预应力索-桁架结构形状优化设计

就预应力索-桁架结构形状优化设计问题,考虑了施加预应力阶段、预应力与荷载共同作用阶段的性态约束条件,建立了设计变量包括截面尺寸、索力值、杆件及索节点坐标的形状优化数学模型;在求解方法上将设计变量分为两个子空间:第一子空间为索力值和截面尺寸优化设计空间,第二子空间为形状优化设计空间; 第一子空间给出新的求解方法以减轻结构重量,第二子空间用节点渐进法优化结构形状和布索位置以增加结构刚度.算例表明,该方法能使结构重量逐步减轻,结构刚度不减,形状逐步达到最优.     

Structural modeling of sandwich structures with lightweight cellular cores

An effective single layered finite element (FE) computational model is proposed to predict the structural behavior of lightweight sandwich panels having two dimensional (2D) prismatic or three dimensional (3D) truss cores. Three different types of cellular core topology are considered: pyramidal truss core (3D), Kagome truss core (3D) and corrugated core (2D), representing three kinds of material anisotropy: orthotropic, monoclinic and general anisotropic. A homogenization technique is developed to obtain the homogenized macroscopic stiffness properties of the cellular core. In comparison with the results obtained by using detailed FE model, the single layered computational model can give acceptable predictions for both the static and dynamic behaviors of orthotropic truss core sandwich panels. However, for non-orthotropic 3D truss cores, the predictions are not so well. For both static and dynamic behaviors of a 2D corrugated core sandwich panel, the predictions derived by the single layered computational model is generally acceptable when the size of the unit cell varies within a certain range, with the predictions for moderately strong or strong corrugated cores more accurate than those for weak cores. The project supported by the National Basic Research Program of China (2006CB601202), the National Natural Science Foundation of China (10328203, 10572111, 10572119, 10632060), the National 111 Project of China (B06024), the Program for New Century Excellent Talents in University (NCET-04-0958), the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment, and the Doctorate Foundation of Northwestern Polytechnical University.     

Periodic patterns and energy states of buckled films on compliant substrates

Thin stiff films on compliant elastic substrates subject to equi-biaxial compressive stress states are observed to buckle into various periodic mode patterns including checkerboard, hexagonal and herringbone. An experimental setting in which these modes are observed and evolve is described. The modes are characterized and ranked by the extent to which they reduce the elastic energy of the film-substrate system relative to that of the unbuckled state over a wide range of overstress. A new mode is identified and analyzed having nodal lines coincident with an equilateral triangular pattern. Two methods are employed to ascertain the energy in the buckled state: an analytical upper-bound method and a full numerical analysis. The upper-bound is shown to be reasonably accurate to large levels of overstress. For flat films, except at small states of overstress where the checkerboard is preferred, the herringbone mode has the lowest energy, followed by the checkerboard, with the hexagonal, triangular, and one-dimensional modes lowering the energy the least. At low overstress, the hexagonal mode is observed in the experiments not the square mode. It is proposed that a slight initial curvature of the film may play role in selecting the hexagonal pattern accompanied by a detailed analysis. An intriguing finding is that the hexagonal and triangular modes have the same energy in the buckled state and, moreover, a continuous transition between these modes exists involving a linear combination of the two modes with no change in energy. Experimental observations of various periodic modes are discussed with reference to the energy landscape. Discrepancies between observations and theory are identified and open issues are highlighted.     

基于层次分解方法的桁架结构形状优化

对于桁架结构形状优化,应用层次分解优化方法,将设计变量分成杆件截面积和节点位置两类变量。求解时分为两层,第一层在给定节点位置下对杆件截面进行优化,同时考虑了应力、局部稳定约束和位移约束的重量最轻;第二层假定截面层的有效位移约束作用不变,求解一个使桁架刚度增强的二次规划问题,获得既不违反约束,又使目标函数不上升的新的节点位置,再返回第一层。两层交替进行直至收敛。     

