黄土地区水平荷载作用下闭合型地下连续墙基础承载 性状分析

地下连续墙基础相对于一般桩基础的一个显著特点就是整体刚度大,水平荷载作用下基础一般有两种工作状态和破坏机理:其一是刚性短桩,表现为转动或平移破坏;其二是弹性长桩,表现为挠曲破坏。数值模拟表明:在一定范围内随着墙体埋深的增加,在大小相等的水平荷载作用下,基础埋深越大,其水平位移则越小。但埋深超过30m后,墙体埋深对基础的水平变形影响变得不显著。即当闭合墙体的埋深超过一定深度后,过分的加大闭合墙体的埋深无助于提高基础的水平承载性能。     

Non-linear dynamic behaviour of multi-folding microstructure systems based on origami skill

This paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability and elasto-plastic stability of a folding multi-layered truss. Both analyses are based on bifurcation theory and include geometrical non-linearity. The dynamic analysis includes an allowance for contact between nodes. Comparisons are made between elastic behaviour and elasto-plastic behaviour obtained from both numerical dynamic methods in which bifurcations are demonstrated as a theoretically elastic analysis. Our analysis reveals that several folding behaviours in the pantographic truss are identified during the elastic and elasto-plastic instabilities, where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading. The authors suggest that understanding this behaviour will be very useful for developing light-weight structures subject to dynamic loading based on static bifurcation analysis and dynamic analysis.     

基于Kriging代理模型的连梁金属阻尼器性能研究与参数优化设计

连梁阻尼器是剪力墙连梁结构中主要的耗能部件,其构造形式直接影响剪力墙的性能。本文从连梁阻尼器的几何特征入手,在用料相同的前提下,对四种典型开孔形式金属平面内屈服连梁阻尼器进行耗能性能对比研究,引入Kriging代理模型,构造出不同开孔尺寸与滞回耗能的关系。然后,分别对四种开孔形式的连梁阻尼器几何参数进行进一步优化,以获得最优构型。为简化优化迭代过程中反复的多步加载非线性求解计算,在优化过程中以Kriging代理模型作为反演优化平台,代替原有的几何参数与滞回耗能关系,并采用最大期望提高加点方法,不断提高代理模型在最优解附近的精度,在提高代理模型的代理精度同时,也提高了优化设计效率。所提算法为寻求一种形式简单、性能优越的金属平面内屈服连梁阻尼器提供了新的解决框架。     

Theory of limit equilibrium of bimetallic shells of revolution and circular plates

Bimetallic shells and plates are widely used in technology (see [1, 2]). An investigation into the flexure and stability of thin shells and various types of loading within the limits of elasticity has been carried out in [3]. An investigation into the load-carrying capacity of cylindrical bimetallic shells made of materials which equally resist tension and compression was carried out in [4]. In many cases the materials of the base and plating layers of bimetallic constructions possess substantially different plastic resistance under tension and compression [5]. The given paper is devoted to the investigation of the load-carrying capacity of bimetallic axisymmetric shells which are made of materials that have different resistances to tension and compression; it is also devoted to the assessment of their economy in comparison with homogeneous shells.     

A homogenized viscoelastic model for masonry structures

A linear viscous model for evaluating the stresses and strains produced in masonry structures over time is presented. The model is based on rigorous homogenization procedures and the following two assumptions: that the structure is composed of either rigid or elastic blocks, and that the mortar is viscoelastic. The hypothesis of rigid block is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies, while the hypothesis of elastic blocks may be assumed for newly constructed brickwork structures. The hypothesis of viscoelastic mortar is based on the observation that non-linear phenomena may be concentrated in mortar joints. Under these assumptions, constitutive homogenized viscous functions are obtained in an analytical form.Some meaningful cases are discussed: masonry columns subject to minor and major eccentricity, and a masonry panel subject to both horizontal and vertical loads. The major eccentricity case is analysed taking into account both the effect of viscosity and the no-tension hypothesis, whereas the bi-dimensional loading case is analysed to verify the sensitivity of masonry behaviour to viscous function. In the masonry wall considered, the principal stresses are both of compression, and the no-tension assumption may therefore be discounted.     

