Método de estrato finito para muros de retención con cimentación flexible ante excitación sísmica

A finite layer method for evaluation of the effects of seismic action on retaining walls is presented, which is based on the wave propagation theory and modal superposition. The system is defined by a rigid wall supported on an elastic stratum, with capacity of sliding and overturning of the base. With this model, the foundation flexibility as well as the energy dissipation by wave radiation is considered. It is demonstrated with numerical results that the magnitude of pressures on the wall depends on its movement capacity.     

Instability in the critical case of pair of pure imaginary roots for a class of systems with aftereffect

The stability of a system described by Volterra integrodifferential equations is investigated in the critical case when the characteristic equation has a pair of pure imaginery roots. Conditions for instability, analogous to the well-known conditions from the theory of differential equations [1], are derived. (A similar result was established previously in [2] for integrodifferential equations of simpler structure with integral kernels of exponential-polynomial type). For the proof, several manipulations are used to simplify the original equation and, in particular, to reduce the linearized equation to the form of a differential equation with constant diagonal matrix. (An analogous approach was used to analyse instability for Volterra integrodifferential equations in the critical case of zero root in [3, 4]). As an example, the sign of the Lyapunov constant in the problem of the rotational motion of a rigid body with viscoelastic supports is calculated.     

Reliability based limit analysis of steel frames with limited residual strain energy capacity

The main structural elements of steel framed multi–storey structures are the columns, the beams and their connectionsmagenta, which can be considered rigid, pinned or semi–rigid. The aim of this paper is to analyze the effect of the semi–rigid connections on the limit analysis of steel structures under multi–parameter static loading where to control the plastic behavior of the structure a bound on the complementary strain energy of the residual forces is applied. The bound value is assumed to be uncertain and is modelled by a random variable. By the use of this constraint a reliability based problem formulation is constructed. The formulation of the problem yields a nonlinear mathematical programming with a nested algorithm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

不同类型近破波作用下沉箱式防波堤的振动-提离摇摆运动

倾覆失稳是沉箱式防波堤的主要破坏形式之一,是稳定性验算的基本内容．采用质量-弹簧-阻尼器集总参数模型模拟沉箱式防波堤在单峰值冲击型、双峰值冲击型和冲击-振荡衰减型等不同类型近破波作用下的振动-提离摇摆运动过程,研究了不同类型近破波和沉箱的提离摇摆运动对沉箱式防波堤动力响应的影响．结果表明,在近破波冲击力幅值相同的条件下,近破波类型对沉箱的动力响应影响很大;提离摇摆运动虽然会使沉箱的转角幅值增大,但可有效地减小沉箱的位移、滑移力和倾覆力矩幅值．研究成果为允许沉箱式防波堤出现提离摇摆运动的设计概念提供了理论基础．     

Flow Past a Swept Wing with a Compliant Surface: Stabilizing the Attachment-Line Boundary Layer

Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier–Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien–Schlichting modes in the classical boundary-layer flow past a compliant surface.     

Oscillations of one-dimensional linear systems with mobile weights under the action of longitudinal impacts : PMM vol. 42, no. 6, 1978, pp. 1141–1145

Longitudinal osciallations of a one-dimensional system which can be represented by a rod interacting with various kinds of inertial mobile media, are considered. It is assumed that the media do not react with each other, can only move along the rod and, that there is no internal interaction between the elements of the media. The model can be used to study the oscillations of sufficiently long chains of rigid bodies to which other mobile bodies are attached by means of deformable elements, oscillations of one-dimensional systems of rigid bodies with cavities partially filled with fluid, etc. A transitional mode of motion in similar systems was studied in [1].     

