Nonlinear sloshing response of cylindrical tanks subjected to earthquake ground motion

A numerical method is proposed for the seismic response analysis of cylindrical tanks accounting for nonlinear hydrodynamic effects. The equations of motion are transformed from the physical domain into a well-defined computational domain by means of a change of variable such that there is no need to remap the computational domain at each time step as the computation of the response progresses in time. The numerical solution is then obtained using finite differences in cylindrical coordinates. The numerical formulation is applied to study the response of cylindrical tanks subjected to ground motion records from the Mexico earthquake of September 19, 1985. The response is studied in terms of wave height on the liquid surface, and shear force and overturning moment at the base wall, and compared against the linear solution. The case of resonance under harmonic excitation is also analysed and discussed. Implications on considering nonlinear hydrodynamic effects are drawn for design purposes.     

岩体p型自适应块体单元法研究

初步研究了岩体p型自适应块体单元法的基本理论和数值实现方法,以解决块体单元法中计算精度的控制问题。根据当前的块体单元法数值解,利用广义刚度矩阵的阶谱特性,估计各更高阶广义节点形函数的引入对提高计算精度所起的作用;然后引入作用较大的高阶广义节点形函数,扩充广义刚度矩阵,并求解新的整体平衡方程,得到更高精度的数值解。经过几次自适应升阶,即可得到满足精度要求的计算结果。通过算例分析,验证了所提方法的准确性和高效性。     

Identification of modal damping ratios of four‐flue chimney of a thermoelectrical plant using pseudo‐inverse matrix method

Some computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo‐inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore–Penrose pseudo‐inverse computation have been tested for modal analysis of a four‐flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well‐known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and b is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. Copyright © 2007 John Wiley & Sons, Ltd.     

Large deflection analysis of flexible plates by the meshless finite point method

The classical finite difference technique and methods based on series expansions can only be adopted for solving plates with simple geometry, loading and boundary conditions. In contrast, the finite element method has been widely used for general analysis of bending and flexible plates (coupled bending and in-plane effects). Lack of stress continuity and relatively expensive mesh generation and remeshing schemes have led to the emergence of meshless methods, such as the finite point method (FPM). FPM is a strong form solution which combines the moving least square interpolation technique on a domain of irregularly distributed points with a point collocation scheme to derive system governing equations. In this study, coupled nonlinear partial differential equations of fourth order are solved to analyse large deflection behaviour of plates subjected to lateral and in-plane loadings. Several plate problems are solved and compared with analytical solution and other available numerical results to assess the performance of the proposed approach.     

非稳定不可压缩流动模拟的改进有限元数值方法

泰勒-伽辽金有限元法在对流扩散问题的数值模拟中存在数值耗散和伪振荡等问题.本文提出改进的二阶和三阶欧拉-泰勒-伽辽金有限元法,求解了粘性不可压缩流动的Navier-Stokes方程.为克服由不可压缩条件引起的压力场振荡问题,引入压力修正法和泰勒-胡德单元.对方腔拖曳流动进行了数值模拟,以验证改进后算法的性能.最后,分析了改进后算法的精度和计算效率.     

Fourier-based maximum entropy method in stochastic dynamics

As the recent research by Tr

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bicki and Sobczyk has demonstrated the principle of maximum entropy is a powerful tool for solving stochastic differential equations. In particular, its use in connection with the moment equations generated by the Ito formula provides accurate estimations of the probability density evolution of some oscillators for which conventional methods such as the diverse closure schemes are not applicable. A major computational requirement of the method, however, lies in the need of calculating a large number of multidimensional integrals at each time step--a numerical task for which both accurate and economic algorithms are required. In this paper it is shown that conventional economic integration techniques often lead to numerical collapse of the solution, especially when dealing with highly nonlinear oscillators. A strategy that overcomes this difficulty is proposed. In essence, the integrals are reformulated in terms of multidimensional Fourier transforms, which are solved by an ad hoc FFT algorithm aimed at obtaining only one single “frequency” point. It is demonstrated that the numerical stability and the accuracy of the proposed algorithm are superior to those afforded by other integration schemes.     

An adaptive numerical scheme based on the Craig–Bampton method for the dynamic analysis of tall buildings

A new numerical scheme is proposed to perform a nonlinear dynamic analysis for tall buildings. The structural components (beams and columns) of tall buildings gradually enter the inelastic phase under strong seismic excitation. Because the distribution of nonlinear components is initially unknown due to the randomness of earthquake inputs, a group of linear and nonlinear substructures are automatically figured out during the time‐history analysis of a structure. Then a modified Craig–Bampton method is proposed to condense the DOFs of the linear substructures in modal coordinates at each time step while keeping the governing equation of the nonlinear substructure in physical coordinates. The dominant modes of the linear substructures are selected to capture the main dynamic characteristics of the structure. The time step integration analysis is used to solve the governing equation of the structures in hybrid coordinates. A 20‐story building is employed as the numerical simulation test to validate the feasibility and effectiveness of the proposed numerical scheme. This scheme provides a new method for the nonlinear dynamic analysis of tall buildings with acceptable simulation accuracy and high computational efficiency.     

