Mechanics of fish skin: A computational approach for bio-inspired flexible composites

Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming.     

Structural interfaces in linear elasticity. Part II: Effective properties and neutrality

The model of structural interfaces developed in Part I of this paper allows us to analytically attack and solve different problems of stress concentration and composites. In particular, (i) new formulae are given for effective properties of composite materials containing dilute suspensions of (randomly oriented) reinforced elliptical voids or inclusions; (ii) a new definition is proposed for inclusion neutrality (to account for the fact that the matrix is always ‘overstressed’, and thus non-neutral in a classical sense, at the contacts with the interfacial structure), which is shown to provide interesting stress optimality conditions. More generally, it is shown that the incorporation of an interfacial structure at the contact between two elastic solids exhibits properties that cannot be obtained using the more conventional approach of the zero-thickness, linear interface. For instance: contrary to the zero-thickness interface, both bulk and shear effective moduli can be optimized for a structural interface; effective properties higher that those possible with a perfect interface can be attained with a structural interface; and neutrality holds with a structural interface for a substantially broader range of parameters than for a zero-thickness interface.     

可重构力学超材料的设计与波动特性研究

力学超材料中的弯曲梁双稳态结构由于其主动调控性强且调控精度高等优点近年来受到广泛关注.文章利用中心受压弯曲梁的不稳定性设计了六角型双稳态结构,首先建立了等效弯曲梁模型,基于梁变形微分方程及能量最低原理探明了结构双稳态特性的产生基理,之后利用有限元数值计算研究了结构几何参数对其整体力学性能的影响,分别得到了具备自恢复及双稳态性能的结构几何参数范围,绘制了几何参数与力学性能之间的相图.同时,可重构结构的可控变形能力有助于调整整体的色散特性,利用数值仿真研究了具备双稳态特性的结构在拉伸和压缩两种构型下的色散关系,对比分析了不同结构几何参数及构型转变对结构产生的带隙位置及范围的影响,之后对由不同构型单胞组成的周期性结构进行了频响分析来验证带隙计算的准确性.通过六角型可重构结构的力学特性、色散特性研究及频响分析表明可以通过结构几何参数的设计实现对结构整体性能的主动调控,为可逆向设计的弹性波超材料结构研究分析提供了一条可靠路径.     

零泊松比手风琴蜂窝等效模量

柔性蒙皮是变形机翼和风力机叶片的关键组成部分。一维变形的柔性蒙皮不仅要求其支撑结构具有良好的面内变形和面外承载能力,还需要具有零泊松比特性。手风琴蜂窝具有零泊松比特性,可用作一维变形柔性蒙皮支撑。为全面分析其面内外弹性变形特性,综合考虑结构的内力弯矩、轴力和剪力,通过卡氏第二定理对其x向等效弹性模量和x-y面内等效剪切模量进行了推导;利用最小余能原理和最小势能原理确定了x-z面内的等效剪切模量;此外还推导了其y和z向的等效弹性模量以及y-z面内的等效剪切模量;然后通过ANSYS有限元仿真对等效模量理论公式进行了验证;最后将本文理论模型与现有模型进行了比较。结果表明,理论公式和有限元仿真吻合较好,在结构设计时采用较大的斜梁高度系数h和斜梁间距系数g,较小的厚度系数t以及较大的竖直梁厚度系数η,有望获得具有较小面内刚度和较大面外刚度的手风琴蜂窝结构。该结果可用于手风琴蜂窝面内外等效模量的快速预测,为一维变形柔性蒙皮的结构设计提供相应的参考。此外,本文理论模型相比传统模型更为精确且具有更加广泛的应用范围。     

Transformational cloaking from seismic surface waves by micropolar metamaterials with finite couple stiffness

Transformational elastodynamics can be used to protect sensitive structures from harmful waves and vibrations. By designing the material properties in a region around the sensitive structure, a cloak, the incident waves can be redirected as to cause minimal or no harmful response on the pertinent structure. In this paper, we consider such transformational cloaking built up by a suitably designed metamaterial exhibiting micropolar properties. First, a theoretically perfect cloak is obtained by designing the properties of an (unphysical) restricted micropolar material within the surrounding medium. Secondly, we investigate the performance of the cloak under more feasible design criteria, relating to finite elastic parameters. In particular, the behavior of a physically realizable cloak built up by unrestricted micropolar elastic media is investigated. Numerical studies are conducted for the case of buried as well as surface breaking structures in 2D subjected to incident Rayleigh waves pertinent to seismic loading. The studies show how the developed cloaking procedure can be utilized to substantially reduce the response of the structure. In particular, the results indicate the performance of the cloak in relation to constraints on the elastic parameters.     

