高承载梯度分层点阵结构的拓扑优化设计方法

随着增材制造技术的迅速发展, 点阵结构由于其高比强度、高比刚度等优异力学性能受到广泛关注, 但其单胞分布设计大多基于均布式假设, 导致其承载能力相对较差. 基于拓扑优化技术提出了一种梯度分层的点阵结构设计方法. 首先, 基于水平集函数建立点阵单胞几何构型的显式描述模型, 引入形状插值技术实现点阵单胞的梯度构型生成; 其次, 构建基于Kriging的梯度点阵单胞宏观等效力学属性预测模型, 建立宏观有限单元密度与微观点阵单胞等效力学属性的内在联系; 然后, 以点阵结构刚度最大为优化目标, 结构材料用量和力学控制方程为约束条件, 构建点阵结构的梯度分层拓扑优化模型, 并采用OC算法进行数值求解. 算例结果表明, 所提方法可实现点阵结构的最优梯度分层设计, 充分提高了点阵结构的承载性能, 同时可保证不同梯度点阵单胞之间的几何连续性. 最后, 开展梯度分层点阵结构与传统均匀点阵结构和线性梯度点阵结构的准静态压缩仿真分析, 仿真结果表明, 与传统均匀点阵结构和线性梯度点阵结构相比, 梯度分层点阵结构的承载能力明显提高. 研究结果可为高承载点阵结构设计提供理论参考.      

Characterization of Polyurethane Rubber at High Deformation Rates

Polyurethane rubber materials have widespread usage in large-deformation energy absorption and dissipation applications. Accurate design modeling with these materials requires an appropriate constitutive material model that accounts for both static (low strain rate) and dynamic (high strain rate) responses. A common modeling approach is the use of hyper-viscoelastic formulations, which couple quasi-static hyperelastic with dynamic viscoelastic responses and describe the material response over a range of deformation rates. In this work the effectiveness of two models, the Modified Quasi-Linear Viscoelastic and Non-Linear Hyper-Viscoelastic, are investigated to describe the high-rate behaviour of two different grades of polyurethane rubber. From quasi-static, uniaxial compression tests, a Rivlin hyperelastic formulation was found to describe the low-rate response well. High-rate, uniaxial compressions test were performed using a Polymeric Split Hopkinson Pressure Bar (PSHPB), supported by high-speed photography. In general, it was found that the Modified Quasi-Linear Viscoelastic model did not fit the experimental data well due to its limited non-linear terms, while the Non-Linear Hyper-Viscoelastic provided very good agreement.     

泡沫材料准静态力学性能实验研究

利用INSTRON-1185型万能材料试验机在准静态加载环境下对不同密度的聚氨酯泡沫的抗压、抗拉及抗弯性能进行了较系统的实验研究,分析了聚氨酯泡沫材料的力学性能及吸能特性随表观密度的变化规律.研究表明,聚氨醋泡沫材料的杭压性能优于其杭拉性能,该材料具有良好的吸能特性,且其吸能特性随密度的增大而提高.     

Nanofluidic energy absorption system: A review

基于纳米流控行为设计的新一代能量吸收耗散系统（nanofluidic en-ergy absorption system,NEAS）将会比传统吸能材料具有更高的能量吸收密度,而且还可以重复使用,特别是在小体积应用环境下具有显著的优势.本文从实验和计算模拟两方面综述了目前关于NEAS能量吸收耗散行为的最新研究进展,其中实验研究主要包括准静态压缩和动态压缩测试,计算模拟研究主要是采用基于经验势的分子动力学模拟方法.通过准静态压缩实验,可以测量NEAS模型的载荷–位移关系曲线,从而获得NEAS模型的临界渗透压强,了解卸载后系统是否能够恢复到加载前的状态（即是否可以重复使用）,并通过载荷–位移关系曲线下面积估算NEAS模型的吸能密度;通过动态压缩实验可以测量NEAS模型对脉冲载荷的缓冲保护作用,主要体现为降低脉冲载荷幅值和扩展脉冲宽度.计算模型研究可以明确给出NEAS对外载荷的微观响应,从而可以准确了解NEAS的能量吸收耗散机制以及吸能密度的主要影响因素.本研究可以帮助我们全面了解NEAS的研究进展,为NEAS的设计与优化提供重要指导.     