Solution of Dynamic Deformation Problems for Prestressed Laminated Plates Based on the Three-Dimensional Theory of Elasticity

A three-dimensional analytical solution describing forced harmonic vibrations of prestressed laminated plates is found for the case of a hinged support. The solution is based on the analytical separation of variables. It is assumed that the prestressed state is homogeneous, subcritical, linear, and momentless and that the vibration amplitudes are small. A solution based on a model with a polynomial approximation of the required displacement functions across the plate thickness is also considered. These functions are found on the front surfaces of the structure. This allows us to solve the problem both in the continuous and discrete structural approaches. In the continuous structural approach, the order of the resolving system of equations is independent of the number of layers. In the discrete structural approach, for rigid contact of layers with similar boundary conditions at the plate end face, an algorithm can be introduced which reduces significantly the number of operations required for realization of the model proposed. In the numerical examples presented, both rigid and sliding contacts of layers and various prestressed conditions are considered. Both approaches give results that agree well.     

Modeling the dynamics of block-and-fault systems and seismicity

A model of block-and-fault system dynamics (a block model) has been developed to analyze how the basic features of seismicity depend on the lithosphere structure in a region under consideration and on the peculiarities of the lithosphere dynamics. The lithosphere in the region is modeled by a system of perfectly rigid blocks divided by infinitely thin fault planes. The viscoelastic interaction between the blocks and with the underlying medium is specified. Displacements and rotations of the blocks at each time are determined so that the whole block system is in a quasi-static equilibrium state. When the ratio of the stress to the pressure exceeds the critical level in some part of a fault zone, a stress drop occurs that is considered in the model as an earthquake. The paper contains a review of results obtained by numerical simulation of the dynamics of different block structures including the structures approximating the lithosphere structure in specific seismic regions. These results suggest that the block model is a useful tool for studying the influence of geometry of faults and motions of blocks on seismicity features.     

Strongly coupling of partitioned fluid–solid interaction solvers using reduced-order models

In this work a powerful technique is described which allows the implicit coupling of partitioned solvers in fluid–structure interaction (FSI) problems. The flow under consideration is governed by the Navier–Stokes equations for incompressible viscous fluids and modeled with the finite volume method. The structure is represented by a finite element formulation. The method allows the use of a black box fluid and structural solver because it builds up a reduced order model of the fluid and structural problem during the coupling process. Each solution of the fluid/structural solver in the coupling process can be seen as a sensitivity response of an applied displacement/pressure mode. The applied modes and their responses are used to build up a reduced-order model. The proposed model is used to predict the unsteady flow fields of a particular flow-induced vibrational phenomenon – a fixed cubic rigid body is submerged in an incompressible fluid flow (water), an elastic plate is attached to the rigid body in the centre of the downstream face, and the vortices, which separate from the corners of the rigid body upstream, generate lift forces which excite continuous oscillations of the elastic plate downstream. The computational results show that a fairly good convergence solution is achieved by using the reduced-order model that is based on only a few displacement and stress modes, which largely reduces the computational cost, compared with traditional approaches. At the same time, comparison of the numerical results of the model with available experimental data validates the methodology and assesses its accuracy.     

基于FLAC-3D砂岩块体超低摩擦鞭梢效应研究北大核心CSCD

随着矿山开采深度的持续增加,深部岩体力学行为呈现出新形式、新特征.广泛应用于建筑行业的鞭梢效应与深部岩体部分动力响应现象极为相似.故从结构特征出发,以砂岩块体为研究对象,工作块体(水平冲击作用块体)水平位移及加速度为参考指标,通过试验及FLAC-3D数值模拟计算的方式,探究工作块体“位置”及“尺寸”对其超低摩擦鞭梢效应影响机制.研究表明:系统产生超低摩擦鞭梢效应的难易程度与工作块体尺寸密切相关,模拟中工作块体边长为标准块体(边长100 mm立方体)边长2/5时,系统结构诱发超低摩擦鞭梢效应尤其显著;在一定范围内,工作块体所处位置距扰动源越远,超低摩擦鞭梢效应强度越大,当超过这一范围时,则会出现减小趋势,即超低摩擦鞭梢效应强度随工作块体与震源块体间距离呈先增后减关系.     