基于响应面方法的结构碰撞优化

应用响应面方法可将结构响应表达为设计变量的显式形式．为拟合响应面，基于中心复合设计和单纯形设计简化出了中心对称和拟单纯形设计，其既可以保证约束近似精度，同时降低计算量．针对常见优化问题，使用响应面方法将其构造为线性或者非线性约束优化模型，并应用Matlab优化工具箱求解．方管碰撞优化数值算例表明文中提出的试验设计方法及优化模型有较好的求解效率和精度．     

MULTISCALE MECHANICS OF BIOLOGICAL AND BIOLOGICALLY INSPIRED MATERIALS AND STRUCTURES

The world of natural materials and structures provides an abundance of applications in which mechanics is a critical issue for our understanding of functional material properties. In particular, the mechanical properties of biological materials and structures play an important role in virtually all physiological processes and at all scales, from the molecular and nanoscale to the macroscale, linking research fields as diverse as genetics to structural mechanics in an approach referred to as materiomics. Example cases that illustrate the importance of mechanics in biology include mechanical support provided by materials like bone, the facilitation of locomotion capabilities by muscle and tendon, or the protection against environmental impact by materials as the skin or armors. In this article we review recent progress and case studies, relevant for a variety of applications that range from medicine to civil engineering. We demonstrate the importance of fundamental mechanistic insight at multiple time- and length-scales to arrive at a systematic understanding of materials and structures in biology, in the context of both physiological and disease states and for the development of de novo biomaterials. Three particularly intriguing issues that will be discussed here include： First, the capacity of biological systems to turn weakness to strength through the utilization of multiple structural levels within the universality-diversity paradigm. Second, material breakdown in extreme and disease conditions. And third, we review an example where the hierarchical design paradigm found in natural protein materials has been applied in the development of a novel hiomaterial based on amyloid protein.     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能，尤其是在有限变形下所呈现的宏观各向异性，是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构（晶粒的形貌和取向等）对宏观塑性各向异性的影响，因此，本文建立了能实际反映晶粒形貌的三维Voronoi模型，并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先，建立反映材料微结构的代表性体积单元RVE模型进行计算，并与实验结果进行对比验证。然后，以单向拉伸为例，分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响，并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明，本文模型能够反映微观结构对宏观力学性能的影响，为实际生产制造领域构件的力学性能提供可靠的预测。     

航天器噪声试验中结构振动响应预示方法研究

航天器在随运载火箭发射过程中要承受严酷的噪声环境,需通过噪声试验来检验航天器承受噪声环境并能正常工作的能力.航天器噪声试验中结构振动的响应特性是结构强度设计应该考虑的因素之一,更是制定器上组件随机振动试验条件的重要依据,因此有必要在航天器研制初期对噪声载荷作用下的结构振动进行响应预示.文章应用商用有限元分析软件MSC.Patran和MSC.Nastran建立了某型号航天器结构舱板的有限元模型,将噪声载荷声压谱转换为脉动压力功率谱密度,进而采用模态法分析结构在噪声载荷作用下的随机振动响应,并将仿真预示结果与试验结果进行对比研究,在仿真分析中考虑阻尼参数模型和流场附加质量效应等因素的影响;通过研究表明:采用阻尼比随频率提高而减小的经验阻尼参数模型可以较好地反映中高频响应特性、得到较为准确的总均方根响应分析结果,进一步采用虚拟质量法考虑流场附加质量效应可以得到较为准确的功率谱密度响应分析结果.文章提出的仿真分析方法建模简便、计算成本低,适用于在航天器研制初期对航天器噪声试验中的结构振动进行响应预示.      

