Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.     

Dynamic analysis of rotating flexible disk subjected to double slider loading systems

Rotating disk subjected to stationary slider loading system is a very common mechanical structure. This paper investigates the multibody dynamics of a rotating flexible annular thin disk subjected to double slider loading systems. Along the rotating disk radial and circumferential directions, two stationary slider loading systems are distributed. System dynamic model is solved by Galerkin's method, and then natural frequency, dynamic stability and mode shape are determined with a quadratic eigenvalue problem. Effects of the distributing positions and interaction mechanism of the double slider loading systems on natural frequency, dynamic stability and mode shape are discussed and investigated.     

基于荷载形函数的大跨桥梁结构移动荷载识别

大跨桥梁结构中的移动荷载识别是结构健康监测的重要组成部分之一,其作为动力学中的反问题,存在唯一性及稳定性等病态问题。本文首先推导出移动荷载作用下结构响应的卷积形式的离散公式,然后利用有限元理论中的形函数拟合移动荷载,推导出基于荷载形函数的移动荷载识别表达式。将移动荷载的识别转化为荷载形函数拟合系数的识别,降低了需要识别的未知量,减小了逆运算的计算量,消除或减弱逆问题病态性,并提高了计算效率。利用某大跨刚构-连续预应力混凝土桥梁修正后的有限元模型进行数值仿真,考虑路面粗糙度,由模态叠加法计算移动荷载作用下的响应;然后采用荷载形函数方法识别移动荷载,证明该方法在5%以下的噪声时能快速并精确识别复杂桥梁结构的移动荷载。     

Dynamic response of a rotating disk submerged and confined. Influence of the axial gap

In this paper, the natural frequencies and mode shapes of a rotating disk submerged and totally confined inside a rigid casing, have been obtained. These have been calculated analytically, numerically and experimentally for different axial gaps disk-casing. A simplified analytical model to analyse the dynamic response of a rotating disk submerged and confined, that has been used and validated in previous researches, is used in this case, generalised for arbitrary axial gaps disk-casing. To use this model, it is necessary to know the averaged rotating speed of the flow with respect to the disk. This parameter is obtained after an analytical discussion of the motion of the flow inside the casing where the disk rotates, and by means of CFD simulations for different axial positions of the disk. The natural frequencies of the rotating disk for the different axial confinements can be calculated following this method. A Finite Element Model has been built up to obtain the natural frequencies by means of computational simulation. The relative velocity of the flow with respect to the disk is also introduced in the simulation model in order to estimate the natural frequencies of the rotating disk. Experimental tests have been performed with a rotating disk test rig. A thin stainless steel disk (thickness of 8 mm, (h/r<5%) and mass of 7.6 kg) rotates inside a rigid casing. The position of the disk can be adjusted at several axial gaps disk-casing. A piezoelectric patch (PZT) attached on the rotating disk is used to excite the structure. Several miniature and submergible accelerometers have measured the response from the rotating frame. Excitation and measured signals are transmitted from the rotating to the stationary frame through a slip ring system. Experimental results are contrasted with the results obtained by the analytical and numerical model. Thereby, the influence of the axial gap disk-casing on the natural frequencies of a rotating disk totally confined and surrounded by a heavy fluid is determined.     

Adaptive shape functions and internal mesh adaptation for modeling progressive failure in adhesively bonded joints

Macroscopic finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.     

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

Perturbation solution of rotating solid disks with nonlinear strain-hardening

In order to determine the stresses and displacement in rotating disks with nonlinear strain-hardening, a polynomial stress-plastic strain relation is proposed and dimensionless quantities are adopted. A dimensionless governing equation for rotating disks is derived from the deformation theory of plasticity, Von Mises' yield criterion, proposed stress-plastic strain relation, equilibrium and compatibility equations. Its perturbation solution is obtained and applied to compute a rotating solid disk with nonlinear strain-hardening. The results are compared with those from the finite element calculation and other existing approaches, which confirms the validity of the method presented in this paper.     