A mixed lumped stress–displacement approach to the elastic problem of masonry walls

We present a novel approach to the elastic problem of masonry walls, which generalizes the lumped stress method presented in [Fraternali, 2001], [Fraternali, 2007] and [Fraternali, 2010] and Fraternali et al. (2002). The generalization consists of a mixed lumped stress-displacement approach to the elastic problem of a wall that incorporates no-tension elements. Such an approach depends on the nodal values of the Airy stress function and the displacements of selected (“pivot”) nodes. The latter coincide with inter-element and boundary nodes. The mixed lumped stress-displacement method can be conveniently coupled with standard finite element and boundary element approaches. Numerical applications dealing with recurrent structural elements are given, showing that such a method is able to capture some essential features of the actual response of masonry constructions.     

Design of armor for protection against blast and impact

The features of blast and impact that can damage a delicate target supported by a structure include both the peak pressure and the impulse delivered to the structure. This study examines how layers of elastic and visco-elastic materials may be assembled to mitigate these features. The impedance mismatch between two elastic layers is known to reduce the pressure, but dissipation is required to mitigate the transmitted impulse in light-weight armor. A novel design concept called impact or blast tuning is introduced in which a multi-layered armor is used to tune the stress waves resulting from an impact or blast to specific frequencies that match the damping frequencies of visco-elastic layers. The material and geometrical parameters controlling the viscous dissipation of the energy within the armor are identified for a simplified one-dimensional system, to provide insight into how the optimal design of multi-use armor might be based on this concept.     

Discrete and continuous models for in plane loaded random elastic brickwork

The aim of this paper is to study non-periodic masonries – typical of historical buildings – by means of a perturbation approach and to evaluate the effect of a random perturbation on the elastic response of a periodic masonry wall. The random masonry is obtained starting from a periodic running bond pattern. A random perturbation on the horizontal positions of the vertical interfaces between the blocks which form the masonry wall is introduced. In this way, the height of the blocks is uniform, while their width in the horizontal direction is random. The perturbation is limited such as each block has still exactly 6 neighboring blocks. In a first discrete model, the blocks are modeled as rigid bodies connected by elastic interfaces (mortar thin joints). In other words, masonry is seen as a “skeleton” in which the interactions between the rigid blocks are represented by forces and moments which depend on their relative displacements and rotations. A second continuous model is based on the homogenization of the discrete model. Explicit upper and lower bounds on the effective elastic moduli of the homogenized continuous model are obtained and compared to the well-known effective elastic moduli of the regular periodic masonry. It is found that the effective moduli are not very sensitive to the random perturbation (less than 10%). At the end, the Monte Carlo simulation method is used to compare the discrete random model and the continuous model at the structural level (a panel undergoing in plane actions). The randomness of the geometry requires the generation of several samples of size L of the discrete masonry. For a sample of size L, the structural discrete problem is solved using the same numerical procedure adopted in [Cecchi, A., Sab, K., 2004. A comparison between a 3D discrete model and two homogenized plate models for periodic elastic brickwork, International Journal of Solids Structures 41 (9–10), 2259–2276] and the average solution over the samples gives an estimation which depends on L. As L increases, an asymptotic limit is reached. One issue is to find the minimum size for L and to compare the asymptotic average solution to the one obtained from the continuous homogenized model.     

极限下限分析的正交基无单元Galerkin法

基于极限分析的下限定理,建立了用正交基无单元Galerkin法进行理想弹塑性结构极 限分析的整套求解算法．下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接 得到,所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模 拟．这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到．通过对自平衡应力场 子空间的不断修正,整个问题的求解将化为一系列非线性数学规划子问题,并通过复合形法 进行求解．算例表明该方法有效地克服了维数障碍问题,使计算效率得到了充分的提高,是 切实可行的．     

Buckling of cracked composite columns

A crack in a structural element introduces a significant local flexibility which enhances the instability. Buckling of an edge-notched beam is studied for isotropic and anisotropic composites. The local compliance due to the presence of cracks in an anisotropic medium is formulated as a function of the crack-tip stress intensity factors and the elastic constants of the material. The general integration of the non-linear differential equations expressing the buckling model of an eccentrically loaded composite beam is derived for two different types of hinged supports ; namely freely approaching and fixed span. The effect of reducing rigidity on the load-carrying capacity and the post-buckling behavior of the beam is discussed and exemplary numerical solutions are provided. The study indicates that the instability increases with the beam slenderness and the crack length. In addition, the material anisotropy conspicuously reduces the load-carrying capacity of an externally cracked member.     

