CAD-consistent adaptive refinement using a NURBS-based discontinuous Galerkin method

This study concerns the development of a new method combining high-order computer-aided design (CAD)-consistent grids and adaptive refinement/coarsening strategies for efficient analysis of compressible flows. The proposed approach allows to use geometrical data from CAD without any approximation. Thus, the simulations are based on the exact geometry, even for the coarsest discretizations. Combining this property with a local refinement method allows to start computations using very coarse grids and then relies on dynamic adaption to construct suitable computational domains. The resulting approach facilitates interactions between CAD and computational fluid dynamics solvers and focuses the computational effort on the capture of physical phenomena, since geometry is exactly taken into account. The proposed methodology is based on a discontinuous Galerkin method for compressible Navier-Stokes equations, modified to use nonuniform rational B-Spline representations. Local refinement and coarsening are introduced using intrinsic properties of nonuniform rational B-Spline associated with a local error indicator. A verification of the accuracy of the method is achieved and a set of applications are presented, ranging from viscous subsonic to inviscid trans- and supersonic flow problems.     

Numerical approximation of a degenerated non‐conservative multifluid model: relaxation scheme

The present work is devoted to the numerical approximation of a system which arises when modelling a two‐phase flow in a pipeline. Two particular difficulties are of special interest, the non‐conservativity and the weakly hyperbolicity of this system. Some elementary waves are characterized and a relaxation system, unconditionally hyperbolic, is proposed. The stability criteria of the resulting relaxation method are achieved by a Chapmann–Enskog‐like expansion. A numerical scheme based on the relaxation system is proposed and computations are performed on a shock tube. Validation is performed by comparison with the exact solution and also to the solution from a modified HLL scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization of characteristics of porous materials based on a modal synthesis method

Complex structures used in the automotive industry often include porous materials, in order to reduce the noise in acoustic cavities. The method proposed in this paper aims at optimizing the characteristics of these porous materials using modal criteria based on the modal analysis of the structure. The use of a generalize modal synthesis method allow to describe the structure and the cavities with sets of modes; the size of the resulting system is smaller, for only generalized degrees of freedom are used for each part of the coupled fluid–structure system. First, a modelization of the porous media is proposed, and the generalized modal analysis method is explained. An optimization is then processed on the thickness of the porous materials.     

One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: Generic formulation

This paper is the first in a series of two that focus on gradient elasticity models derived from a discrete microstructure. In this first paper, a new continualization method is proposed in which each higher-order stiffness term is accompanied by a higher-order inertia term. As such, the resulting models are dynamically consistent. A new parameter is introduced that accounts for the nonlocal interaction between variables of the discrete model and of the continuous model. When this parameter is set to proper values, physically realistic behavior is obtained in statics as well as in dynamics. In this sense, the proposed methodology is superior to earlier approaches to derive gradient elasticity models, in which anomalies in the dynamic behavior have been found. A generic formulation of field equations and boundary conditions is given based on Hamilton's principle. In the second paper, analytical and numerical results of static and dynamic response of the second-order model and the fourth-order model will be treated.     

A stable and accurate projection method on a locally refined staggered mesh

In this paper, a robust projection method on a locally refined mesh is proposed for two‐ and three‐dimensional viscous incompressible flows. The proposed method is robust not only when the interface between two meshes is located in a smooth flow region but also when the interface is located in a flow region with large gradients and/or strong unsteadiness. In numerical simulations, a locally refined mesh saves many grid points in regions of relatively small gradients compared with a uniform mesh. For efficiency and ease of implementation, we consider a two‐level blocked structure, for which both of the coarse and fine meshes are uniform Cartesian ones individually. Unfortunately, the introduction of the two‐level blocked mesh results in an important but difficult issue: coupling of the coarse and fine meshes. In this paper, by properly addressing the issue of the coupling, we propose a stable and accurate projection method on a locally refined staggered mesh for both two‐ and three‐dimensional viscous incompressible flows. The proposed projection method is based on two principles: the linear interpolation technique and the consistent discretization of both sides of the pressure Poisson equation. The proposed algorithm is straightforward owing to the linear interpolation technique, is stable and accurate, is easy to extend from two‐ to three‐dimensional flows, and is valid even when flows with large gradients cross the interface between the two meshes. The resulting pressure Poisson equation is non‐symmetric on a locally refined mesh. The numerical results for a series of exact solutions for 2D and 3D viscous incompressible flows verify the stability and accuracy of the proposed projection method. The method is also applied to some challenging problems, including turbulent flows around particles, flows induced by impulsively started/stopped particles, and flows induced by particles near solid walls, to test the stability and accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Calculation of contact temperatures generated by the rotation of a shaft in a bearing

