A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Functionally graded structure of a nitride-strengthened Mg_(2)Si-based hybrid composite

The ex-situ incorporation of the secondary SiC reinforcement,along with the in-situ incorporation of the tertiary and quaternary Mg_(3)N_(2) and Si_(3)N_(4) phases,in the primary matrix of Mg_(2)Si is employed in order to provide ultimate wear resistance based on the laser-irradiation-induced inclusion of N_(2) gas during laser powder bed fusion.This is substantialized based on both the thermal diffusion-and chemical reactionbased metallurgy of the Mg_(2)Si–SiC/nitride hybrid composite.This study also proposes a functional platform for systematically modulating a functionally graded structure and modeling build-direction-dependent architectonics during additive manufacturing.This strategy enables the development of a compositional gradient from the center to the edge of each melt pool of the Mg_(2)Si–SiC/nitride hybrid composite.Consequently,the coefficient of friction of the hybrid composite exhibits a 309.3%decrease to–1.67 compared to–0.54 for the conventional nonreinforced Mg_(2)Si structure,while the tensile strength exhibits a 171.3%increase to 831.5 MPa compared to 485.3 MPa for the conventional structure.This outstanding mechanical behavior is due to the(1)the complementary and synergistic reinforcement effects of the SiC and nitride compounds,each of which possesses an intrinsically high hardness,and(2)the strong adhesion of these compounds to the Mg_(2)Si matrix despite their small sizes and low concentrations.

Tree‑Inspired Structurally Graded Aerogel with Synergistic Water,Salt,and Thermal Transport for High‑Salinity Solar‑Powered Evaporation

Solar-powered interfacial evaporation is an energy-efficient solution for water scarcity.It requires solar absorbers to facilitate upward water transport and limit the heat to the surface for efficient evaporation.Furthermore,downward salt ion transport is also desired to prevent salt accumulation.However,achieving simultaneously fast water uptake,downward salt transport,and heat localization is challenging due to highly coupled water,mass,and thermal transport.Here,we develop a structurally graded aerogel inspired by tree transport systems to collectively optimize water,salt,and thermal transport.The arched aerogel features root-like,fan-shaped microchannels for rapid water uptake and downward salt diffusion,and horizontally aligned pores near the surface for heat localization through maximizing solar absorption and minimizing conductive heat loss.These structural characteristics gave rise to consistent evaporation rates of 2.09 kg m^(-2) h^(-1) under one-sun illumination in a 3.5 wt%NaCl solution for 7 days without degradation.Even in a high-salinity solution of 20 wt%NaCl,the evaporation rates maintained stable at 1.94 kg m^(-2) h^(-1) for 8 h without salt crystal formation.This work offers a novel microstructural design to address the complex interplay of water,salt,and thermal transport.

Microstructure of TA2/TA15 graded structural material by laser additive manufacturing process

TA2/TA15 graded structural material（GSM） was fabricated by the laser additive manufacturing（LAM） process. The chemical composition, microstructure and micro-hardness of the as-deposited GSM were investigated. The results show that the TA2 part of exhibiting near-equiaxed grains was Widmanst？tten α-laths microstructure. The TA15 part containing large columnar grains was fine basket-weave microstructure. The graded zone was divided into four deposited layers with 3000 μm in thickness. As the distance from the TA2 part increases, the alloy element contents and the β phase volume fraction increase, the α phase volume fraction decreases and the microstructure shows the evolution from Widmanst？tten α-laths to basket-weave α-laths gradually. The micro-hardness increases from the TA2 part to the TA15 part due to the solid solution strengthening and grain boundary strengthening.

Effect of Different Spacing on Structure of Fluecure Tobacco Leaf Grade

[Objective] This study was conducted to investigate the effects of different plant spacing on tobacco grade structure, growth stages, agronomic traits, yield and chemical composition under fixed row spacing. [Method] Under fixed row spacing （120 cm）, 4 treatments were designed （40, 50, 60 and 45 cm）. The growth stages, agronomic traits, economic traits and chemical composition of flue-cured tobacco leaves were compared and analyzed. [Result] with the increase of plant spacing, there were no significant differences in the emergence time of growth stages be- tween different treatment groups before resettling stage, and the resettling stage ap- peared 1-2 d in advance. At different tobacco growth stages, the changing trends of tobacco agronomic traits with the change of plant spacing were different. [Conclusion] With the increase of plant spacing, the planting density of tobacco de- creased, and the nicotine content increased; and the yield of tobacco decreased continuously, while the quality was improved, but when the plant spacing was im- proved to certain degree, the quality of tobacco also decreased, and at the plant spacing of 50 cm, the output value of tobacco was the highest.

