATTERING OF ELECTROMAGNETIC WAVES ON FLAT GRID TWO-PERIODIC STRUCTURES

Context. One of the scientific hypotheses for the creation of nonreciprocal optical metasurfaces is based on the use of a wave channel in which rays of the direct and reverse diffraction scenarios are realized on two-periodic flat structures with nonlinear elements. Such processes in the nanometer wavelength range of electronic devices require precise calculations of the interaction of waves and microstructures of devices. It is also important to describe the behavior of antenna devices in mobile communications. Expanding the wavelength range of stable communication is achieved by using prefractal structures in antenna devices in combination with periodic structuring. Similar modeling problems arise when electromagnetic waves penetrate materials with a crystalline structure (radio transparency).
 Objective. To test this hypothesis, it is necessary to carry out mathematical modeling of the process of scattering of electromagnetic waves by metasurfaces under conditions of excitation of several diffraction orders. It is known that among two-periodic flat lattices of different structures there are five types that fill the plane. These are the Bravais grilles. The problem of scattering of an incident monochromatic TE polarized wave on a metal screen with recesses in two-periodic structures filled with silicon was considered.
 Method. The paper builds mathematical models for the study of spatial-amplitude spectra of metasurfaces on Brave lattices and gives some results of their numerical study. The condition for determining the diffraction orders propagating over the grating is proposed. Scattered field amplitudes are from the solution of the boundary value problem for the Helmholtz equation in the COMSOL Multiphysics 5.4 package. Similar problem formulations are possible when studying the penetration of an electromagnetic field into a crystalline substance.
 Results. Obtained relations for diffraction orders of electromagnetic waves scattered by a diffraction grating. The existence of wavelengths incident on a two-periodic lattice for which there is no reflected wave is shown for different shapes (rectangular, square, hexagonal) of periodic elements in the center of which a depression filled with silicon was made. Distributions of reflection coefficients for different geometric sizes of colored elements and recesses are given. The characteristics of the electric field at resonant modes in the form of modulus isolines show the nature of the interaction of the field over the periodic lattice and the scatterersdepressions. At the resonant wavelengths of the incident waves, standing waves appear in the scatterers.
 Conclusions. A mathematical model of the set of diffraction orders propagating from a square and hexagonal lattice into halfspace is proposed z >= 0. It has been shown that flat periodic lattice with square or hexagonal periodicity elements and resonant scatterers in the form of cylindrical recesses filled with silicon can produce a non-mirrored scattered field in metal. The response of the lattices to changes in the wavelength of the incident field by the structure of diffraction orders of the scattered field and high sensitivity to the rotation of the incident plane were revealed. The two-periodic lattices have prospects for creating anti-reflective surfaces of various devices. Two-periodic lattices have prospects for creating anti-reflective surfaces for various devices, laser or sensor electronic devices, antennas in mobile communication elements, and radio transparency elements. They have more advanced manufacturing technologies in relation to spatial crystal structures.

Aeroacoustic investigation of a ducted wind turbine employing bio-inspired airfoil profiles

Ducted wind turbines for residential purposes are characterized by a lower diameter with respect to conventional wind turbines for on-shore applications. The noise generated by the rotor plays a significant role in the overall aerodynamic noise. By making modifications to the blade sections of the wind turbine, we can alter the contributions of aeroacoustic noise sources. This study introduces innovative wind turbine blade designs inspired by owl wing characteristics, achieving significant noise reduction without compromising aerodynamic performance. A three-dimensional scan of an owl wing was first employed to derive a family of airfoils. The airfoils were employed to modify the blade of a referenced wind turbine airfoil section at various positions on the blade span to determine a blade operating more efficiently at the tip-speed ratio of the original one. While maintaining the same aerodynamic performance, the bio-inspired profiles show a more uniform pressure coefficient distribution, considerably decreasing in the noise level. Furthermore, this study makes considerable progress in ducted wind turbine design by obtaining an 8 dB noise reduction and a 12% improvement in sound pressure level. An in-depth aerodynamic examination shows a 6.4% rise in thrust force coefficient and optimized power coefficients, reaching a peak at a tip speed ratio of 8, demonstrating improved energy conversion efficiency. The results highlight the dual advantage of the innovative design: significant noise reduction and enhanced aerodynamic efficiency, offering a promising alternative for urban wind generation.