纳米流控能量吸收耗散系统

基于纳米流控行为设计的新一代能量吸收耗散系统(nanofluidic en-ergy absorption system,NEAS)将会比传统吸能材料具有更高的能量吸收密度,而且还可以重复使用,特别是在小体积应用环境下具有显著的优势.本文从实验和计算模拟两方面综述了目前关于NEAS能量吸收耗散行为的最新研究进展,其中实验研究主要包括准静态压缩和动态压缩测试,计算模拟研究主要是采用基于经验势的分于动力学模拟方法.通过准静态压缩实验,可以测量NEAS模型的载荷–位移关系曲线,从而获得NEAS模型的临界渗透压强,了解卸载后系统是否能够恢复到加载前的状态(即是否可以重复使用),井通过载荷–位移关系曲线下面积估算NEAS模型的吸能密度;通过动态压缩实验可以测量NEAS模型对脉冲载荷的缓冲保护作用,主要体现为降低脉冲载荷幅值和扩展脉冲宽度.计算模型研究可以明确给出NEAS对外载荷的微观响应,从而可以准确了解NEAS的能量吸收耗散机制以及吸能密度的主要影响因素.本研究可以帮助我们全面了解NEAS的研究进展,为NEAS的设计与优化提供重要指导.     

单轴荷载下饱水岩石静态和动态抗压强度的细观力学分析

由于单轴荷载下饱水岩石的动态力学特性与静态力学特性存在很大差异,从宏观上进行力学分析 存在局限性。根据岩石受压全应力应变曲线的细观机制,分析了静态及动态单轴荷载条件下孔隙水影响饱水 岩石裂纹扩展的情况。在静态单轴压缩条件下,初始裂隙受压使自由水产生孔隙水压力,自由水对翼裂纹有 向外挤压的应力,促进裂纹扩展。在动态单轴压缩条件下,自由水会产生粘结力,抑制裂纹扩展。根据翼裂纹 受压扩展原理,推导出饱水单轴条件下动态抗压强度、静态抗压强度的计算公式,在相同断裂韧度下,饱水岩 石静态抗压强度风干岩石静态抗压强度饱水岩石动态抗压强度。对自然风干和饱水砂岩进行单轴静态、 动态压缩实验,结果与理论模型的结果相符。     

冲击载荷下轻质夹芯拱最大刚度拓扑优化及动力响应

基于双向渐进结构优化方法（bi-directional evolutionary structural optimization,BESO）框架,将传统动态载荷优化法中的内外层迭代引入到ABAQUS-MATLAB平台集成优化中,改进动态载荷拓扑优化流程。对初速度为100 m/s的子弹冲击下的夹芯拱结构进行拓扑优化设计和动力学响应分析。优化后夹芯拱芯层的变形模式可分为3个对称的部分,跨中区域的中部和上部主要发生压缩变形,呈现类三角点阵桁架结构,边界区域上部发生拉伸变形,下部发生压缩变形,呈现C形型结构,跨中和边界之间的过渡区域以拉弯联合变形为主,呈现Y形结构。通过与两种等质量的拱结构对比,分析了3种结构在不同初速度的子弹冲击下结构的挠度以及芯层的能量吸收情况。结果表明:在相同的冲击速度下,优化后的结构挠度最小,芯层比吸能最高;当冲击速度较低时,优化后的结构的抗冲击性能优势并不明显;在所研究的冲击速度范围内,冲击速度越高,优化后结构的抗冲击性能越好。对比对称载荷与非对称载荷（冲击点偏移量为100%）下2种优化结构在不同载荷工况下的动态响应,结果表明:载荷工况不同,得到的最终优化结果也略有所不同,但在相同载荷下结构的响应相差较小,每种工况下得到的优化结果在相应工况下所展现的力学性能略优,但均明显优于传统结构。因此,在对称冲击载荷下优化所得的结构具有一定的普遍性。     

Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load

Based on the theory of piezoelasticity, a functionally graded piezoelectric sandwich cantilever under an applied electric field and/or a heat load is studied. All materials may be arbitrary functional gradients in the thickness direction. The static solution for the mentioned problems is presented by the Airy stress function method. As a special case, assuming that the material composition varies continuously in the direction of the thickness according to a power law distribution, a comprehensive parametric study is conducted to show the influence of electromechanical coupling (EMC), functionally graded index, temperature change and thickness ratio on the bending behavior of actuators or sensors. The distribution of electric field or normal stress in present FGPM actuators is continuous along the thickness, which overcomes the problem in traditional layered actuators. The solution facilitates the design optimization for different piezoelectric actuators and has another potential application for material parameter identification.     