Microstructure and mechanical properties of TA15/TC11 graded structural material by wire arc additive manufacturing process

A graded structural material(GSM)with a material transition from TA15 to TC11 was fabricated by wire arc additive manufacturing(WAAM)method.The grain morphology,chemical composition,microstructure and mechanical properties of the as-deposited GSM were all characterized to investigate their variations along the deposition direction.The results indicate that from TA15 to TC11,the grain size decreases and a transition from columnar grains to equiaxed grains occurs.The content of alloy element alters greatly within a short distance,and the width of the mutation zone is 800μm.Both TA15 and TC11 regions exhibit basketweave microstructure withα-phase andβ-phase.However,during the transition from TA15 to TC11,theα-lath becomes fine,which leads to an increase in microhardness.The tensile test shows that the bonding strength at the interface is higher than the longitudinal strength of TA15,and the lateral elongation at the interface is higher than that of TA15 and TC11.

Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

Functional graded cellular structure(FGCS)usually shows superiormechanical behaviorwith lowdensity and high stiffness.With the development of additivemanufacturing,functional graded cellular structure gains its popularity in industries.In this paper,a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method(PLSM)under local volume constraints(LVC).In this method,a subdomain level set function is defined,parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective.Additionally,the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional constraint.Furthermore,the local volume constraint for each subdomain is applied by virtue of the augmented Lagrange multiplier method.Finally,several numerical examples are given to verify the correctness and effectiveness of the proposed approach in designing the functionally graded cellular structure.From the optimized results,it is also found that the number of local volume constraints has little influence on the convergence speed of the developed approach.

Effective Pyroelectric Coefficient and Polarization Offset of Compositionally Step-like Graded Ferroelectric Structures

In this paper, the effective pyroelectric coefficient and polarization offset of the compositionally step-like graded multilayer ferroelectric structures have been studied by use of the first-principles approach. It is exhibited that the dielectric gradient has a nontrivial influence on the effective pyroelectric coefficient, but has a little influence on the polarization offset; and the polarization gradient plays an important role in the abnormal hysteresis loop phenomenon of the co.mpositionally step-like graded ferroelectric structures. Moreover, the origin of the polarization offset is explored,which can be attributed to the polarization gradient in the compositionally step-like graded structure.

Discussion on "Thermomagnetic viscoelastic responses in a functionally graded hollow structure"

Allam and Tantawy [1] presented an analytical solu- tion for stress distribution and perturbations of the magnetic field vector in FGM hollow structures made from viscoelas- tic composite materials .While studying this article, the dis- cusser noticed a confusion in regarding Maxwell＇s electro- magnetic stress expression

Simultaneous optimization and control for polypropylene grade transition with two-layer hierarchical structure

In this paper,a two-layer hierarchical structure of optimization and control for polypropylene grade transition was raised to overcome process uncertain disturbances that led to the large deviation between the open-loop reference trajectory and the actual process.In the upper layer,the variant time scale based control vector parametric methods(VTS-CVP) was used for dynamic optimization of transition reference trajectory,while nonlinear model predictive controller(NMPC) based on closed-loop subspace and piece-wise linear(SSARX-PWL) model in the lower layer was tracking to the reference trajectory from the upper layer for overcoming high-frequency disturbances.Besides,mechanism about trajectory deviation detection and optimal trajectory updating online were introduced to ensure a smooth transition for the entire process.The proposed method was validated with the real data from an industrial double-loop propylene polymerization reaction process with developed dynamic mechanism mathematical model.

Bonding strength of graded anti-corrosive coatings of fluoroethylenepropylene (FEP)/polyphenylene sulfide (PPS)

Fluororesin-based anti-corrosive coatings including graded FEP/PPS were prepared on carbon steel by melt powder coating, the bonding strength of all coating systems was determined by the pull-off test. It is found that the poor adhesion of fluororesin coatings to metallic substrates is improved obviously by the graded coating structure of FEP/PPS, and the bonding strength reaches up to 11.8 MPa for the five-layer system. Examination by electron probe microanalysis （EPMA） verifies that the distribution of main components is graded in the five-layer system, which is responsible for the enhancement of the interfacial bonding.

Mechanical properties and shape memory behavior of 4D printed functionally graded cellular structures

The properties of functionally graded(FG) cellular structures vary spatially, and the varying properties can meet the requirements of different working environments. In this study, we fabricated FG cellular structures with shape memory effect by 4D printing and evaluated the compressive performance and shape memory behavior of these structures with temperature through experimental analysis and finite element simulations. The results show that the maximum energy absorption gradually decreases but the compressive modulus gradually increases with increasing gradient parameters. Moreover, the finite element simulations also show that the compressive deformation mode of the structure shifts from uniform to non-uniform deformation with increasing gradient parameters. The compressive modulus and compressive strength of 4D printed FG structures decrease with increasing temperature due to the influence of the shape memory polymer, and they exhibit outstanding shape recovery capability under high-temperature stimulus. The proposed 4D printed FG structures with such responsiveness to stimulus shed light on the design of intelligent energy-absorbing devices that meet specific functional requirements.