Flame soot absorption coefficient and temperature reconstruction through line-of-sight attenuation and light field imaging

The accuracy and efficiency of 3-D flame temperature field reconstruction using the light field imaging technique heavily depend on soot radiation characteristics. In this study, we employ the line-of-sight attenuation method to reconstruct the soot absorption coefficient distribution in a pure absorbing flame. Utilizing these soot absorption coefficients, the radiative transfer equation is effectively transformed within the framework of the light field imaging technique into a linear inverse problem and also outlines the flame boundary. This proposed strategy reduces the unwanted detection rays significantly, thus eliminating the extensive computational processing. Consequently, the proposed approach substantially enhances the accuracy and efficiency of flame temperature reconstruction. Numerical simulations were carried out on a bimodal asymmetric flame to validate the noise tolerance capabilities, investigate the effects of varying voxel numbers on flame division and carry out a comparative study. Experimental studies were also conducted to reconstruct flame temperature and soot absorption coefficient distributions under different combustion operating conditions. Thermocouple measurements were performed and compared with the reconstructed temperatures. Outcomes achieved from both numerical simulations and experimental studies demonstrate the feasibility, accuracy and robustness of the proposed method.

A Multi-Fidelity Uncertainty Propagation Model for Multi-Dimensional Correlated Flow Field Responses

Given the randomness inherent in fluid dynamics problems and limitations in human cognition, Computational Fluid Dynamics (CFD) modeling and simulation are afflicted with non-negligible uncertainties, casting doubts on the credibility of CFD. Scientifically and rigorously quantifying the uncertainty of CFD is paramount for assessing its credibility and informing engineering decisions. In order to quantify the uncertainty of multidimensional flow field responses stemming from uncertain model parameters, this paper proposes a method based on Gappy Proper Orthogonal Decomposition (POD) for supplementing high-fidelity flow field data within a framework that leverages POD and surrogate models. This approach enables the generation of corresponding high-fidelity flow fields from low-fidelity ones, significantly reducing the cost of high-fidelity flow field computation in uncertainty propagation modeling. Through an analysis of the impact of uncertainty in the coefficients of the Spalart–Allmaras (SA) turbulence model on the distribution of wall friction coefficients for the NACA0012 airfoil and pressure coefficients for the M6 wing, the proposed multi-fidelity modeling approach is demonstrated to offer significant advancements in both accuracy and efficiency compared to single-fidelity methods, providing a robust and efficient prediction model for large-scale random sampling.

Optimizing thermal stability in permafrost regions: A comprehensive evaluation of encapsulated phase change material enhanced energy storage embankments

The melting of permafrost can cause serious damage to road structures. This study prepares a phase change geotextile (PCG) with heat absorption and waterproofing properties and proposes a new type of cooling structure called a phase change energy storage embankment (PCESE). A finite element model of the road is established to quantify the artificial permafrost table (APT), mean annual ground temperature (MAGT) at the bottom of the embankment, and mean daily cooling rate (MDCR) of the asphalt pavement surface under different PCESE structures. This study focuses on exploring the effects of the type of epoxy resin composite phase change material (ERPCM), dosage of ERPCM, and position of the PCG on various indices. The Entropy-TOPSIS method is used to evaluate the comprehensive performance of the PCESE and determine the optimal structure and optimization strategy. The results demonstrate that the addition of PCG to an embankment always improves the APT and MDCR, but does not necessarily reduce the MAGT. The optimal type of ERPCM, dosage of ERPCM, and position of PCG are ERPCM2, 12 kg/m2, and 3.0 m, respectively. The dosage of the ERPCM had the highest positive correlation with comprehensive performance. Considering the distribution of comprehensive performance and coefficient of variation under different structures, the recommended type of ERPCM, dosage of ERPCM, and position of the PCG are ERPCM1, 12 kg/m2, and 2.5 m, respectively.