The problem of the distribution of contact stresses resulting from the interaction between a journal and its bearing was considered in [1]. This paper deals with the problem of temperature distribution in the area of contact of a rotating cylindrical shaft and a bearing. The process is assumed to be stabilized.The problem reduces to an integral equation with respect to the contact temperature at the shaft surface.An approximate method is proposed for solving the integral equation which had permitted the derivation of a simple approximate formula for the contact temperature within any range of variation of the parameters of this problem.     

Stress-strain state in the vicinity of a crack tip under mixed loading

A method is proposed to calculate the eigenvalues of the class of nonlinear eigenvalue problems resulting from the problem of determining the stress-strain state in the vicinity of a crack tip in power-law materials over the entire range of mixed modes of deformation, from the opening mode to pure shear. The proposed approach was used to found eigenvalues of the problem that differ from the well-known eigenvalue corresponding to the Hutchinson-Rice-Rosengren solution. The resulting asymptotic form of the stress field is a self-similar intermediate asymptotic solution of the problem of a crack in a damaged medium under mixed loading. Using the new asymptotic form of the stress field and introducing a self-similar variable, we obtained an asymptotic solution of the problem of a crack in a damaged medium and constructed the regions of dispersed material near the crack.     

Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process.In this paper,a new model updating method named as cross-model cross-frequency response function(CMCF) method is proposed and a new iterative method associating the model updating method with the model reduction technique is investigated.The new model updating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency response function,which could greatly increase the number of the equations and the updating parameters.Based on the traditional iterative method,a correction term related to the errors resulting from the replacement of the reduction matrix of the experimental model with that of the finite element model is added in the new iterative method.Comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels,and both of these two iterative methods combine the CMCF method and the succession-level approximate reduction technique.Results show the effectiveness of the CMCF method and the proposed iterative method.     

斑马鱼C型起动中动力学特性的活体实验研究

提出了一种从鱼类自主游动的运动学实验数据出发推算其动力学特性的实验研究方法。该方法基于变形体动力学方程,不仅可以计算出变形鱼体的整体转动角速度以完善其运动学数据,还可以计算出作用在自主游动的鱼体上的流体合力和流体合力矩,进而分析鱼体的力能学特征。本文运用此方法研究了斑马鱼的两种典型C型起动,对比分析了它们的运动学及力能学特征。结果表明,在相仿的C型弯曲变形下,逃逸型C型起动与非逃逸型C型起动相比,前者推力较大,导致其在前进方向上的质心速率较大;前者侧向力较大,导致其转弯半径较小;前者转矩较大,但因在起动中后期的S型摆动产生了反向转矩,最终导致转动角度小于后者。通过对两种典型C型起动的实验研究发现,斑马鱼会因不同的运动需求而表现出不同的机动性能。     

Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot

In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i)?the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii)?the problem of ??explosion of complexity?? is avoided.     

A new multistage spectral relaxation method for solving chaotic initial value systems

In this paper, we present a new pseudospectral method application for solving nonlinear initial value problems (IVPs) with chaotic properties. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a novel technique of extending Gauss–Siedel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudo-spectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous chaotic systems such as the such as Lorenz, Chen, Liu, Rikitake, Rössler, Genesio–Tesi, and Arneodo–Coullet chaotic systems. The accuracy and validity of the proposed method is tested against Runge–Kutta and Adams–Bashforth–Moulton based methods. The numerical results indicate that the MSRM is an accurate, efficient, and reliable method for solving very complex IVPs with chaotic behavior.     