大范围运动刚体上矩形薄板力学行为分析

采用Hamilton变分原理建立了大范围运动平板的动力学模型．从理论上证明了不同大范围运动状态下平板中既可存在动力刚化效应,也可存在动力软化效应,且动力软化效应还可使板的平衡状态发生分岔而失稳．采用假设模态法验证了理论分析结果并得到了分岔临界值和近似后屈曲解．     

Stochastic orders of scalar products with applications

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma [Ma, C., 2000. Convex orders for linear combinations of random variables. J. Statist. Plann. Inference 84, 11-25], we first obtain more general conditions under which linear combinations of random variables can be ordered in the increasing convex order. As an application of this result, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. Finally, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. This application is a further study of Cheung [Cheung, K.C., 2007. Optimal allocation of policy limits and deductibles. Insurance: Math. Econom. 41, 382-391].     

Computational implementation of the rigid finite element method in the statics and dynamics analysis of forest cranes

A general mathematical model of a forest crane for statics and dynamics analysis is presented in the paper. This model allows to take into account the crane's flexible connections with the ground, the flexibility of its links and drives. The rigid finite element method is used to discretize the flexible links. Joint coordinates and homogeneous transformation matrices are used to describe the geometry of the system. Equations of motion are derived using the formalism of Lagrange equations. As an example, a forest crane built of eight links is presented. It is assumed that only one selected link of the crane is flexible. The influence of the flexibility of the link on the movements of load and driving torques in the revolute joints and the driving force in the prismatic joint are analyzed. The results may have practical significance, e.g. in terms of the selection of drives.     

Role of Pectoral Fin Flexibility in Robotic Fish Performance

Pectoral fins play a vital role in the maneuvering and locomotion of fish, and they have become an important actuation mechanism for robotic fish. In this paper, we explore the effect of flexibility of robotic fish pectoral fins on the robot locomotion performance and mechanical efficiency. A dynamic model for the robotic fish is presented, where the flexible fin is modeled as multiple rigid elements connected via torsional springs and dampers. Blade element theory is used to capture the hydrodynamic force on the fin. The model is validated with experimental results obtained on a robotic fish prototype, equipped with 3D-printed fins of different flexibility. The model is then used to analyze the impacts of fin flexibility and power/recovery stroke speed ratio on the robot swimming speed and mechanical efficiency. It is found that, in general, flexible fins demonstrate advantages over rigid fins in speed and efficiency at relatively low fin-beat frequencies, while rigid fins outperform flexible fins at higher frequencies. For a given fin flexibility, the optimal frequency for speed performance differs from the optimal frequency for mechanical efficiency. In addition, for any given fin, there is an optimal power/recovery stroke speed ratio, typically in the range of 2–3, that maximizes the speed performance. Overall, the presented model offers a promising tool for fin flexibility and gait design, to achieve speed and efficiency objectives for robotic fish actuated with pectoral fins.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

Modelling of coupled vibro-acoustic interactions in an active casing for the purpose of control

The aim of active casing is to reduce device noise generated to the acoustic environment by controlling vibrations of the walls of the device casing. The article concerns theoretical modelling of an active casing composed of six walls mounted to a rigid frame. The casing is considered as a complex coupled vibro-acoustic system, where the walls are excited by the acoustic field inside the casing, and by actuators bonded to the walls and used for active control. The acoustic field inside the casing is, in turn, formed by the noise originating from the device itself, and the secondary sound generated by all vibrating walls. The structure of such system is described in detail and, after being represented as interconnected subsystems, its state-space model is developed. The model includes fluid loading effect and imperfect fastening of wall edges to the frame. The system of coupled partial differential equations, subject to defined boundary conditions, is reformulated as an abstract first order evolution equation in an appropriate infinite dimensional function space. All assumptions and the structure of the model are chosen to make it useful for the purpose of control. In particular, the model can be used for analysis of controllability and observability of the whole casing as a vibro-acoustic system and, based on that, for optimisation of placement of actuators and structural sensors to efficiently reduce noise over required frequency band. On the basis of the obtained state equation, a block diagram of the system is constructed. It shows the structure of the whole system and the nature of interactions occurring between distinguished subsystems.     