Deformation of a fluid-filled compliant cylinder in a uniform flow

We investigated surface compliance effects of a fluid-filled object in flow on its shape and internal flow through numerical simulation. A two-dimensional compliant cylinder containing fluid in a flow is a simple model of a cell, e.g. an erythrocyte, leukocyte or platelet. The thin membrane of the cylinder consisted of a network of mass-spring-damper (MSD) systems, representing its mechanical characteristics. We assumed that the stiffness and damping coefficients were those of latex gum. The two-dimensional flow inside and outside the membrane was obtained by solving the two-dimensional Navier–Stokes equations by using the finite element scheme at Re=400, based on the external flow velocity and diameter of an initial circular cylinder. The deformation of the membrane was calculated by solving the equation of motion for an MSD system by using the fourth-order Runge-Kutta method. The compliant cylinder deformed more if its stiffness was smaller than that of latex gum. The initial circular section of the cylinder became oval, with a flat front and a convex rear. The aspect ratio of the lateral to streamwise axis length of the oval became larger than unity, and increased with decreasing stiffness. The drag coefficient of the oval cylinder became larger than that of the circular cylinder, and increased with decreasing stiffness. The partial vibration at the rear, caused by shedding vortices, induced oscillating internal flows between two antinodes of the vibrating membrane. Since the object with smaller stiffness had higher ductility, velocity fluctuations of the external flow influenced the internal flow of the compliant object through deformation of the membrane.     

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.     

Shock enhancement of cellular structures under impact loading: Part I Experiments

This paper aims at showing experimental proof of the existence of a shock front in cellular structures under impact loading, especially at low critical impact velocities around 50 m/s. First, an original testing procedure using a large diameter Nylon Hopkinson bar is introduced. With this large diameter soft Hopkinson bar, tests under two different configurations (pressure bar behind/ahead of the supposed shock front) at the same impact speed are used to obtain the force/time histories behind and ahead of the assumed shock front within the cellular material specimen.Stress jumps (up to 60% of initial stress level) as well as shock front speed are measured for tests at 55 m/s on Alporas foams and nickel hollow sphere agglomerates, whereas no significant shock enhancement is observed for Cymat foams and 5056 aluminium honeycombs. The corresponding rate sensitivity of the studied cellular structures is also measured and it is proven that it is not responsible for the sharp strength enhancement.A photomechanical measurement of the shock front speed is also proposed to obtain a direct experimental proof. The displacement and strain fields during the test are obtained by correlating images shot with a high speed camera. The strain field measurements at different times show that the shock front discontinuity propagates and allows for the measurement of the propagation velocity.All the experimental evidences enable us to confirm the existence of a shock front enhancement even at quite low impact velocities for a number of studied materials.     

Shock enhancement of cellular structures under impact loading: Part II analysis

Numerical simulations of two distinct testing configurations using a Hopkinson bar (pressure bar behind/ahead of the shock front) are performed with an explicit finite element code. It allows us to confirm the observed test data such as velocity and force time histories at the measurement surface. A comparison of the simulated local strain fields during shock front propagation with those measured by image correlation provides an additional proof of the validity of such simulations.Very simple rate insensitive phenomenological constitutive model are used in such simulations. It shows that the shock effect is captured numerically with a basic densification feature. It means that strength enhancement due to shock should not be integrated in the constitutive model of foam-like materials used in industrial FE codes.In order to separate shock enhancement from entire strength enhancement, an improvement of an existing model with easily identifiable parameters for shock enhancement prediction is proposed. For a quick estimate of the shock enhancement level, a simple power law densification model is proposed instead of the classical RPPL model proposed by Reid and co-workers [Tan et al., 2005. Dynamic compressive strength properties of aluminium foams. Part I—experimental data and observations. J. Mech. Phys. Solids 53, 2174-2205]. It is aimed at eliminating the parameter identification uncertainty of the RPPL model. Such an improved model is easily identifiable and gives a good prediction of the shock enhancement level.     

Finite width effect of thin-films buckling on compliant substrate: Experimental and theoretical studies

Buckling of stiff thin films on compliant substrates has many important applications ranging from stretchable electronics to precision metrology and sensors. Mechanics plays an indispensable role in the fundamental understanding of such systems. Some existing mechanics models assume plane-strain deformation, which do not agree with experimental observations for narrow thin films. Systematic experimental and analytical studies are presented in this paper for finite-width stiff thin films buckling on compliant substrates. Both experiments and analytical solution show that the buckling amplitude and wavelength increase with the film width. The analytical solution agrees very well with experiments and therefore provides valuable guide to the precise design and control of the buckling profile in many applications. The effect of film spacing is studied via the analytical solutions for two thin films and for periodic thin films.     