基于耦合算法的三维复杂结构冲击动力学特性

光滑粒子流体动力学-有限元耦合算法（SPH-FEM）较好地结合了SPH和FEM的优势,近年来逐渐被引入冲击动力学相关问题研究中。然而早期的研究对象多为单一材料的简单结构,所取得的研究成果距离实际工程应用仍有一定差距。为此,在总结前人工作的基础上,对SPH-FEM耦合算法进行适当改进,通过引入复合材料损伤模型,对复合材料蒙皮结构飞行器舱段结构进行建模计算,分析其在爆炸冲击激励下的冲击动力学特性。将数值计算结果与试验结果进行对比分析,验证该算法和模型的有效性和准确性,初步实现SPH-FEM的工程实际应用。最后总结了复合材料蒙皮结构飞行器在爆炸冲击激励下的一系列结构动态响应规律,以期为航天飞行器结构设计与防护提供参考。     

考虑表面层厚度不确定的稳健性拓扑优化方法

采用增材制造工艺制备结构件时, 较差的成型精度和表面粗糙度会导致结构表面层异质, 引起表面层厚度的不确定性. 为了研究不确定性对拓扑优化结构性能的影响, 进而获得对不确定性具有更低敏感性的结构构型, 提出了考虑结构表面层厚度不确定性的稳健性拓扑优化方法. 首先, 采用一种基于腐蚀操作的表面层识别技术, 通过基于Helmholtz偏微分方程的PDE光滑过滤和基于Heaviside过滤、tanh函数的离散映射两个过程实现表面层异质等效模型的建立. 其次, 将表面层厚度作为服从高斯分布的随机变量, 基于摄动有限元方法开展了不确定性传播的分析和系统随机响应的预测; 以结构柔顺性均值和标准差的加权和作为优化目标, 建立了考虑表面层厚度不确定性的拓扑优化模型, 并推导了目标函数关于设计变量的敏度. 最后, 通过数值算例验证了该方法的有效性. 数值结果表明, 在设计过程中考虑表面层厚度不确定性对结构性能的影响, 可以得到具有更强抵抗不确定性能力的结构构型, 有效提升了结构性能的稳健性.      

考虑瞬态效应的承载隔热多功能结构拓扑优化

同时满足承载和隔热要求的多功能结构在高超飞行器热防护结构设计中倍受关注.实际隔热材料通常承载能力弱,而高承载材料隔热性能差,如何在有限空间内协同结构的承载与隔热成为关键问题.高超飞行器气动加热时间有限,存在加热时间短、热荷载变化大的特点.因此结构设计需要考虑时间因素和瞬态效应,而现有稳态传热与承载的多功能协同优化设计模...     

Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the inde-pendent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization inter-polation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimiza-tion model based on the minimum structural compliance and the specified fiber material volume constraint has been estab-lished. The sensitivity information about the two geometrical scales design variables are also deduced considering the char-acteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can fur-ther explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultra-light design of the composite frame structure. The novel two geometrical scales optimization model provides a new oppor-tunity for the design of composite structure in aerospace and other industries.     

离散变量框架结构的可靠性优化

以框架结构系统的可靠性分析为基础,给出离散变量框架结构可靠性优化的相对差商方法及迭代格式,并用算例证明了该法的有效性及实用性。     

Experimental dynamic analysis of elastic-plastic shear frames with secondary structures

Various experimental models are developed to study the influence of lightweight secondary structures on the dynamic response of elastic and elastic-plastic shear frames. Small-scale two-story model frames, with an elastic single-degree-of-freedom secondary structure attached, are considered for sinusoidal and random in-plane support excitation. Both elastic and elastic-plastic responses are recorded by varying the material properties of the columns of a distinguished floor. Parametric studies are performed by varying the secondary structure's fundamental frequency and damping. Experimental results are compared with those obtained by computational simulations. Experimental and numerical results are in excellent agreement, however they show that the material properties have to be determined very carefully. The statistic response of randomly excited elastic-plastic structures is not much affected by the motion of tuned secondary structures. However, this dynamic behavior is not true for elastic main structures. In this case, an optimally tuned secondary structure decreases the structural response up to 25%.     