Filtration of ground waters with drainage flushings of a layer of soil with an impermeable base

Various investigators have recently taken up the question of developing a practical and effective technology for the drainage washing of saline soils [1–6]. As an alternative to continuous flooding with the nonuniformity inherent in this method and the resulting low degree of washing, it is proposed to differentiate the duration of the flooding of individual sectors of the area being washed, taking account of their distance from the drains. This point of view is presented most completely in [3], in which an analysis is made of washing under field conditions. Some of the results of this work are justified theoretically below.     

Experimental and Analytical Study of Free-Fall Drop Impact Testing of Portable Products

Portable products can suffer critical damage due to drop impact and thus, such load cases must be taken into account in the conceptual and detailed design phases of such products. One method explored in the current study for alleviating the peak accelerations resulting from impact is to isolate fragile components from the product housing using internal shock mounts. There is a lack of studies that address this method in a systematic and reliable manner. This paper presents an experimental and analytical study on the dynamic behaviour during impact of portable products with internal shock mounting. Using a special drop tower with guiding frame for controlled-angle free-fall drop impact, representative products are dropped at different angles and the acceleration is recorded both on the outer case and on an internally-mounted plate. A simplified analytical procedure, suitable for conceptual design purposes, is proposed for predicting the resulting dynamic response. The work affirms the suitability of guide-and-release facilities in impact experiments; additionally, it may facilitate the conceptual design for impact resistance of portable products.     

Unraveling surfactant transport on a thin liquid film

When a drop of insoluble surfactant is deposited on the surface of a thin liquid film, a radial flow is induced by the resulting surface tension gradient. It is difficult in practice to measure or visualize the evolution of the surfactant concentration and the corresponding surface tension field. In this contribution, we propose a numerical technique which allows, in theory, the reconstruction of the surfactant concentration and surface tension fields from the knowledge of the free surface velocity. The method also requires the knowledge of the equation of state relating the surfactant concentration to the surface tension. The proposed method is based on a reformulation of the lubrication approximation which then takes as an input the free surface velocity field. As a by-product, the film thickness is also reconstructed. We also show in this contribution, that the surface diffusion coefficient can also be estimated, in principle. The methodologies are successfully tested on ideal, synthetic data-sets but also on under-resolved, noisy, data-sets more representative of true experimental conditions. This contribution may help shed some light on the phenomena involved in surfactant transport.     

A dynamic injection operator in a multigrid solution of convection-diffusion equations

A multigrid method is studied for the solution of a linear system resulting from the high-order nine-point discretization of the convection-diffusion equations. The residual injection operator is used as a substitute for the usual full-weighting in the multigrid process. A heuristic analysis is given to obtain a dynamic injection operator that is cost-effective for both diffusion- and convection-dominated problems. Numerical experiments are employed to test the stability and efficiency of the proposed method. © 1998 John Wiley & Sons, Ltd.     

An atomistic-based finite deformation membrane for single layer crystalline films

A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.     

Anisotropic goal‐oriented error analysis for a third‐order accurate CENO Euler discretization

In this paper, a central essentially non‐oscillatory approximation based on a quadratic polynomial reconstruction is considered for solving the unsteady 2D Euler equations. The scheme is third‐order accurate on irregular unstructured meshes. The paper concentrates on a method for a metric‐based goal‐oriented mesh adaptation. For this purpose, an a priori error analysis for this central essentially non‐oscillatory scheme is proposed. It allows us to get an estimate depending on the polynomial reconstruction error. As a third‐order error is not naturally expressed in terms of a metric, we propose a least‐square method to approach a third‐order error by a quadratic term. Then an optimization problem for the best mesh metric is obtained and analytically solved. The resulting mesh optimality system is discretized and solved using a global unsteady fixed‐point algorithm. The method is applied to an acoustic propagation benchmark.     

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.