用拓扑优化设计多体分比蜂窝状结构

提出用拓扑优化及增材制造法设计同一材料制作的蜂窝状结构,并把设计可归结为在不同的设计域内使用不同的体分比的拓扑优化问题。首先推导了多体分比约束条件下的蜂窝状结构拓扑优化问题;然后提出了基于多阈值的等值面法及与商用有限元分析软件对接的算法。给出了有三个体积约束的最小柔顺性问题的数值算例。计算结果表明,对于具有三个体积约束的拓扑优化设计问题,存在一个最佳的体积约束组合;使用等量的材料,与两个体积约束的最佳拓扑设计相比,用最佳体积约束组合所得到的优化结构的柔顺性还要小10%。     

Nonlinear analysis of slow drift extreme responses of a compliant offshore structure

This paper first demonstrates that the accuracy and efficiency of the method of numerical simulation often used is not very high in predicting the slow drift surge extreme responses of a compliant offshore structure. Next, the slow drift surge extreme responses of the structure are analyzed via the path integral solution racy and efficiency of the PIS （PIS） method, and the accumethod is found to be higher than those of the numerical simulation method. A compound PIS （CPIS） method is first proposed in this article to further improve the efficiency of the path integral solution method, and the accuracy and efficiency of the CPIS method is validated.     

Influence of transverse curvature on the stability of pre-stressed helical structures

This study is concerned with the stability characteristics of helix shaped structures made of anisotropic, pre-stressed, thin flanges arranged in such a way as to enable and develop multi-stability. Previous research on similar structures assumed the structural response of the flanges to be one-dimensional due to the narrow width of the pre-stressed members in comparison to their length. In this work, a refined two-dimensional model of the flanges is employed to model the influence of transverse curvature as well as the membrane strain energy associated with the non-zero Gaussian curvature deformations. While longitudinal curvature changes and twist are inherent to the geometry of the helices; the transverse curvature results from a consideration of boundary effects and the minimisation of the (expensive) membrane elastic energy. A qualitative study of the changes in transverse curvature reveals ways of simplifying the two-dimensional model into a simpler, closed form, one-dimensional version applicable to helices with relatively narrow flanges. Correlation is found between experimental results, finite element modelling and analytical predictions for the two models.     

H_2—O_2爆轰时Ar浓度对产生胞格结构的影响

作者在方形爆轰管中进行了H_2—O_2—Ar系统的实验研究。在由Ar稀释的H_2—O_2混合物的爆轰实验中得到了规则的胞格结构图案。也得到了胞格形成的临界曲线,并与爆炸极限曲线进行了对照,两者的趋势是一致的。另外,测量了从点火处到胞格形成处之间的距离及胞格区的长度。最后分析了氩Ar浓度对H_2—O_2爆轰的抑制作用。     

基于水平集方法的均布式柔性机构的拓扑优化设计

提出一种利用水平集方法进行均布武柔性机构设计的新方法.根据水平集边界表达方法中具有几何信息的特点,将图像分析中的二次能量函数引入到水平集模型中,以控制柔性机构拓扑优化设计结果的几何尺寸,得到等宽带状均布的柔性机构,较好地解决了传统柔性机构拓扑优化中容易出现单点铰链问题.应用半隐式的加性分裂算子(AOS)算法求解水平集方程,松弛了逆风格式中CFL(Courant-Frie drichs-Lewy)条件对时间步长的限制,提高了求解效率.通过一个典型的二维算例来验证方法的有效性.     

