Nonlinear finite element reliability analysis of Concrete-Faced Rockfill (CFR) dams under static effects

The response of concrete slab on Concrete-Faced Rockfill (CFR) dams is very important. This study investigates the reliability of the concrete slab on a CFR dam by the improved Rackwitz–Fiessler method under static loads. For this purpose, ANSYS finite element analysis software and FERUM reliability analysis program are combined with direct coupled method and response surface method. Reliability index and probability of failure of the concrete are computed in the all critical points of the concrete slab by dam height. This study is also expanded for the reliability of CFR dams including different concrete slab thickness. In addition to the linear behavior, geometrically and materially non-linear responses of the dam are considered in the finite element analysis which is performed with reliability analysis. The Drucker–Prager method and the multi linear kinematic hardening method are, respectively, used for concrete slab and for rockfill and foundation rock. Finite element model used in the analyses includes dam–reservoir–foundation interaction. Reservoir water is modeled by the Lagrangian approach. Welded and friction contact based on the Coulomb’s friction law are considered in the joints of the dam. One-dimensional two noded contact elements are used to define friction. The self-weight of the dam and the hydrostatic pressure of the reservoir water are considered in the numerical solutions. According to this study, hydrostatic pressure, nonlinear response of the rockfill and the decrease in the concrete slab thickness reduce the reliability of the concrete slab of the CFR dam. Besides, the CFR dam models including friction are safer than the models including welded contact in the joints.     

结构可靠性分析的支持向量机方法

针对结构可靠性分析中功能函数不能显式表达的问题,将支持向量机方法引入到结构可靠性分析中．支持向量机是一种实现了结构风险最小化原则的分类技术,它具有出色的小样本学习性能和良好的泛化性能,因此提出了两种基于支持向量机的结构可靠性分析方法．与传统的响应面法和神经网络法相比,支持向量机可靠性分析方法的显著特点是在小样本下高精度地逼近函数,并且可以避免维数灾难．算例结果也充分表明支持向量机方法可以在抽样范围内很好地逼近真实的功能函数,减少隐式功能函数分析（通常是有限元分析）的次数,具有一定的工程实用价值．     

Dynamic inversion method for the material parameters of a high arch dam and its foundation

The overall mechanical behavior of the structure of an arch dam is comprehensively reflected by the vibration modal information included in measured vibration response. Hence, the results obtained from inverting material parameters based on measured vibration data are often superior to those based on static monitoring data. In this study, a dynamic inversion method for the material parameters of a high arch dam and its foundation is proposed on the basis of the measured vibration response. First, an arch dam prototype test is conducted to obtain the measured dynamic displacement response as input. Then, a stochastic subspace identification method based on singular entropy is formulated to determine the modal parameters. Second, a dynamic elastic modulus (DEM) with a great influence on the modal parameters is selected as the material parameter to be inverted. Then, a response surface model (RSM), which reflects the nonlinear relationship between the material and modal parameters of each zone, is constructed. Latin hypercube sampling is used to generate the sample library of the DEM. The RSM is fitted by modal parameters calculated on the basis of the arch dam finite element model (FEM) and is applied to replace the FEM. Finally, the optimization mathematical model of the inversion of the DEM is established. Then, the objective function is optimized through a genetic algorithm, and the optimal combination of the DEM in each zone is inverted. The modal parameters of the arch dam calculated by inversion results are consistent with those measured by variation law and values. Therefore, the inversion results are reasonable and reliable. This method provides a new idea for determining the material parameters of a high arch dam and its foundation during the operation period.     

Crankshaft-bearing evolution indexes investigation and asperity contact identification based on neural network

The dynamic and lubrication characteristic analyses of the crankshaft–bearing system is quite a complex problem, and it is important to avoid asperity contact which may lead to bearing wear and increase of friction loss significantly in dynamic lubrication condition. In this paper, the dynamic characteristic that has an essential impact on lubrication was investigated over an inline six-cylinder engine. Multi-body dynamics method, tribology, finite element method (FEM), finite difference method (FDM) and component mode synthesis method (CMS) were combined to analyze the dynamic characteristic of crankshaft, oil leakage, oil film pressure, asperity contact pressure and friction loss. Then the orthogonal experiment that included 5 levels and 6 factors was conducted to obtain the training sample sets for neural network, and the probabilistic neural network (PNN) was employed to identify weather the asperity contact happened or not according to its nonlinear characteristic. The analyses which can provide the guidance for the design of main bearing, and avoid the asperity contact in the lubrication are significant to the design of the bearing at the development stage of the engine.     

Non-linear seismic response of concrete gravity dams to near-fault ground motions including dam-water-sediment-foundation interaction

This study focuses on non-linear seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. The elasto-plastic behavior of the dam concrete is idealized using Drucker–Prager yield criterion based on associated flow rule assumption. Water in the reservoir is represented by 9-noded isoparametric quadrilateral fluid finite elements while the dam, the foundation rock and the sediment layer are modeled by using 8-noded isoparametric quadrilateral solid finite elements. The program NONSAP modified for elasto-plastic analysis of fluid-structure systems using the Lagrangian fluid finite element is employed in the response calculations. The fluid element includes the effects of surface waves and sloshing behavior of fluids. Non-linear seismic analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from linear and non-linear analyses are compared with each other.     