Modeling of failure wave propagation in impact compression of brittle materials (Glasses)

For a plane brittle failure wave in a material loaded by an elastic compression wave, an analytic solution is obtained on the basis of a model with a Drucker-Prager type condition and a given value of the failure wave propagation velocity. The wave failure model supplemented with threshold criteria is generalized to two-dimensional flows in breaking plates. Collision of glass plates with a rigid wall is modelled and three- and two-wave failure structures in the plate are obtained. Some data on the leading elastic wave decay and the arrest of the failure wave under the action of the overtaking unloading that propagates from the region of spread of the fractured material near the wall are obtained.     

Is the concept of “average shape” legitimate,for a mixture of inclusions of diverse shapes?

In heterogeneous materials, inhomogeneities (pores, cracks, particles) usually represent a mixture of diverse shapes. In modeling the effective elastic and conductive properties, they are often replaced by identical spheroidal shapes – for which exact solutions are available – that intend to represent certain “average shape” (for cracks, for example, the circular shape is routinely used). We find that, in anisotropic cases of non-random orientations, such a replacement cannot generally be done (with the exception of flat cracks). In other words, the concept of “average spheroid’ is not legitimate, and its use may lead to large errors in predicting the effective properties – information on shape distribution is needed. In cases of overall isotropy, the replacement is possible in certain cases; even in these cases, however, the aspect ratio of the “average shape” may not be intuitively obvious.     

Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

The propagation of oscillatory waves through periodic elastic composites has been analysed on the basis of the Floquet theory. This leads to self-adjoint differential equation systems which it was proved convenient to solve by variational methods. Many composites, such as the light-weight high-strength boron-epoxy material, consist of strong reinforcing components in a plastic matrix. The latter can exhibit viscoelastic properties which can have a significant influence on wave propagation characteristics. Replacement of the elastic constant by the viscoelastic complex modulus changes the mathematical structure so that the differential equation system is no longer self-adjoint. However, a modification of the variational principles is suggested which retains formal self-adjointness, and yields variational principles which contain additional boundary terms. These are applied to the determination of wave speeds and mode shapes for a laminated composite made of homogeneous elastic reinforcing plates in a homogeneous viscoelastic matrix for plane waves propagating normally to the reinforcing plates. These results agree well with the exact solution which can be evaluated in this simple case. The variational principles permit solutions for periodic, but otherwise arbitrary variation of material properties.     

轻质多层热防护结构的一体化优化设计研究

大面积防热结构在航天航空领域应用广泛, 其创新结构设计是关键技术之一. 航天飞行器的工作条件要求热防护材料与结构同时具备轻质、隔热、抗冲击的特点, 因此热防护材料与结构正在朝着一体化的方向发展. 基于这种发展趋势, 提出了一种轻质多层热防护结构设计方案. 以一体化多层防热结构在航天器再入过程中的传热为研究对象, 引入大面积防热结构的一维传热假设, 依照航天器再入大气层的温度条件, 建立了防热结构一维非稳态传热的物理模型和封闭的控制方程, 使用差分方法求解方程, 进行一维非稳态的传热分析, 并采用商业有限元软件ABAQUS的传热分析进行验证. 得到了航天器再入大气过程中多层防热结构的各层温度分布, 提出了在满足一定的热约束要求的条件下, 以轻质多层热防护结构的总重量为目标函数的优化设计方法, 得到了多层结构的最优几何参数, 并将优化后的结构进行了有限元承载分析.      

Inverse doubly periodic problem of the theory of bending of a plate with elastic inclusions

Based on the balanced strength principle, a problem of determining the optimal interference for fitting elastic inclusions into holes of an isotropic elastic plate weakened by a doubly periodic system of circular holes is solved. A closed system of algebraic equations is derived, which allows solving this problem. The resultant interference increases the load-carrying capacity of the composite plate being bent. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 153–161, July–August, 2006.     