The influence of cellular structure on detonation transmission

We present two-dimensional numerical simulations of the transmission of detonation from a rectangular channel into a larger volume. The simulations solve the Euler equations on a Cartesian grid using the method of Flux-Corrected Transport for the fluid equations and a two-step induction parameter model for the chemistry. We simulate detonation in a H₂/O₂/Ar mixture and use sufficient grid resolution to resolve the cellular structure of the detonation. When a planar detonation front without a resolved cellular structure expands into the larger volume, the reaction front separates from the shock front and the detonation fails. When the planar front is perturbed to induce a quasi-regular cellular structure in the detonation, it again initially begins to fail, but now the presence of the transverse waves leads to reignition of the detonation in the larger volume. The form of this reignition shows striking similarities to the reignition of detonation which has been seen experimentally in H₂/O₂ mixtures. We describe this reignition mechanism in detail, and also investigate the dependence of the reignition on the number of cells in the detonation front. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Dynamics study of detonation-wave cellular structure 1. Statistical properties of detonation wave front

We have investigated the evolution of cellular detonation-wave structure as a gaseous detonation travels along a round tube and measured cell lengths as a function of the initial pressure of the gas. We have tested acetylene-containing combustible gas mixtures with different degrees of regularity. Along with the smoked-foil technique, an emission method has been used to the measure current and average values of the detonation cell length. The method is based on the detection of an emission spectrum behind the detonation front in the spectral range corresponding to local gas temperatures that are much higher than those for the Chapman-Jouguet equilibrium condition. This technique provides quasi-continuous cell-length measurements along the normal to the detonation front over the length of several factors of ten times the tube. Our study has experimentally identified the steady states of detonation structure in round tubes, referred to here as the single detonation modes. When the state of a single mode is fully established, then both the flow structure and the energy release at detonation front develop strictly periodically along the tube at a constant frequency inversely proportional to the cell length of the mixture. The mixture regularity has had no influence on the occurrence of the detonation mode, which is defined by the value of initial pressure or the total energy release of the mixture. Outside of the pressure range where a detonation mode was most likely to occur, the detonation front is unstable and may exhibit an irregular cellular pattern. Monitoring the evolution of cells over a long distance revealed that the local gas emissivity, which is time dependent and corresponds to axial pulsations of the detonation structure, has the appearance of a superposition of separate harmonics describing the states of emissivity oscillations and cell structure of single detonation modes. Received 18 October 1999 / Accepted 10 June 2001     

Shape optimization of an accommodative intra-ocular lens

Cataract surgery consists in replacing the clouded or opacified crystalline lens by an Intra-Ocular Lens (IOL) having the same mean dioptrical power. Clear vision is then achieved at a given distance and glasses are needed in many situations. A new kind of IOL, potentially accommodative, is proposed. Its design is based on the deep understanding of the accommodation mechanism and on the mathematical modeling and the numerical simulation of the IOL's comportment in vivo. A preliminary version of this IOL is now commercialized by the company HumanOptics under the name ‘1CU’. In a second phase, shape optimization techniques equipped with strong mechanical and physiological constraints, are used to enhance the IOL performance and build a new design. To cite this article: F. Jouve, K. Hanna, C. R. Mecanique 333 (2005).     

Scaling theory of adsorption-induced stresses in polymer brushes grafted onto compliant structures

The lateral forces exerted on a substrate by a layer of end-grafted polymer molecules are calculated on the basis of simple scaling arguments. The results are cast in terms of an equilibrium surface stress and an elastic constant, which describes the rate of change of the surface stress upon deformation of the substrate. This allows for straightforward integration of the present results into a continuum framework describing the response of a compliant structure, which facilitates device design and analysis. The results are illustrated with calculations for end-grafted poly(styrene) and poly(ethylene oxide), and the implications for building micromechanical devices based on adsorption-induced deformation are discussed.     

Analytical study of idealized two-dimensional cellular detonations

In this study, the idealized two-dimensional detonation cells were decomposed into the primary units referred to as sub-cells. Based on the theory of oblique shock waves, an analytical formula was derived to describe the relation between the Mach number ratio through triple-shock collision and the geometric properties of the cell. By applying a modified blast wave theory, an analytical model was developed to predict the propagation of detonation waves along the cell. The calculated results show that detonation wave is, first, strengthened at the beginning of the cell after triple-shock collision, and then decays till reaching the cell end. The analytical results were compared with experimental data and previous numerical results; the agreement between them appears to be good, in general. Received 13 February 2001 / Accepted 2 August 2001