Surface Deformation due to Shear and Ploughing in a Halfspace

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robustness of mechanical systems against uncertainties

In this paper, one can propose a method which takes into account the propagation of uncertainties in the finite element models in a multi-objective optimization procedure. This method is based on the coupling of stochastic response surface method (SRSM) and a genetic algorithm provided with a new robustness criterion. The SRSM is based on the use of stochastic finite element method (SFEM) via the use of the polynomial chaos expansion (PC). Thus, one can avoid the use of Monte Carlo simulation (MCS) whose costs become prohibitive in the optimization problems, especially when the finite element models are large and have a considerable number of design parameters.The objective of this study is on one hand to quantify efficiently the effects of these uncertainties on the responses variability or the cost functions which one wishes to optimize and on the other hand, to calculate solutions which are both optimal and robust with respect to the uncertainties of design parameters.In order to study the propagation of input uncertainties on the mechanical structure responses and the robust multi-objective optimization with respect to these uncertainty, two numerical examples were simulated. The results which relate to the quantification of the uncertainty effects on the responses variability were compared with those obtained by the reference method (REF) using MCS and with those of the deterministic response surfaces methodology (RSM).In the same way, the robust multi-objective optimization results resulting from the SRSM method were compared with those obtained by the direct optimization considered as reference (REF) and with RSM methodology.The SRSM method application to the response variability study and the robust multi-objective optimization gave convincing results.     

Application of fuzzy sets to transient analysis of space structures

An application of fuzzy sets, in conjunction with finite elements, to the transient analysis of a precision-deployable space structure is presented. The structural members are modeled by using beam finite elements, and the structure's latch joint is modeled by using a spring–damper–Coulomb friction element. Two types of transient response simulations are performed: slow transient load–deflection response and transient impulse response. The first simulation is used to evaluate the stiffness and buckling loads at the structure's tip. The second simulation is used to evaluate the structure's natural frequencies, mode shapes and the precision of the final shape. For each simulation the possibility distributions of various response quantities are obtained. Fuzzy sets are used to represent three beam properties, namely: damping coefficient, bending stiffness, and axial stiffness; as well as two joint parameters: Coulomb friction force and damping coefficient. Fuzzy set techniques provide an insight into the range of possible responses associated with the combined selected variations in the system parameters.     

Analysis of lumped models with contact and friction

We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction. In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions. In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples of systems with contact and friction conditions for which our results are valid.     

The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters

This paper investigates the variability of dynamic responses of a beam resting on an elastic foundation, which is subjected to a vehicle with uncertain parameters, such as random mass, stiffness, damping of the vehicle and random fields of mass density, and the elastic modulus of the beam and stiffness of elastic foundation. The vehicle is modeled as a two-degree-of-freedom spring-damper-mass system. The equations of motion of the beam was constructed using a finite element method. The mass and elastic properties of the beam, and the stiffness of foundation are assumed to be Gaussian random fields and were simulated by the spectral represent method. Masses, stiffness of the spring, and the damping coefficient of the vehicle are assumed as Gaussian random variables. The numerical analyses were performed using the finite element method (FEM) in conjunction with the Monte Carlo simulation (MCS). The variability of dynamic responses of the beam were investigated with various cases of random parameters. For each sample, the equations of motions were solved with the Wilson-q integral method to find dynamic responses. The influence of random system parameters and their correlation on the response variability is discussed in detail.     

Numerical modelling and analysis of high frequency dynamic contact in the hybrid transducer type ultrasonic motor

The finite element model for describing the intermittent contact dynamics between the stator and the rotor of a hybrid transducer type piezoelectric ultrasonic motor is presented. The contact simulations are performed using an augmented Lagrangian method to determine the normal contact force, the interface condition between the stator and the rotor as dependency of the other factors such as pre-load force on the stator, the thickness of friction layer, the electrical driving voltage and the operational frequency of the stator. Effects of friction layer, both for elastic and viscoelastic frictional materials, are numerically investigated. The numerical results provide some aspects to make the impact that may occur between the contact interface pairs effectively softer. Furthermore, the noncontact phase between the stator and the rotor of this kind of piezoelectric ultrasonic motor will also be optimized. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottementFinite element method with Lagrange multipliers for contact problems with friction

In this Note, we propose a finite element method with Lagrange multipliers in order to approximate contact problems with friction. The discretized normal and tangential constraints at the candidate contact interface are expressed by using continuous piecewise linear Lagrange multipliers in the saddle-point formulation. An optimal error estimate is established and several numerical studies corresponding to this choice of the discretized normal and tangential constraints are achieved. To cite this article: L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.     