梯度蜂窝面外动态压缩力学行为与吸能特性研究

蜂窝材料具有优异的抗冲击吸能特性。为进一步提高蜂窝材料的比吸能与压缩力效率,提出了一种几何参数或材料参数沿厚度方向梯度渐变的蜂窝材料模型,并针对六边形蜂窝构型研究了胞元壁厚和屈服强度梯度变化的蜂窝材料在面外动态压缩载荷下的力学行为与吸能特性。研究结果表明,通过调控梯度变化的指数,胞元壁厚或母体材料屈服强度的梯度设计均可有效降低初始峰值应力,并使蜂窝材料的比吸能和压缩力效率同时增大。研究结果可为蜂窝材料的防撞性优化设计提供新的思路。     

Elasticity solutions for functionally graded plates in cylindrical bending

The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.     

Post-buckling analysis of FGM annular sector plates based on three dimensional elasticity graded finite elements

In this article, post-buckling and non-linear bending analysis of functionally graded annular sector plates based on three dimensional theory of elasticity in conjunction with non-linear Green strain tensor is considered. In-plane normal compressive loads have been applied to either radial, circumferential, or all edges of annular sector plates. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents while Poisson׳s ratio is assumed to be constant. The governing equations are developed based on the principle of minimum total potential energy and solved based on graded finite element method. Non-linear equilibrium equations are solved based on iterative Newton–Raphson method. The effects of material gradient exponent, different sector angles, thickness ratio, loading condition and two different boundary conditions on the post-buckling behavior of FGM annular sector plates have been investigated. Results denote that due to the stretching–bending coupling effects of the FGMs, the post-buckling behavior of movable simply supported FGM plates is not of the bifurcation-type buckling. Moreover, FGM annular sector plates subjected to uniaxial compression at radial edges show a non-linear bending behavior with unique and stable equilibrium paths following a flattening feature.     

软质聚氨酯泡沫的动态压缩力学性能和本构模型

采用Instron 9350落锤试验机研究了中低应变率下软质聚氨酯泡沫的动态压缩力学性能,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对材料应变率敏感性指数和能量吸收特性的影响,并基于实验结果建立了可准确描述其压缩力学响应的率相关本构模型。结果表明,软质聚氨酯泡沫的静动态压缩应力-应变响应具有典型的三阶段特征,且呈现出明显的应变率强化效应。准静态加载下,材料具有较高的吸能效率但能量吸收值较小,应变率对最大吸能效率和比吸能的影响较小;动态加载下,随着应变率的增加,最大吸能效率显著减小而比吸能明显增大。考虑应变率影响的修正Sherwood-Frost模型和修正Avalle模型都能够很好地表征软质聚氨酯泡沫的静动态压缩应力-应变响应,但修正Avalle模型的参数较少,更便于工程应用。研究结果可为软质聚氨酯泡沫抗冲击结构的设计和优化提供指导。     

Design,Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.     

正多边形基多胞薄壁管的吸能特性

多胞薄壁结构具有轻量化、高比吸能的特点，在汽车、轮船、航空航天等领域得到了广泛的应用。已有研究表明结构的耐撞性与结构的拓扑方式及胞元数量密切相关。为了研究结构形状和拓扑优化对其吸能效果的影响，基于正多边形结构，通过内嵌多边形和外接圆管的方式设计了两类新型多胞薄壁结构，并对这两类多胞薄壁结构进行准静态和落锤冲击实验，利用高速相机记录结构的变形模式，并定量分析了结构的吸能特性。实验结果表明:除正三角形二级内嵌四边形所得结构在准静态加载实验后期出现了局部失稳现象外，其余结构在准静态和落锤冲击实验过程中均保持垂直受压，结构变形模式与吸能效果较好。通过比较两类结构的实验结果得出:不论是在准静态加载还是在落锤冲击的情况下，内嵌多边形结构的各项吸能指标都明显优于外接圆管的结构；同等质量的情况下，内嵌四边形结构的吸能效果明显优于内嵌三角形的结构。     