Well‐posedness of the equations governing the motions of a one‐dimensional hybrid thermo‐elastic structure

In this paper a model for the vibrations of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end, with a rigid body attached to its free end, is studied with a view to establishing the existence of a unique solution in a weak sense. The model takes account of the effect of stretching on bending and rotational inertia. By treating eigenvalue problems with the spectral parameter also in the boundary conditions, we are able to employ the method of Faedo–Galerkin approximations. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of stability of the structural parameters of laminated reinforced plastics on their strength properties

Conclusion As a result of the completed analysis, we estimated the effect of scatter of the strength properties of the layers, instability of the layers' strain properties, and instability of the geometry of the structure on the strength properties of multidirectional LRP's in a plane stress state. It was established that instability of the structural parameters produces two negative tendencies: a reduction in the mean values of LRP strength and an increase in their scatter. From the viewpoint of ensuring the reliability of structures (structural elements) made of such materials, these tendencies reinforce one another and are thus even more dangerous. It follows from this that the production method employed should not only (or not even mainly) solve the problem of increasing the values of the parameters of the materials (and their semifinished structural elements), it should also address the problem of alleviating their instability — improving the quality of production.The numerical analysis established the limits at which it is necessary to account for instability of structural parameters in engineering calculations: for the strain properties of the layers — a coefficient of variation of the elastic modulus greater than 10%; for the scatter of the angles of orientation of the layers — a standard deviation greater than 5 °. These numerical results and the computer program developed may prove useful in evaluating the actual properties of structural parameters determined in indirect tests of LRP's, as well as in more adequately comparing empirical data with corresponding calculations based on structural theories. The development of such an approach to analyzing the strength properties of multidirectional LRP's in bending also holds promise.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 659–666, July–August, 1990.     

Equilibrium failure processes of granular composites

The macroscopic failure of inhomogeneous media results from damage accumulation on different structural levels. During rigid loading, when given displacements of boundary points are ensured, irrespective of the body's resistance, structural-failure processes of composite materials take place in an equilibrium regime and result in the manifestation of such nonlinear-behavior effects as a descending branch on the strain diagram. the structural elements of a granular composite are homogeneous and firmly connected along the interface. Their geometry and mutual arrangement are given and do not change during deformation and failure of the medium, and the medium itself is macrohomogenous. The strength of isotropic structural elementsis estimated by comparing the second invariant of the stress tensor with its critical value. Nonfulfillment of the indicated strength criterion is associated with loss of ability to resist changes in form; at this point, the positive value of the first invariant corresponds to loss of such ability to resist and increase in volume. The deformation and structural failure of the medium are investigated as a single process that can be described under quasi-static loading by a boundary problem consisting of a closed system of Eqs. (1) and (2) and boundary conditions providing for a macrohomogeneous strain state. A principal feature of the boundary problem under consideration is the possibility of considering in constitutive relationships the states of the inhomogeneous medium, which correspond to partial or complete loss of bearing capacity of the structural elements. The random structural strength constants correspond to three-parameter Weibull distribution (6). The representative volume of a granular composite, which fills a domain in the form of a cube, is modeled by a set of istropic elastobrittle strain diagrams containing a descending branch are obtained as a result of the mathematical modeling of deformation processes and structural failure to realized a representative volume containing 384 structural elements with different strength and similar elastic constants.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Perm'State Mechanical University, Russia. Translated From Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 808–817, November–December, 1996.     

Mitigating supply risk: an approach with quantity flexibility procurement

This paper considers a buyer that procures from its major supplier whose production is subject to random yield risk. To mitigate supply risk, the buyer can procure from another reliable supplier who provides quantity flexibility (QF) contract. Under both deterministic and stochastic demand, we study the buyer’s optimal procurement decisions. We analyze the structural properties of optimal solutions and identify the conditions under which the quantity flexibility procurement policy should be used. We also examine the effect of supply risk, flexibility, wholesale price and demand risk on the procurement decisions. We find that the higher supply risk and demand risk reduce the buyer’s profit but have different impact on the buyer’s order policy. For the QF supplier, it may not obtain more orders by providing larger flexibility to the buyer, on the contrary, doing this may benefit the risky supplier. For the QF supplier or risky supplier, given its competitor’s wholesale price, it can increase its order share by lower wholesale price.