Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Microstructure and thermal properties of dissimilar M300–CuCr1Zr alloys by multi-material laser-based powder bed fusion

Multi-material laser-based powder bed fusion (PBF-LB) allows manufacturing of parts with 3-dimensional gradient and additional functionality in a single step. This research focuses on the combination of thermally-conductive CuCr1Zr with hard M300 tool steel.Two interface configurations of M300 on CuCr1Zr and CuCr1Zr on M300 were investigated. Ultra-fine grains form at the interface due to the low mutual solubility of Cu and steel. The material mixing zone size is dependent on the configurations and tunable in the range of0.1–0.3 mm by introducing a separate set of parameters for the interface layers. Microcracks and pores mainly occur in the transition zone.Regardless of these defects, the thermal diffusivity of bimetallic parts with 50vol% of CuCr1Zr significantly increases by 70%–150%compared to pure M300. The thermal diffusivity of CuCr1Zr and the hardness of M300 steel can be enhanced simultaneously by applying the aging heat treatment.

A 2D Staggered Multi-Material ALE Code Using MOF Interface Reconstruction

Hydrocodes are necessary numerical tools in the fields of implosion and high-velocity impact,which often involve large deformations with changing-topology interfaces.It is very difficult for Lagrangian or Simplified Arbitrary Lagrangian-Eulerian(SALE)codes to tackle these kinds of large-deformation problems,so a stag-gered Multi-Material ALE(MMALE)code is developed in this paper,which is the explicit time-marching Lagrange plus remap type.We use the Moment Of Fluid(MOF)method to reconstruct the interfaces of multi-material cells and present an adaptive bisection method to search for the global minimum value of the nonlinear objective function.To keep the Lagrangian computations as long as possible,we develop a ro-bust rezoning method named as Combined Rezoning Method(CRM)to generate the convex,smooth grids for the large-deformation domain.Regarding the staggered remap phase,we use two methods to remap the variables of Lagrangian mesh to the rezoned one.One is the first-order intersection-based remapping method that doesn’t limit the distances between the rezoned and Lagrangian meshes,so it can be used in the applications of wide scope.The other one is the conservative second-order flux-based remapping method developed by Kucharika and Shashkov[22]that requires the rezoned element to locate in its adjacent old elements.Numerical results of triple point problem show that the result of first-order remapping method using ALE computations is gradually convergent to that of second-order remapping method using Eulerian computations with the decrease of rezoning,thereby telling us that MMALE computations should be performed as few as possible to reduce the errors of the interface reconstruction and the remapping.Numerical results provide a clear evidence of the robustness and the accuracy of this MMALE scheme,and that our MMALE code is powerful for the large-deformation problems.

Simultaneous multi-material embedded printing for 3D heterogeneous structures

In order to mimic the natural heterogeneity of native tissue and provide a better microenvironment for cell culturing,multi-material bioprinting has become a common solution to construct tissue models in vitro.With the embedded printing method,complex 3D structure can be printed using soft biomaterials with reasonable shape fidelity.However,the current sequential multi-material embedded printing method faces a major challenge,which is the inevitable trade-off between the printed structural integrity and printing precision.Here,we propose a simultaneous multi-material embedded printing method.With this method,we can easily print firmly attached and high-precision multilayer structures.With multiple individually controlled nozzles,different biomaterials can be precisely deposited into a single crevasse,minimizing uncontrolled squeezing and guarantees no contamination of embedding medium within the structure.We analyse the dynamics of the extruded bioink in the embedding medium both analytically and experimentally,and quantitatively evaluate the effects of printing parameters including printing speed and rheology of embedding medium,on the 3D morphology of the printed filament.We demonstrate the printing of double-layer thin-walled structures,each layer less than 200μm,as well as intestine and liver models with 5%gelatin methacryloyl that are crosslinked and extracted from the embedding medium without significant impairment or delamination.The peeling test further proves that the proposed method offers better structural integrity than conventional sequential printing methods.The proposed simultaneous multi-material embedded printing method can serve as a powerful tool to support the complex heterogeneous structure fabrication and open unique prospects for personalized medicine.