Analytical/experimental investigation of energy absorption in grid-stiffened composite structures under transverse loading

In this paper we summarize preliminary results from an analytical/experimental study of the energy absorption characteristics of grid-stiffened composite structures under transverse loading. Tests and quasi-static finite element analysis simulations were carried out for isogrid E-glass/polypropylene panels in three-point bending. The results of the tests and simulations show that these types of structures have excellent damage tolerance and that most of the energy absorption occurs beyond initial failure. It is also observed that even though the peak load is greater for loading on the skin side, the specific energy absorption and the range of displacements over which energy is absorbed are significantly better when the load is applied on the rib side.     

Molecular dynamics simulation of polycrystalline copper

An approach for molecular dynamics simulation of the formation of polycrystalline materials from a melt during its cooling is proposed. Atomic configurations of copper corresponding to polycrystals with the mean grain size from 2 to 16 nm are obtained. Isothermal uniaxial tension and compression of these polycrystals is studied by the molecular dynamics method. For the mean grain size of polycrystalline copper being smaller than 10 nm, it is shown that Young’s modulus and yield stress decrease as the grain size decreases. Shock adiabats for polycrystalline copper are constructed. For a material with the grain size approximately equal to 2 nm, the temperature behind the shock wave front is demonstrated to be 10% higher than that in a polycrystal with the grain size greater than 10 nm. Molecular dynamics calculations predict the presence of copper with a body-centered cubic lattice behind the shock wave front at pressures ranging from 100 to 200 GPa.     

重组竹顺纹冲击力学性能研究

重组竹是一种新型竹基复合材料,其力学性能优于落叶松等木材。为评价重组竹在动态加载下的顺纹抗冲击力学性能,以密度1.06 g/cm3、含水率8.52%、龄期3～5年的毛竹基重组竹为研究对象,通过准静态单轴压缩和循环加卸载以及动态加载实验,研究了重组竹加载变形过程、各项力学性能指标以及对应变率的敏感性。结果表明:重组竹顺纹压缩过程可以分为弹性变形和弹塑性变形阶段,破坏类型为延性破坏,其各项强度指标随应变率的提高而提高,动态增长因子与应变率之间呈现线性关系,斜率为0.0024;重组竹压缩过程中的应变比能与应变之间呈线性关系,且随应变率的增长而增大,证明其吸能能力随着应变率的增大而提高。实验结果证明,重组竹顺纹具有良好的抗冲击力学性能和显著的应变率效应。     

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling

This paper presents a comprehensive experimental and theoretical investigation of the deformation behavior of high-purity, polycrystalline α-titanium under quasi-static conditions at room temperature. The initial material in this study was a cross-rolled plate with a strong basal texture. To quantify the plastic anisotropy and the tension–compression asymmetry of this material, monotonic tensile and compressive tests were conducted, on samples cut along different directions of the plate. A new anisotropic elastic/plastic model was developed to describe the quasi-static macroscopic response of the aggregate. Key in its formulation is the use of an anisotropic yield criterion that captures strength-differential effects and an anisotropic hardening rule that accounts for texture evolution associated to twinning. A very good agreement between FE simulations using the model developed and uniaxial data was obtained.     

粘接多胞管三点弯曲实验与数值研究

基于实验和数值模拟方法,本文研究了一种易制备粘接多胞薄壁结构的弯曲性能,分析了粘接多胞管在横向三点弯曲加载下的变形和能量吸收性能。三点弯曲准静态实验表明：由于粘接的作用,通常情况下粘接多胞管的能量吸收性能高于其基本构成单胞管能量吸收的总和,但在某些情况下粘接可以带来70%的性能提升。借助于LSDYNA,我们计算模拟了三点弯曲实验,计算得到的粘接多胞管变形模式和力-位移曲线与实验结果吻合良好。此外,采用计算模拟方法,我还对三种不同接触条件下的结构响应进行了对比分析,结果表明：如果未出现明显的粘接脱开,则粘接多胞管的吸能特性与完整的多胞结构相当,否则其能量吸收性能会被严重削弱。     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。