平面滑动型岩质边坡稳定性极限分析上限法

在极限分析理论框架体系的基础上,提出了平面滑动型岩质边坡极限分析上限法。该方法按照外力所做的功率等于内力所消耗的功率,即滑体处于极限状态时两功率相等的条件——虚功率方程,综合考虑作用在岩质边坡上的后缘裂缝静水压力、沿滑面扬压力、重力、水平地震作用力、锚固力等外力,按照强度折减法,推导得出了岩质边坡稳定性评价的极限分析上限解。锦屏一级水电站右岸泄洪洞引渠内侧工程边坡属于典型的多级台阶状岩质高边坡,该边坡岩体结构为层状结构,变形破坏模式为平面滑动。对引渠内侧岩质边坡稳定性分析结果表明,极限分析上限法对平面滑动型岩质边坡有较好的适用性。     

Generalized limit analysis in poroplasticity by mathematical programming

Classical limit analysis of structures by the statical approach computationally means maximization of a load multiplier under equilibrium and yield condition constraints, namely convex mathematical programming. In elastoplasticity, generalizations of limit analysis had been proposed in order to achieve, still by load factor constrained optimization, the safety factor with respect to plastic collapse. This paper presents similar generalization in two-phase poroelastoplasticity. A method is here developed (and validated by numerical application to a masonry dam) apt to assess the safety factor of a structure interpretable as a poroplastic system, with respect to both plastic collapse and critical thresholds on deformations, by solving a nonconvex nonsmooth constrained optimization problem usually referred to in the literature as “mathematical program under equilibrium constraints”. Piece-wise linearization of yield surfaces and reduction of yield planes by a “sifting” procedure are adopted to reduce computing efforts.     

A hybrid numerical approach to predict the vibrational responses of panels excited by a turbulent boundary layer

In this work, a hybrid numerical approach to predict the vibrational responses of planar structures excited by a turbulent boundary layer is presented. The approach combines an uncorrelated wall plane wave technique with the finite element method. The wall pressure field induced by a turbulent boundary layer is obtained as a set of uncorrelated wall pressure plane waves. The amplitude of these plane waves are determined from the cross spectrum density function of the wall pressure field given either by empirical models from literature or from experimental data. The response of the planar structure subject to a turbulent boundary layer excitation is then obtained from an ensemble average of the different realizations. The numerical technique is computationally efficient as it rapidly converges using a small number of realizations. To demonstrate the method, the vibrational responses of two panels with simply supported or clamped boundary conditions and excited by a turbulent flow are considered. In the case study comprising a plate with simply supported boundary conditions, an analytical solution is employed for verification of the method. For both cases studies, numerical results from the hybrid approach are compared with experimental data measured in two different anechoic wind tunnels.     

基于均匀化理论韧性复合材料塑性极限分析

运用细观力学中的均匀化方法分析了韧性复合材料的塑性极限承载能力.从反映复合材料细观结构的代表性胞元入手,将均匀化理论运用到塑性极限分析中,计算由理想刚塑性、Mises组分材料构成的复合材料的极限承载能力.运用机动极限方法和有限元技术,最终将上述问题归结为求解一组带等式约束的非线性数学规划问题,并采用一种无搜索直接迭代算法求解.为复合材料的强度分析提供了一个有效手段.     

Computational limit analysis of rigid-plastic bodies in plane strain

This paper deals with the computational methods for limit analysis of plane strain problems. The finite element mathematical programming formula (FE-MPF) for determining the upper bound load multiplier established by the authors earlier is adopted and modified for plane strain problems. The penalty method is used to impose the incompressibility constraint. The FE-MPF is solved by a direct iteration procedure without the need of a searching process. This algorithm is not sensitive to the volumetric locking effect. And it can be easily extended to the limit analysis of three dimensional problems. The results of numerical examples are satisfactory and show the stable convergency of the present algorithm.     

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.

     

Upper-bound limit analysis based on the natural element method

The natural element method (NEM) is a newly-developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic theorem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nonsmoothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.     

An algorithm for the shakedown analysis of plane frames

Summary A quite straightforward procedure for the shakedown analysis of plane frames is presented. Plastic deformability is assumed as due to the bending moment only and lumped in a finite number of sections of the structure. This procedure is also suitable for the limit analysis problems of frames.

---

Sommario Si propone un procedimento speditivo per il calcolo a shakedown di strutture intelaiate piane, sotto l'ipotesi di deformabilità plastica concentrata in sezioni isolate e dipendente dal solo momento flettente. Il procedimento è anche applicabile alla risoluzione di problemi di calcolo a rottura di telai.