Evaluation of different crosslinking methods in altering the properties of extrusion-printed chitosan-basedmulti-material hydrogel composites

Three-dimensional printing technologies exhibit tremendous potential in the advancing fields of tissue engineering and regenerative medicine due to the precise spatial control over depositing the biomaterial.Despite their widespread utilization and numerous advantages,the development of suitable novel biomaterials for extrusion-based 3D printing of scaffolds that support cell attachment,proliferation,and vascularization remains a challenge.Multi-material composite hydrogels present incredible potential in this field.Thus,in this work,a multi-material composite hydrogel with a promising formulation of chitosan/gelatin functionalized with egg white was developed,which provides good printability and shape fidelity.In addition,a series of comparative analyses of different crosslinking agents and processes based on tripolyphosphate(TPP),genipin(GP),and glutaraldehyde(GTA)were investigated and compared to select the ideal crosslinking strategy to enhance the physicochemical and biological properties of the fabricated scaffolds.All of the results indicate that the composite hydrogel and the resulting scaffolds utilizing TPP crosslinking have great potential in tissue engineering,especially for supporting neo-vessel growth into the scaffold and promoting angiogenesis within engineered tissues.

Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

This study establishes amultiscale andmulti-material topology optimization model for thermoelastic lattice structures(TLSs)consideringmechanical and thermal loading based on the ExtendedMultiscale Finite ElementMethod(EMsFEM).The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint,respectively.The Solid Isotropic Material with Penalization(SIMP)interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure.The modified volume preserving Heaviside function(VPHF)is utilized to obtain a clear 0/1 material of truss microstructure.Compared with the classic topology optimization of single-material TLSs,multi-material topology optimization can get a better structural design of the TLS.The effects of temperatures,size factor,and mass fraction on optimization results have been presented and discussed in the numerical examples.

基于流固耦合ALE理论的船桥碰撞试验和分析

以船桥碰撞为研究对象,对此现象进行了试验和数值模拟研究,基于流固耦合ALE(Arbitrary Lagrangian–Eulerian)分析理论,采用数值模拟的方法,对不同质量不同速度下的小球撞击桥墩进行了研究,小球撞击桥墩的撞击力合力与小球的质量和速度成正相关,撞击力时程曲线存在多个尖刺,且撞击过程为多次碰撞;试验合力峰值和数值模拟合力峰值的相关误差小于10%,证明了流固耦合ALE数值模拟的可行性及正确性。

基于梯度提升树的ALE图特征解释效果分析

理解特征效应有助于机器学习模型进行调优与预测结果解读,累积局部效应(ALE)图是一种独立于模型的黑盒预测特征解释新方法,文章基于梯度提升树分析其稳定性与解释效果。首先,推导输入特征服从联合高斯分布的累积局部效应与偏相关函数,分析特征间相关性的影响;其次,对估计的稳定性与特征效应解释的效果进行模拟研究,并提出将纵坐标统一设置用于特征选择参考;最后,针对实际数据集给出ALE图的应用实例,并将特征解释结论与传统统计模型显著性分析进行对比。

基于ALE算法的高速水射流对船体表面冲击特性研究

为探究水射流清洗附着物对船体表面的损伤影响,基于ALE算法研究了不同入射角θ和不同流速v冲击船体表面过程中射流的冲击压力特征和应力特征。结果显示,随着入射角θ增大,靶件所受冲击压力会出现水锤压力与滞止压力阶段。高压水射流动能在适当入射角θ增加,入射角过大(θ=20°)反而会使其降低。以一定入射角θ冲击靶体时,由于剪切效应加强靶体表面与内部应力分布比垂直冲击时更复杂,得出对船体表面材料影响最小的参数组合和最大主应力与射流参数入射角和速度的拟合公式。研究结果对水射流清洗船体表面附着物的应用具有较好的理论意义与实际应用价值。