Laboratory-scale investigation of the material distribution characteristics of landslide dams in U-shaped valleys

Material distribution characteristics during sliding and depositing is particularly significative to investigate the internal structure and spatial variation of landslide dams,which are fundamentally determining the mechanical and hydraulic behavior and the susceptibility to cause dam failure.However,limited by longevity shortages and special geographic environments,the material distribution characteristics and their formation mechanisms are difficult to observe in the field.Therefore,an experimental apparatus modeling a landslide dam was developed in this paper,designing three sampling methods with two valley states.The internal deposit characteristics,void ratio variation and relative content of the particle size range(PSR)were analyzed,and the mechanics of deposit structure were also delicately ascertained.The results indicate that granular material deposited in valley shows a structure of inverse grain size accumulation in both vertical and horizontal directions,exhibiting spatial variability of particle gradation and void ratio.The characteristic PSR decreases from 22-30 mm in the two-dimensional state to 10-14 mm in the threedimensional state.Vibration excitation and vibration sieve are the intrinsic mechanisms of granular flow segregation,intrinsically inducing the formation of inverse grading deposit structures.Consequently,spatial variability in size is mainly trig gered by segregation,whereas coarse particle content and deposition boundaries merely exacerbate the difference degree.

Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method

This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.

A New BEM for Fractional Nonlinear Generalized Porothermoelastic Wave Propagation Problems

The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependent functionally graded anisotropic(FGA)structures.The system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity,fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous structures.Therefore,an efficient boundary element method(BEM)has been proposed to overcome this difficulty,where,the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the Cartesian transformation method(CTM).The generalized modified shift-splitting(GMSS)iteration method was used to solve the linear systems resulting from BEM,also,GMSS reduces the iterations number and CPU execution time of computations.The numerical findings show the effects of fractional order parameter,anisotropy and functionally graded material on the nonlinear porothermoelastic stress waves.The numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.

Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics

In this paper,a semi-discrete model based on peridynamics(PD)for engineered cementitious composites(ECCs)is applied to simulate the fracture behavior of functionally graded ECC(FGECC)beams.This is a new application of PD in ECC.Prior to simulating the crack behavior,the convergence of the PD model for ECC is discussed and the appropriate horizon size 5 and nonlocal ratio m are obtained,i.e.,S=1.6 mm and m=4.In addition,when the bond strain exceeds the elastic limit,a damage variable is introduced into the model,and the model is validated using a simple numerical algorithm.Finally,the dynamic fracture behavior of a two-dimensional FGECC beam under four-point bending is investigated,and the effect of the initial crack location on the fracture behavior is analyzed.Simulation results show that the initial crack location can affect the crack propagation pattern,thereby enabling one to understand the dynamic fracture behavior of ECC structures and guide the engineering practice.

Design and preparation of gradient graphite/cermets self-lubricating composites

Based on the functionally graded materials （FGMs） design concept, the laminated-graded graphite/cermets self-lubricating composite was prepared to achieve the integration of mechanical prop- erties and lubrication performance of the cermet. The effects of the layer number and thickness of graded structure on residual stresses in the gradient composites were investigated by finite element method （FEM）. From the FEM analyses, the optimal gradient structure design was obtained correspond- ing to the following parameters： the number of graded layers n = 2 and the thickness of graded structure t = I ram. According to the optimum design, a graded graphite/cermets self-lubricating material with two layers was fabricated by a typical powder metallurgy technique. Compared with the homogenous graphite/cermets composite, the surface hardness and indentation fracture toughness of graded compos- ite were increased by approximately 15.9% and 6.3%, respectively. The results of X-ray diffraction （XRD） stress measurement identified the existence of residual compressive stress on the surface of graded com- posite. Additionally, the friction and wear tests revealed that the wear resistance of the graphite/cermets self-lubricating composite was improved significantly via the graded structural design, whereas the coefficient of friction changed slightly.

Central Place Theory and Distribution of Post Offices in Cities

The feasibility of application of the Central Place Theory in the distribution of post offices in cities is analysed, the grade scale structure and space distribution structure Shijiazhauang of post offices in city are studied, the research results prove the actual value of the Central Place Theory, and the suggestion of adjustment in the space distribution Shijiazhuang of post offices in city is put forward.