Parameter identification based on FE‐models by genetic algorithms

A realistic and reliable model is an important precondition for the simulation of revitalization tasks as well as for the estimation of properties of existing buildings. Within one theory the parameters of the model should be approximated best by gradually performed experiments and their analysis. Usually this kind of optimization problems leads into non‐convex non‐differentiable objective function spaces with high dimensions. Normally ore complex structures are modeled using finite element method. We present a method of identifying Young's modulus for a beam and a plate by using FE‐models and genetic optimization algorithms for parameter identification.     

Finite element solution of nonlinear diffusion problems

In this paper we describe the Rothe-finite element numerical scheme to find an approximate solution of a nonlinear diffusion problem modeled as a parabolic partial differential equation of even order. This scheme is based on the Rothe’s approximation in time and on the finite element method (FEM) approximation in the spatial discretization. A proof of convergence of the approximate solution is given and error estimates are shown.     

Multiscale Rubber Friction Analysis on Rough and Flexible Surfaces

In this work, a multiscale homogenization approach is introduced to provide friction features between rubber and rough contact partners. Different length scales of the rough surface are considered by using a decomposition of the height difference correlation (HDCF) or the power spectral density function (PSDF) in several sinusoidal waves to accumulate the micro- and mesoscopic friction into a macroscopic friction coefficient. By using the finite element method (FEM), the sensitivity of the influencing factors for instance slip velocity and contact pressure may be investigated for rigid and flexible surfaces in the two- and the three-dimensional case. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类抛物型方程组的特征修正区域分解有限元方法

在实际生产和科学研究中,有许多物理问题的数学模型为抛物型方程组问题,如可压缩核废料污染问题,地下水资源问题,杨青提出了差分格式和有限元格式,应用先验估计得到了最优的l^2和L^2模误差估计,江城顺等利用交替方向有限元方法得到了H^1模和L^2模误差估计．杨国强等采用显式可解的三层差分格式求解二维方程组得到了H^1模误差估计．     

Damage analysis of arch concrete dams subjected to underwater explosion

The nonlinear behavior of arch concrete dams subjected to underwater explosions was investigated. Pressure waves were spherically modeled using a 3-D finite element method. The nonlinear behavior of concrete was modeled using the concrete damage plasticity model. In addition, absolute wave formulation was used to develop a fully-coupled model incorporating the propagation of the shock wave and water–dam interaction. Analysis of an arch concrete dam subject to underwater explosion was performed upon model verification. The dynamic response of the dam subject to the underwater explosion was studied for different sizes of explosions at different depths. The results showed that the closer the point to the explosive source, the sooner the impression and damage was caused by the blast. It was clear that the middle part of the dam facing the explosion was the first location to incur damage and then cracks extended to the downstream face and abutments. Finally, cracks extended to the bottom of the dam. The results of the dynamic analysis and dissipated energy by the loss of elements’ resistance indicated that the time slice of 150 ms was appropriate to analyze arch concrete dam structure subject to an underwater explosion. In addition, for a given amount of explosives, an increase in the depth of explosion corresponded to an increase in the maximum displacement of the upstream face of the dam. The results also confirmed that the damage distribution to the arch concrete dam subject to an underwater explosion depended upon the amount and depth of explosive materials.     

Dynamic responses to sinusoidal excitations of beams with frictional joints

We consider the dynamic responses of a beam with a frictional joint. The frictional force at the joint is modeled using the Coulomb friction model. The frictional force at the joint makes the nature of the boundary conditions at the joint uncertain. Therefore, this problem represents a type of nonlinear problems where the boundary conditions are coupled to the solutions. Using numerical integration of the resulting differential equations obtained by combining the finite element method and the Lagrange equations, we study the steady-state solutions of the system to sinusoidal excitations. We explore the dependence of the system responses to various parameters including the frictional force, the forcing frequency and the forcing amplitude. A result of special interest is the existence of an optimum friction force if the frictional joint is used to control the system response amplitude. We also examine the ways that friction affects the resonance frequency of the structure. Experiments are carried out, which agree qualitatively with the numerical results.     

Finite element analysis of a static contact problem with Coulomb friction

A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.     

Accurate modeling of contact using cubic splines

In this paper, we develop and implement a new method for the accurate representation of contact surfaces. This approach overcomes the difficulties arising from the use of traditional node-to-linear surface contact algorithms. In our proposed method, contact surfaces were modeled accurately using C¹-continuous cubic splines, which interpolate the finite element nodes. In this case, the unit normal vectors are defined uniquely at any point on the contact surfaces. These splines preserve the local deformation of the nodes on each flexible contact surface. Consequently, a consistent linearization of the kinematic contact constraints, based on the spline interpolation, was derived. Moreover, the gap between two contact surfaces was modeled accurately using an efficient surface-to-surface contact search algorithm. Since the continuity of the splines is not affected by the number of nodes, accurate stress distribution can be obtained with less finite elements at the contact surface than that using the traditional linear discretization of the contact surface. Two numerical examples are used to illustrate the advantages of the proposed representation. They show a significant improvement in accuracy compared to traditional piecewise element-based surface interpolation. This approach overcomes the problem of mismatch in a finite element mesh. This is very useful, since most realistic engineering problems involve contact areas that are not known a priori.