强夯置换的ALE法仿真与夯击参数研究

为揭示强夯置换动态变形特征与地基加固变化规律,将基于有限差分原理的ALE法引入强夯置换仿真分析,建立三维ALE法强夯置换动力分析模型,模拟单次夯击与连续强夯置换地基加固过程,分析不同夯击参数对高能级强夯置换加固效果影响并应用于工程实例。结果表明:ALE法可描述碎石填料夯击流动变形,实现连续强夯置换仿真;回填碎石对夯击能吸收作用可削弱夯击地基加固效果,故采取“少填多夯”方式较合理;针对8000 kN·m高能级强夯置换,采用2.5 m夯锤直径有利于地基加固深度向下发展;夯锤高径比在0.3~0.5时能充分利用夯击能形成承载力均衡的复合地基结构,研究结论可为夯击参数比选提供依据。

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

ALE方法评估黏土场地的自升式平台桩靴承载力

为研究自升式平台桩靴在黏土场地中的极限承载力,建立Abaqus桩靴-土模型,采用任意拉格朗日-欧拉(Arbitrary Lagrangian-Eulerian,ALE)方法对桩靴的贯入过程进行模拟,提出大值法、中值法、小值法等3种数据处理方法,并拟合桩靴承载力估算公式。将模拟计算结果与SNAME规范公式计算结果进行对比分析,对比结果证明ALE方法模拟桩靴贯入的可行性。为提高工程的安全性,提出对SNAME公式计算结果进行折减的具体公式,以使其与ALE小值法处理结果更吻合。

基于ALE算法的水射流破土特性

为探究水射流破土过程中射流参数对破土特性的影响,通过拉格朗日-欧拉方法(Arbitrary Lagrange-Euler, ALE)流固耦合算法建立了淹没状态下水射流破土的数值模型,开展水射流破土的室内试验验证了数值计算结果的准确性。基于数值模型分析不同射流速度和靶距下冲蚀深度与体积的变化特征,探讨射流参数对破土特性的影响机制。研究结果表明:水射流破土形成的冲蚀深度随着射流速度的增大而逐渐变大,且随着射流时间的增加会呈现线性增长、缓慢稳定增长和稳定三个阶段;靶距越大冲蚀深度越小,但冲蚀体积受射流速度的影响较大,在低速时冲蚀体积随靶距的减小而增大,而在高速时冲蚀体积则会先减小后增大再减小;基于试验结果分析敏感性可知射流速度对冲蚀深度与体积的影响程度要大于靶距。

STUDY ON DESIGN TECHNIQUES OF A LONG LIFE HOT FORGING DIE WITH MULTI-MATERIALS

A new design technique for the long life hot forging die has been proposed. By finite element analysis, the reason .for the failure of hot forging die was analyzed and it was concluded that thermal stress is the main reason for the failure of hot forging die. Based on this conclusion, the whole hot forging die was divided into the substrate part and the heat-resistant part according to the thermal stress distribution. Moreover, the heat-resistant part was further subdivided into more zones and the material of each zone was reasonably selected to ensure that the hot forging die can work in an elastic state. When compared with the existing techniques, this design can greatly increase the service life because the use of multi-materials can alleviate the thermal stress in hot forging die.