Fitted finite element discretization of two‐phase Stokes flow

We propose a novel fitted finite element method for two‐phase Stokes flow problems that uses piecewise linear finite elements to approximate the moving interface. The method can be shown to be unconditionally stable. Moreover, spherical stationary solutions are captured exactly by the numerical approximation. In addition, the meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations, a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments for our numerical method, which demonstrate the accuracy and robustness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

A fictitious domain finite element method for simulations of fluid–structure interactions: The Navier–Stokes equations coupled with a moving solid

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier–Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by Newton׳s laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.     

不确定动力系统平稳随机响应分析

由于设计、建造以及测量等诸多不确定因素的影响,通常的有限元力学分析模型只是原型结构的一种均值近似,采用随机结构模型是更为合理的.本文应用随机矩阵模拟不确定线性动力系统有限元模型中质量阵、阻尼阵和刚度阵的随机不确定性,并进一步建立此类非参数概率系统在平稳随机外载作用下动力响应的虚拟激励高效求解算法.数值结果表明,均值有限元模型和随机矩阵模型的动力响应具有很大的差异.对于精细制造,模型的随机性是不能忽略的,本文提出的算法为此类问题求解提供了一条有效途径.     

Out-of-plane responses of a circular curved Timoshenko beam due to a moving load

For the cases of using the finite curved beam elements and taking the effects of both the shear deformation and rotary inertias into consideration, the literature regarding either free or forced vibration analysis of the curved beams is rare. Thus, this paper tries to determine the dynamic responses of a circular curved Timoshenko beam due to a moving load using the curved beam elements. By taking account of the effect of shear deformation and that of rotary inertias due to bending and torsional vibrations, the stiffness matrix and the mass matrix of the curved beam element were obtained from the force–displacement relations and the kinetic energy equations, respectively. Since all the element property matrices for the curved beam element are derived based on the local polar coordinate system (rather than the local Cartesian one), their coefficients are invariant for any curved beam element with constant radius of curvature and subtended angle and one does not need to transform the property matrices of each curved beam element from the local coordinate system to the global one to achieve the overall property matrices for the entire curved beam structure before they are assembled. The availability of the presented approach has been verified by both the existing analytical solutions for the entire continuum curved beam and the numerical solutions for the entire discretized curved beam composed of the conventional straight beam elements based on either the consistent-mass model or the lumped-mass model. In addition to the typical circular curved beams, a hybrid curved beam composed of one curved-beam segment and two identical straight-beam segments subjected to a moving load was also studied. Influence on the dynamic responses of the curved beams of the slenderness ratio, moving-load speed, shear deformation and rotary inertias was investigated.     

Deformation of thin straight pipes under concentrated forces or prescribed edge displacements

The purpose of this paper is to present an efficient analytic method for obtaining the deformation of thin straight pipes, subjected to prescribed edge displacements or concentrated loads.The approach uses the mixed formulation where unknown functions are combined with trigonometric terms. A variational procedure is used to obtain the system of ordinary differential equations. For the applied load a Fourier approach is used to represent the load as an analytical function. For the prescribed displacement, three solutions for the ovalization are evaluated and a method based on energy contribution of each term is used to obtain their superposition.In contrast to finite element method the proposed method is efficient and can be applied to other boundary condition problems leading to continuous displacement and stress fields with a low number of unknowns. Comparisons with experimental and finite element procedures show good agreement that enhances the merits of the analytical solutions proposed.The value of this method is based on solving the differential equations rather than using commercial codes. So far, the solution of prescribed edge displacements has been limited to one term. This paper discusses how to add further terms using the mixed formulation, thus, presenting a novel procedure.     