Investigation of mechanically attrited structures induced by repeated impacts on an AISI1045 steel

Under repeated impact loadings – shot peening process, surface mechanical attrition treatment, erosive wear – metallic surfaces undergo severe plastic deformation which leads sometimes to a local change of their microstructure. These mechanically attrited structures (MAS) exhibit very interesting physical properties: high hardness, better tribological properties, etc. Consequently it is of primary importance to understand the mechanism explaining how these MAS are created and grow under such loadings. In this article, this mechanism is investigated with the help of a coupled experimental and finite element approach. First, the MAS are generated on an AISI1045 steel with a micro-impact tester which allows to know the impact energy and the location of impacts with a very good accuracy. The evolution of the MAS shape as a function of the impact number is presented. Then, the finite element investigation is presented. It is shown that a macroscopic stabilized elastic regime is reached after one hundred impacts. It also appears that a close cycle of plastic strain is observed locally in the zone where material transformation should happen during this regime. The severe plastic deformation achieved after a given number of cycles may thus explain the material transformation. Based on these results, we propose a mechanism based on a plastic strain threshold to explain the growth of the MAS. The resulting MAS size and shape appear to be in very good agreement with the experimental results. Finally, we conclude on the influence of the mechanical parameters that are involved in the proposed mechanism.     

Stability of a flexible insert in one wall of an inviscid channel flow

A hybrid of computational and theoretical methods is extended and used to investigate the instabilities of a flexible surface inserted into one wall of an otherwise rigid channel conveying an inviscid flow. The computational aspects of the modelling combine finite-difference and boundary-element methods for structural and fluid elements respectively. The resulting equations are coupled in state-space form to yield an eigenvalue problem for the fluid–structure system. In tandem, the governing equations are solved to yield an analytical solution applicable to inserts of infinite length as an approximation for modes of deformation that are very much shorter than the overall length of the insert. A comprehensive investigation of different types of inserts – elastic plate, damped flexible plate, tensioned membrane and spring-backed flexible plate – is conducted and the effect of the proximity of the upper channel wall on stability characteristics is quantified. Results show that the presence of the upper-channel wall does not significantly modify the solution morphology that characterises the corresponding open-flow configuration, i.e. in the absence of the rigid upper channel wall. However, decreasing the channel height is shown to have a very significant effect on instability-onset flow speeds and flutter frequencies, both of which are reduced. The channel height above which channel-confinement effects are negligible is shown to be of the order of the wavelength of the critical mode at instability onset. For spring-backed flexible plates the wavelength of the critical mode is much shorter than the insert length and we show very good agreement between the predictions of the analytical and the state-space solutions developed in this paper. The small discrepancies that do exist are shown to be caused by an amplitude modulation of the critical mode on an insert of finite length that is unaccounted for in the travelling-wave assumption of the analytical model. Overall, the key contribution of this paper is the quantification of the stability bounds of a fundamental fluid–structure interaction (FSI) system which has hitherto remained largely unexplored.     

The plastica: The large elastic-plastic deflection of a strut

An extension of the theory of the Elastica is developed to determine the shape of a strut (or a cantilever) which undergoes large plastic deflection. The equations governing such a behaviour and known as the Plastica equations are set up and then solved by a perturbation method and by numerical integration. The post-buckling elastic-plastic deformation of a strut after initial elastic buckling is analysed, and some numerical results are given to show the variation of its load-carrying capacity with the development of the plastic region.     

Photoelastic analysis of I-beams with elliptic-type web cutouts

An investigation of the fully plastic load-carrying capacity of aluminum-alloy I-beams with web cutouts leads to an interest in the elastic stress distribution for these cutouts. The photoelastic procedure was used to evaluate the elastic stress distribution at the surface of the web cutouts. The shear-difference method was used to establish the probable location of the fully plastic hinges which might be expected to form in the aluminum-alloy prototype. The data obtained were in good agreement with experimental results obtained on aluminum-alloy I-beams.     

The stability and load-carrying capacity of incomplete shells

The survey is devoted to problems on the stability and load-carrying capacity of imperfect shells in a nonhomogeneous stress-strain state. Methods recently developed at the Institute of Mechanics (Kiev, Ukraine) are briefly described. The approaches proposed are based on the generalized Euler criterion. Special attention is focused on numerical methods. The stability and load-carrying capacity of shells with symmetric and asymmetric, local and regular imperfections are considered. The data presented are compared with the well-known theoretical results and experimental data. At the end of the review, an analytical method (of reduced stiffness) is presented for predicting the lower bounds of sensitivity to imperfection in elastic buckling of longitudinally compressed stiffened shells with a nearly cylindrical shape. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 36–59, July, 2000.