Coating process of multi-material composite sand mold 3D printing

Sand mold 3 D printing technology is an advanced manufacturing technology which has great flexible manufacturing ability. A multi-material composite sand mold can control the temperature field of metallic parts during the pouring process, while the current sand mold 3 D printing technology can only fabricate a single material sand mold. The casting temperature field can not be adjusted by using single sand mold material with isotropous heat exchange ability during the pouring process. In this work, a kind of novel coating device was designed. Multi-material composite sand molds could be manufactured using the coating device according to the casting process demands of the final parts. The influences of curing agent content, coating velocity and scraper shape on compactness and surface roughness of the sand layer(silica sand and zircon sand) were studied. The shapes and sizes of transition intervals of two kinds of sand granules were also tested. The results show that, with the increase of the added volume of curing agent, the compactness of sand layer reduces and the surface roughness value rises. With the increase of the velocity of the coating device, the compactness of sand layer reduces and the surface roughness value rises similarly. In addition, the scraper with a dip angle of 72 degrees could increase the compactness value of the sand layer. The criteria of quality parmeters of the coating procedure are obtained. That is, the surface roughness(δ) of sand layer should be equal to or lesser than half of main size of the sand particles(Dm). The parameter H of the coating device which is the distance between the base of hopper and the surface of sand layer impacts the size of transition zone. The width of the transition zone is in direct proportion to the parameter H, qualitatively. Through the optimization of the coating device, high quality of multi-material sand layers can be obtained. This will provide a solution in manufacturing the multi-material composite sand mold.

A robust algorithm for moving interface of multi-material fluids based on Riemann solutions

In the paper, the numerical simulation of interface problems for multiple material fluids is studied. The level set function is designed to capture the location of the material interface. For multi-dimensional and multi-material fluids, the modified ghost fluid method needs a Riemann solution to renew the variable states near the interface. Here we present a new convenient and effective algorithm for solving the Riemann problem in the normal direction. The extrapolated variables are populated by Taylor series expansions in the direction. The anti-diffusive high order WENO difference scheme with the limiter is adopted for the numerical simulation. Finally we implement a series of numerical experiments of multi-material flows. The obtained results are satisfying, compared to those by other methods.

Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties.To characterize the random-field uncertainties with a reduced set of random variables,the Karhunen-Lo`eve(K-L)expansion is adopted.The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization.Under dividing the design domain,the volume fraction of each preset gradient layer is extracted.Based on the ordered solid isotropic microstructure with penalization(Ordered-SIMP),a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer.The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions.Then,the method of moving asymptotes(MMA)is introduced to iteratively update the design variables.Several numerical examples are presented to verify the validity and applicability of the proposed method.The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions,and robust design structures are more stable than that indicated by the deterministic results.

CONSERVATION LAW AND APPLICATION OF J- INTEGRAL IN MULTI-MATERIALS

The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of Ⅰ-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.

Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model

This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint.A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost.Different from the traditional material penalization scheme,the algorithm is established on the ordered ersatz material model,which linearly interpolates Young’s modulus for relaxed design variables.To achieve a multi-material design,the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values.For the convergent element-based solution,the multiple level-set functions are constructed to tentatively extract the smooth interface between two adjacent materials.Some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed algorithm and the possible advantage of the multi-material designs over the traditional solid-void designs.

Abnormal interfacial bonding mechanisms of multi-material additive-manufactured tungsten-stainless steel sandwich structure

Tungsten(W)and stainless steel(SS)are well known for the high melting point and good corrosion resistance respectively.Bimetallic W-SS structures would offer potential applications in extreme environments.In this study,a SS→W→SS sandwich structure is fabricated via a special laser powder bed fusion(LPBF)method based on an ultrasonic-assisted powder deposition mechanism.Material characterization of the SS→W interface and W→SS interface was conducted,including microstructure,element distribution,phase distribution,and nano-hardness.A coupled modelling method,combining computational fluid dynamics modelling with discrete element method,simulated the melt pool dynamics and solidification at the material interfaces.The study shows that the interface bonding of SS→W(SS printed on W)is the combined effect of solid-state diffusion with different elemental diffusion rates and grain boundary diffusion.The keyhole mode of the melt pool at the W→SS(W printed on SS)interface makes the pre-printed SS layers repeatedly remelted,causing the liquid W to flow into the sub-surface of the pre-printed SS through the keyhole cavities realizing the bonding of the W→SS interface.The above interfacial bonding behaviours are significantly different from the previously reported bonding mechanism based on the melt pool convection during multiple material LPBF.The abnormal material interfacial bonding behaviours are reported for the first time.