Resonant and Stationary Waves in Rotating Disks

The analytical conditions for resonant and stationary waves inrotating disks are presented. These conditions are derived from anonlinear plate theory pertaining to initial configurations and areapplicable to rotating disks with initial waviness and/or undergoinglarge-amplitude displacements. The rotational speeds at which theresonant and stationary waves occur for a 3.5-inch diameter computermemory disk are computed. The resonant waves for linear and nonlinear,rotating disks are simulated numerically. It is found that some diskmodes exhibit a hardening effect under which the rotational speeds forthe resonant and stationary waves increase with increasing waveamplitude, while other modes experience a softening effect with thoserotational speeds decreasing with increasing wave amplitude. Therotating-disk resonant spectrum presented in this paper is relevant tothe disk drive industry for determining the range of operationalrotation speed.     

移动荷载作用下非局部地基梁动力响应分析的有限元法Dynamic response of beams with nonlocal foundations subjected to moving loads using finite element method

基于非局部地基理论,推导了移动荷载作用下非局部地基梁动力响应问题的有限元解,分别讨论了地基的非局部参数、刚度、阻尼系数以及移动荷载速度对非局部地基梁动力响应的影响,并比较了非局部结果与局部结果的差异。结果表明,地基的非局部参数、刚度和阻尼是地基梁的动力响应的主要影响参数,地基梁最大响应及其发生的时刻与移动荷载速度有关。研究成果可为轨道地基系统设计提供参考。     

Heat (mass) transfer between an impinging jet and a rotating disk

The aim of this experimental study is to investigate the heat (mass) transfer of a rotating disk with an impinging circular jet. To facilitate the experiments, the naphthalene sublimation technique was employed. In order to analyze the results, measurements of the heat (mass) transfer of a stationary disk with an impinging jet and a rotating disk without jet impingement were also made. From the experimental results, it is found that the heat (mass) transfer are precisely divided into three regimes, namely the impingement dominated regime; the mixed regime and the rotation dominated regime. Correlation of Sherwood number of a rotating disk with jet impingement is also proposed in the present work. Received on 12 January 1998     

Elastic structural response of prismatic metal sandwich tubes to internal moving pressure loading

The analytical and numerical modeling of the structural response of a prismatic metal sandwich tube subjected to internal moving pressure loading is investigated in this paper. The prismatic core is equivalent to homogeneous and cylindrical orthotropic solids via homogenization procedure. The sandwich tube with the “effective” homogenized core is modeled using multi-layer sandwich theory considering the effects of transverse shear deformation and compressibility of the core; moreover, the solutions are obtained by using the precise integration method. Several dynamic elastic finite element (FE) simulations are carried out to obtain the structural response of the tube to shock loading moving at different velocities. The comparison between analytic solutions and FE simulations demonstrates that the transient analytical model, based on the proposed sandwich model, is capable of predicting the critical velocity and the dynamic structural response of the sandwich tube with the “effective” homogenized core with a high degree of accuracy. In addition, the critical velocity predicted using FE simulations of the complete model is not in agreement with that of the effective model. However, the structural response and the maximum amplification factors obtained using FE simulations of the complete model are nearly similar to that of the effective model, when the shock loading moves at the critical velocity. The influences of the relative density on the structural response are studied, and the capabilities of load bearing for sandwich tubes with different cores are compared with each other and with the monolithic tube. The results indicate that Kagome and triangle-6 are preferred among five topologies.     

P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

High-precision solution to the moving load problem using an improved spectral element method

In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.     

爆炸荷载作用下地下拱形结构动力响应样条小波有限元研究

采用小波有限元方法研究爆炸荷载作用下地下结构的动力响应,克服在模拟过程中由于材料的奇异性、地质条件的复杂性和加载的快速性出现的应力集中和计算效率低下,根据样条有限点法,构造了单向和双向区间B样条圆环扇形小波单元,用尺度函数作为插值函数;结合工程实例,通过Matlab软件编程对爆炸荷载作用地下拱形结构的动力响应进行了数值模拟,并与应用传统有限元程序模拟结果进行对比。结果表明,小波有限元用很少单元取得了较高的精度,计算效率比传统有限元提高一倍。     

Dynamic response and reliability analysis of random structures

The finite element method determining dynamic response of random structuressubjected to random dynamic load is studied,the formulas for dynamic response ofrandom structures and reliability based on random resistibility are proposed in thispaper.