CFD simulation of the inundation effect for saturated propane vapor condensation on the surface of a horizontal tube using the volume of fluid method

The inundation of the lower tubes in a tube bundle with condensate formed on the upper tubes is among the major causes of reduced condensation rate. Experimental methods can hardly be used to get detailed information on the inundation effect, since each factor that controls the condensation process should be considered individually. However, CFD modelling using direct interface-tracking methods is an effective tool for analyzing such processes. This paper reports the results of simulation of the saturated propane vapor condensation on the surface of a horizontal tube using the Volume of Fluid method with the modified Lee model. The study presents, for the first time, the characteristics of saturated vapor condensation including the effect of inundation predicted using a 3D model. The interphase surface and the distribution of instantaneous heat transfer coefficients over the surface of the inundated pipe are presented. It has been shown that increasing the temperature of the condensate flow can substantially affect the distribution of the heat transfer rate over the tube surface due to the formation of a thermal entrance region. These results may become a starting point for modelling condensation in a tube bundle that enjoys current interest in practice.

Toward the Usage of Deep Learning Surrogate Models in Ground Vehicle Aerodynamics

This study introduces a deep learning surrogate model designed to predict the evolution of the mean pressure coefficient on the back face of a Windsor body across a range of yaw angles from 2.5∘ to 10∘. Utilizing a variational autoencoder (VAE), the model effectively compresses snapshots of back pressure taken at yaw angles of 2.5∘, 5∘, and 10∘ into two latent vectors. These snapshots are derived from wall-modeled large eddy simulations (WMLESs) conducted at a Reynolds number of ReL=2.9×106. The frequencies that dominate the latent vectors correspond closely with those observed in both the drag’s temporal evolution and the dynamic mode decomposition. The projection of the mean pressure coefficient to the latent space yields an increasing linear evolution of the two latent variables with the yaw angle. The mean pressure coefficient distribution at a yaw angle of 7.5∘ is predicted with a mean error of e¯=3.13% when compared to the WMLESs results after obtaining the values of the latent space with linear interpolation.

Conceptual design and feasibility analysis of a heat pipe cooled cermet fuel space nuclear reactor for mars surface application

The compact, safe, light-weight and highly reliable Space Nuclear Reactor (SNR) with heat pipe cooling is an excellent candidate for the potential needs of Mars surface applications. This work proposed a heat pipe reactor concept design which can provide 1 MWth power for more than 8 years. Reactivity control is accomplished by 6 rotating control drums. Cermet fuel with dispersion granules characteristics adopted in this design is processed into prismatic-type tube-in-duct (TID) and composed of Mo-14 wt%Re matrix and highly enriched uranium nitride (UN) granules. Both heterogeneous and homogeneous models of Cermet fuel are evaluated by OpenMC code, indicating an extreme weak resonance self-shielding effect. Neutronics characteristics such as the effective multiplication factor, burnup depth, fuel temperature coefficient, neutron spectrum, reactivity control, neutron flux and power distribution are obtained. Drum stuck accidents and submersion criticality accidents are also analyzed. The designed reactor achieves a shutdown depth of −1521 pcm in the worst launch or reentry accident scenario considered without relying on the reactivity control device. The arrangement forms and content of Spectral Shift Absorber (SSAs) that affect the safety worth are also analyzed. Furthermore, thermal analysis is performed by Fluent and the maximum temperature is lower than 1570K during normal operation. The maximum temperature reaches 1805K and core has sufficient margin to respond to a single point failure of the heat pipe. Overall, the scheme preliminarily satisfies neutronics, thermal and safety requirements.