     

A non‐iterative numerical approach for two‐dimensional viscous flow problems governed by the Falker–Skan equation

In this paper, a non‐iterative numerical approach for two‐dimensional laminar viscous flow over a semi‐infinite flat plane, governed by the Falkner–Skan equation is proposed. This approach can solve the non‐linear Falkner–Skan equation without any iteration and verifies that a direct numerical approach could be proposed even for non‐linear problems. Furthermore, this approach can also provide a family of iterative formulae, so that it logically contains traditional iterative techniques. Copyright © 2001 John Wiley & Sons, Ltd.     

水下航行体螺栓法兰连接结构可靠性分析

螺栓法兰连接结构中的摩擦、接触、间隙及预紧力等因素,会导致水下航行体结构在复杂载荷环境中出现非线性的动力学响应特性,甚至破坏连接结构.目前,常取指定时段内的各类内力最大值同时施加于连接结构进行可靠性分析,导致结构设计偏于保守.为解决此问题,本文基于随机水动力载荷作用下水下航行体结构内力响应数据,分析螺栓法兰连接结构在端面内力组合作用下的最大Mises应力,由此建立连接结构端面内力组合的极限状态面,利用最大熵方法开展螺栓法兰连接结构可靠性分析.为提高分析效率,根据连接结构端面各类内力在塑性极限状态面附近的线性相关性,提出以端面等效弯矩为指标的工程可靠性分析方法,并通过数值仿真分析对可靠性分析结果精度进行校核.     

Limit analysis of composite materials based on an ellipsoid yield criterion

Employing repeating unit cell (RUC) to represent the microstructure of periodic composite materials, this paper develops a numerical technique to calculate the plastic limit loads and failure modes of composites by means of homogenization technique and limit analysis in conjunction with the displacement-based finite element method. With the aid of homogenization theory, the classical kinematic limit theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. Based on nonlinear mathematical programming techniques, the finite element modelling of kinematic limit analysis is then developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the limit load of a composite is then obtained. The nonlinear formulation has a very small number of constraints and requires much less computational effort than a linear formulation. An effective, direct iterative algorithm is proposed to solve the resulting nonlinear programming problem. The effectiveness and efficiency of the proposed method have been validated by several numerical examples. The proposed method can provide theoretical foundation and serve as a powerful numerical tool for the engineering design of composite materials.     

An Eigenvalue Method for Calculation of Stability and Limit Cycles in Nonlinear Systems

In the calculation of periodic oscillations of nonlinear systems –so-called limit cycles – approximative and systematic engineeringmethods of linear system analysis are known. The techniques, working inthe frequency domain, perform a quasi-linearization of the nonlinear system,replacing nonlinearities by amplitude-dependent describing functions.Frequently, the resulting equations for the amplitude and frequency ofpresumed limit cycles are solved directly by a graphical procedure in aNyquist plane or by solving the nonlinear equations or a parameteroptimization problem. In this paper, an indirect numerical approach isdescribed which shows that, for a system of nonlinear differentialequations, the eigenvalues of the quasi-linear system simply indicateall limit cycles and, additionally, yield stability regions for thelinearized case. The method is applicable to systems with multiplenonlinearities which may be static or dynamic. It is demonstrated foran example of aircraft nose gear shimmy dynamics in the presence ofdifferent nonlinearities and the results are compared with those fromsimulation.     

Influence of splices on the buckling of columns

The paper presents a procedure for the analysis of stability and initial post-buckling behaviour of spliced columns in sway and non-sway steel frames. The main assumptions are linear elasticity and geometrically perfect columns that are loaded by a compressive force which retains its direction as the column deflects. An energy-based formulation that includes a polynomial Rayleigh–Ritz approximation into the potential energy function, in combination with the Lagrange’s method of undetermined multipliers, has been found very convenient for this type of problem. The system is thus described by a set of kinematically admissible generalized coordinates and a single loading parameter. First, the critical state is characterized by means of linear eigenvalue analysis. A parametric study is implemented to assess the critical load. The numerical results are used to develop a relatively simple yet reasonably accurate engineering method for predicting the critical behaviour of spliced columns in sway and non-sway steel frames. The energy formulation is then applied to the search of post-buckling branches of bifurcation points. The approach embraces path-following methods based on perturbation schemes built on a Newton type iterative procedure. This is illustrated in the application to post-bifurcation in columns with different splice mechanical characteristics. The findings suggest that the splice tangent stiffness has a major influence on the overall column behaviour.     

Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations

Most of the currently employed vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from dynamic response measurements, and strictly speaking, are only suitable for linear system. However, the inception and growth of damage in engineering structures under severe dynamic loadings are typical nonlinear procedures. Consequently, it is crucial to develop general structural restoring force and excitation identification approaches for nonlinear dynamic systems because the restoring force rather than equivalent stiffness can act as a direct indicator of the extent of the nonlinearity and be used to quantitatively evaluate the absorbed energy during vibration, and the dynamic loading is an important factor for structural remaining life forecast. In this study, based on the instantaneous state vectors and partially unknown excitation, a power series polynomial model (PSPM) was utilized to model the nonlinear restoring force (NRF) of a chain-like nonlinear multi-degree-of-freedom (MDOF) structure. To improve the efficiency and accuracy of the proposed approach, an iterative approach, namely weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), where a weight coefficient and a learning coefficient were involved, was proposed to identify the restoring force of the structure as well as the unknown dynamic loadings simultaneously. The response measurements of the structure, i.e., the acceleration, velocity, and displacement, and partially known excitations were utilized for identification. The feasibility and robustness of the proposed approach was verified by numerical simulation with a 4 degree-of-freedom (DOF) numerical model incorporating a nonlinear structural member, and by experimental measurements with a four-story frame model equipped with two magneto-rheological (MR) dampers mimicking nonlinear behavior. The results show the proposed approach by combining the PSPM and WAILSE-IME algorithm is capable of effectively representing and identifying the NRF of the chain-like MDOF nonlinear system with partially unknown external excitations, and provide a potential way for damage prognosis and condition evaluation of engineering structures under dynamic loadings which should be regarded as a nonlinear system.     

损伤识别一种改进的残余力向量法

提出了一种改进的残余力向量法用于工程结构损伤识别.分析了利用结构有限元模型缩聚技术给残余力向量法所造成的误差,提出了一种改进的残余力向量法.以平面桁架结构为算例,比较了改进方法与原方法的损伤识别结果.结果表明,改进的方法合理可靠、精度高.     

A direct approach for continuous topology optimization subject to admissible loading

In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load. A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.     

平面刚架弹塑性大位移分析的多刚体离散元法

本文基于多刚体－弹簧系统模型，给出了求解平面刚架结构弹塑性、大位移极限承载力分析的多刚体离散元法。文中首先推导了多刚体离散元法在总体坐标下的切线刚度阵，建立多刚体离散元法的增量平衡方程；而后推导了多刚体离散元的弹塑性弹簧系数矩阵，建立了多刚体离散元内力屈服面塑性铰法的增量求解格式，成功地进行了平面钢框架的弹塑性、大位移极限承载力分析。计算结果与其他数值方法或实验结果吻合良好，显示了多刚体离散元方法进行结构极限承载力分析这一复杂问题的优越性     

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work, the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is estab-lished to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method (FEM). The convergent stresses have good agreements with those results obtained by three dimensional (3D) FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kan-torovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.     

Structure and stability of non-adiabatic reverse smolder waves

The structure and stability of non-adiabatic reverse smolder waves are investigated numerically. First, the 1D steady-state responses of reverse smolder waves in the presence of convective heat losses are studied with the rate of incoming air flow as the control parameter. Based on the 1D steady solutions, the linear stability and the Lewis number effects on the stability are examined by a numerical normal mode analysis. Finally, the dynamical evolution processes of unstable reverse smolder waves are studied by direct numerical simulations. It is shown that, in comparison with the adiabatic case, the presence of heat losses leads to a backward shift of the extinction limit. For varying Lewis numbers, the extinction limit shifts forward with the increase of the Lewis number while the smolder temperature remains unchanged. Furthermore, results of a linear stability analysis show that the maximum growth rate decreases with the increasing Lewis number, implying that increasing the Lewis number tends to weaken the thermal-diffusive instability of non-adiabatic reverse smolder waves. Direct numerical simulation results show that, on the fuel-rich branch, the unstable plane reverse smolder wave gradually develops to a regular steady fingering pattern, whereas on the fuel-lean branch, similar to the adiabatic case, vigorous fragmentation instability occurs, and is accompanied by a substantial local temperature rise, which may be sufficiently high to trigger the transition to flaming combustion.     

Shear to longitudinal mode conversion via second harmonic generation in a two-dimensional microscale granular crystal

Shear to longitudinal mode conversion via second harmonic generation is studied theoretically and computationally for plane waves in a two-dimensional, adhesive, hexagonally close-packed microscale granular medium. The model includes translational and rotational degrees of freedom, as well as normal and shear contact interactions. We consider fundamental frequency plane waves in all three linear modes, which have infinite spatial extent and travel in one of the high-symmetry crystal directions. The generated second harmonic waves are longitudinal for all cases. For the lower transverse–rotational mode, an analytical expression for the second harmonic amplitude, which is derived using a successive approximations approach, reveals the presence of particular resonant and antiresonant wave numbers, the latter of which is prohibited if rotations are not included in the model. By simulating a lattice with adhesive contact force laws, we study the effectiveness of the theoretical analysis for non-resonant, resonant, and antiresonant cases. This work is suitable for the analysis of microscale and statically compressed macroscale granular media, and should inspire future studies on nonlinear two- and three-dimensional granular systems in which interparticle shear coupling and particle rotations play a significant role.