精密及缺陷信息条件下的结构可靠性设计

概率方法一直以来被认为是处理不确定现象的最有效的方法.传统的概率可靠性模型建立在随机变量的分布函数基础上,需要较完整的数据信息.在结构设计问题中,有关载荷、抗力等影响因素的统计数据一般是稀少的或缺乏的,信息往往以非完整的形式出现.此外,结构的安全设计还需考虑结构和环境的相互作用,结构设计、分析、评价以及制作过程中可能存在的误差等,有些不确定因素不能归于随机性.因此,需要发展新的结构可靠性设计模型和方法,以克服传统的概率可靠性方法的局限和不足.本文对精密及缺陷信息条件下的可靠性设计模型和方法进行综述,内容包括随机可靠性设计模型与方法、非完整信息下的可靠性分析和设计、模型误差和主观不确定的影响、复杂系统优化求解策略、以及今后的研究展望.      

An efficient implementation of aeroelastic tailoring based on efficient computational fluid dynamics-based reduced order model

Current and future trends in the aerospace industry leverage on the potential benefits provided by lightweight materials that can be tailored to realize desired mechanical characteristics when loaded. For aircraft design, the deployment of aeroelastic tailoring is hindered by the need to re-compute, for any possible modification of the structure, the dependence of the aerodynamic field on the underlying structural properties. To make progress in this direction, the work presents a rapid computational fluid dynamics based aeroelastic tool which is built around a reduced order model for the aerodynamics that is updated for any modification of the structure by using the structural dynamics reanalysis method. The aeroelastic tailoring tool is demonstrated in transonic flow for the AGARD 445.6 wing, suitably modified with composite materials. It was found that the proposed method provides accurate engineering predictions for the aeroelastic response and stability when the structure is modified from the baseline model.     

Damage detection with spatial wavelets

This paper discusses a structural damage detection technique based on wavelet analysis of spatially distributed structural response measurements. The premise of the technique is that damage (e.g. cracks) in a structure will cause structural response perturbations at damage sites. Such local perturbations, although they may not be apparent from the measured total response data, are often discernible from component wavelets. The viability of this new technique is demonstrated with two examples: one based on numerically simulated deflection responses of a uniform beam containing a short transverse crack under both static and dynamic loading conditions, and the other based on smooth analytical crack-tip displacement fields. In each of these examples, the deflection or displacement response is analyzed with the wavelet transform, and the presence of the crack is detected by a sudden change in the spatial variation of the transformed response. This damage detection technique may serve the purpose of structural health monitoring in situations where spatially distributed measurements of structural response in regions of critical concern can be made with, for example, networks of distributed sensors, optical fibers, computer vision and area scanning techniques. It appears that this new technique does not require any analysis of the complete structure in question, nor any knowledge of the material properties and prior stress states of the structure.     

Structural Responses of Underground Pipelines to Dynamic Loadings

ABSTRACT

This study develops a simple analytical model to assess the dynamic response of a pipeline under ground shaking. Since many observed failures of buried pipes are attributable to pullout or crushing at joints and breaks along the pipeline itself, the present model is proposed to estimate the maximum relative joint displacement and the maximum structural strain, under various soil conditions and material properties. Outcomes from both the quasi-static approach and dynamic analysis are compared, to examine the effect of inertia and damping, which are generally neglected in dealing with such a structure. The effect of excitation frequency, joint stiffness, pipe size, and pipe length on structural response is studied. Numerical results may serve as a guide for design, as well as for reliability analysis.     

考虑材料性能空间分布不确定性的可靠度拓扑优化

论文研究了考虑材料性能空间分布不确定性的连续体结构可靠度拓扑优化问题。其中,材料的弹性模量视为具有给定概率分布特征的随机场,其离散采用级数最优线性估值法（EOLE）。随机结构的响应以及相应的灵敏度分析采用多项式混沌展开（PCE）近似表达,并采用Monte Carlo方法验证了该方法的精度。结构的可靠度分析采用一次可靠度方法（FORM）,在优化问题的求解中,对双层嵌套方法和序列近似规划（SAP）方法进行了对比。数值算例中,该方法应用于二维和三维结构的拓扑优化问题,优化结果验证了方法的正确性和有效性。