Modelling flame-to-fuel heat transfer by deep learning and fire images

In numerical fire simulations, the calculation of thermal feedback from the flame to the solid and liquid fuel surface plays a critical role as it connects the fundamental gas-phase flame burning and condensed-phase fuel gasification. However, it is a computationally intensive task in CFD fire modelling methods because of the requirement of a high-resolution grid for calculating the interface heat transfer. This paper proposed a real-time prediction of the flame-to-fuel heat transfer by using simulated flame images and a computer-vision deep learning method. Different methanol pool fires were selected to produce the image database for training the model. As the pool diameters increase from 20 to 40 cm, the dominant flame-to-fuel heat transfer shifts from convection to radiation. Results show that the proposed AI algorithm trained by flame images can predict both the convective and radiative heat flux distributions on the condensed fuel surface with a relative error below 20%, based on the input of real-time flame morphology that can be captured by a larger grid size. Regardless of growing or decaying fires or puffing flames induced by buoyancy, this method can further predict the non-uniform distribution of heat transfer coefficient on the interface rather than using empirical correlations. This work demonstrates the use of AI and computer vision in accelerating numerical fire simulation, which helps simulate complex fire behaviours with simpler models and smaller computational costs. Highlights A total framework between AI model and fire simulation software is designed to further enhance the reliability of AI-based fire simulations. A standard pool fire simulation database is built using numerical model recommend by the IAFSS Computation Group. A deep learning model is developed to predict both the convective and radiative heat flux distributions on the condensed fuel surface using numerical images database. The demonstration showcases the application of AI and computer vision to accelerate numerical fire simulation.

Stochastic thermodynamics of Brownian motion in temperature gradient

We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction coefficient, and steady state distribution, all of which are experimentally measurable. We then study the associated stochastic thermodynamics theory. We analyze the excess entropy production both at trajectory level and at ensemble level, and derive the Clausius inequality as well as the transient fluctuation theorem (FT). We also use molecular dynamics to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT. Remarkably we find that the FT remains valid even in the under-damped regime. We explain the possible mechanism underlying this surprising result.

Energy Absorption Characteristic of Biomimetic Gradient Hierarchical Multicellular Tubes Under Axial Impact

This paper introduces a biomimetic gradient hierarchical multicellular structure consisting of two tree-like fractal variants: one based on vertex connections (HCV) and the other based on wall connections (HCW). We investigate their mechanical behavior and deformation through numerical simulations. Our findings reveal that, irrespective of whether they have the same wall thickness or mass, second-order and third-order structures exhibit superior energy absorption capacity (EA) and crushing force efficiency (CFE) compared to first-order structures, resulting in significantly enhanced crashworthiness performance. In the case of HCV structures with identical wall thickness, the third-order structure outperforms the first-order structure by 79.73% in specific energy absorption (SEA) and by 38.51% in CFE. Similarly, for HCW structures, the third-order variant surpasses the first-order one by 45.57% in SEA and 28.39% in CFE. We also conduct a parametric study, exploring the influence of inner circle diameter, fractal coefficient, and fractal angle on the crashworthiness of biomimetic gradient hierarchical multicellular structures. We identify the optimal fractal coefficient and inner diameter distribution range for HCV when the fractal angle is 60°. Lastly, we compare these structures with traditional multicellular tubes, demonstrating that biomimetic gradient hierarchical multicellular tubes achieve up to 50.34% higher SEA and 55.13% higher CFE. The results of this study offer valuable design insights for developing lightweight and efficient energy-absorbing structures.

Static analysis of functionally graded porous beam-column frames by the complementary functions method

In this paper, an efficient and accurate numerical approach is implemented to examine the static behavior of Functionally Graded Porous (FGP) planar frames for the first time. The symmetric material constitutive relationship (SMCR), monotonic material constitutive relationships (MMCR), and uniform material constitutive relationship (UMCR) models are used to define the gradation of porosity along the thickness direction. The effects of porosity coefficient and material porosity distribution type on the static behavior of the FGP frames are investigated in detail. A direct relation between porosity coefficient and nodal deformations is observed.The effect of shear deformation is considered in the governing equations based on the Timoshenko Beam Theory (TBT). Within the scope of the presented procedure, fifth-order Runge-Kutta (RK5) algorithm is applied in the solution of the initial value problems. Imposing the rigidity matrix-based Complementary Functions Method (CFM) on the static analysis of the FGP planar frames is the novelty of this research. The results of the suggested approach are verified with the those of the finite element method (FEM), and those of the available literature. It has been carried out that type of the porosity distribution and porosity gradient index have an important impact on the response of FGP planar frames. By increasing the porosity coefficient, the displacement values of the frames made of UMCR and MMCR porosity distribution are affected more than those of the UMCR distributions. It can be noted that the SMCR can be preferred for designing the FGP beam-column structure as the minimum deformation values are obtained.