Numerical analysis of coupled flows in porous and fluid domains by the Darcy-Brinkman equations

A numerical method to achieve the simultaneous computation of the seepage flows in porous media and the Navier-Stokes flows in the domain occupied purely by a fluid is presented in this paper. The method uses the Darcy-Brinkman equations with the continuous modelling of the interfacial flow velocity, and applies the finite volume method to the spatial discretization and the fractional step method to the numerical simulation of the incompressible fluid. The coupling of the two different flows is realized by the relevant interpolation of the pressure and the flow velocity onto the interface at which permeability and porosity are discontinuous. The interpolation schemes provide simple solutions to overcome the computational instability caused by the discontinuous change in permeability and to avoid having to resolve the considerably thin transition zone near the interface. Numerical analyses of the one-dimensional uniform flow, the lid-driven cavity flow, and the pipe-flow in a porous medium have been carried out. The results have shown that the proposed schemes enable a stable computation and fulfill the accurate and physically realistic numerical solutions.     

An accurate predictor-corrector time integration method for structural dynamics

In this paper, a new accurate predictor-corrector time integration method is proposed, which has an appropriate stability domain. The dispersion error of the suggested approach is considerably smaller than that of the central difference scheme. Moreover, the presented technique introduces effectively numerical damping, which can be used to remove the spurious highfrequency components from the numerical responses. The authors’ approach has second-order accuracy for structures with and without damping. It is worth mentioning that the scheme solves the nonlinear problems without using iterative processes. The new algorithm is tested by using several linear and nonlinear numerical examples, and the outcomes are compared against the results of the central difference and explicit second-order Runge-Kutta schemes. The findings confirm the high accuracy and good performance of the suggested technique.     

时域逐步积分算法稳定性与精度的对比分析

 的概念：计算时间步长趋于0时算法表现出来的精度为理论精度,而在实际计算中一般选取在满足稳定性条件下尽可能大的时间步长,此时算法表现出来的精度为计算精度。分析结果表明,算法的计算精度与理论精度是不一致的,算法的计算精度与其振幅衰减率和周期延长率相一致。对算法的计算精度从理论上进行推导分析,得到无阻尼情况下振幅衰减率与周期延长率的显式表达公式。给出线弹性和弹塑性情况下的单自由度结构振动算例,对算法在弹塑性情况下的表现进行初步研究。结合算例计算结果与理论分析,可以清楚地揭示不同算法在实际计算中的表现,从而为在实际计算中选取合适的积分算法提供参考。     

Mesh-free Method for Soil-water Coupled Problem within Finite Strain and Its Numerical Validity

A formulation of the Element-Free Galerkin Method (EFG method), i.e., one of the mesh-free/meshless methods developed in the field of computational mechanics for solving partial differential equations, is furnished for consolidation within finite strain and its validity for application to soil-water coupled problems is examined through a numerical analysis. The numerical strategy is constructed to solve a set of governing equations, e.g., the equilibrium for the nominal stress rate and the continuity of pore water, and the numerical discretization of the weak form of the governing equations leads to an updated Lagrangian scheme. The accuracy of the proposed numerical strategy is examined through an analysis of unconfined compression tests and simple shear tests under undrained and plane strain conditions through a comparison of stress paths integrated directly from the Cam-clay model within the framework of finite strain. It is also revealed that the particular type of weight function to be adopted in the moving least-squares (MLS) approximation, even in the same order, can determine the resultant shape functions of the EFG method for both the displacement and the pore water pressure field such that they are smoother than those of the usual FEM. The functions are advantageous in that they avoid spatial instability in the numerical solutions for pore water pressure under undrained conditions appearing in saturated soil column tests, where the shape function of the pore water pressure in the conventional FEM computation is adopted as a lower order than that of the displacement to remedy this type of numerical difficulty. To emphasize the applicability and the feasibility of the mesh-free computation, the consolidation phenomena are demonstrated in the analysis of a punch problem for a soft soil foundation which has stress singularity under both ends of a rigid loading platen for the same problem which Yatomi et al. (1989) solved with FEM.     

单层正交索网结构有限分析计算方法及实验研究

建立了幕墙正交索网结构的计算力学模型,研究单层索网在网点分配荷载及预张力作用下的平衡方程、位移协调和变形体位能驻值方程,构成多变元的非线性耦合方程组。采用有限分析法将非线性耦合方程组解耦,寻求局部解析解再转化为全局数值解,设计小尺度实际模型在多点荷载作用下的内力和变形的实验,最后给出相关算例。     

节理岩体渗流的无网格与有限元耦合方法

节理岩体的渗透破坏、节理岩体中石油渗流、地下工程的防渗设计等无不与渗流计算有关,而节理岩体渗流介质的非均质性和各向异性特性、边界条件和几何形状的复杂性、初始条件的不确定性等因素制约着解析法在渗流计算中的应用。应用无网格法来求解节理岩体的渗流问题,建立节理岩体渗流的无网格与有限元耦合方法。通过变分原理详细推导无网格与有限元耦合方法求解节理岩体渗流的离散方程及相关计算公式,并利用耦合方法对边界条件进行处理。最后,给出的数值算例说明该方法的正确性和有效性。     

Nonlinear inelastic analysis of concrete-filled steel tubular frames

This paper presents a reliable numerical procedure for the nonlinear inelastic analysis of concrete-filled steel tubular frames. Geometric nonlinearities are taken into account by the use of stability functions derived from the exact stability solution of a beam–column subjected to axial force and bending moments. The spread of plasticity over the cross section and along the member length is captured by tracing the uniaxial stress–strain relationships of each fiber on the cross sections located at the selected integration points along the member length. The nonlinear equilibrium equations are solved using an incremental-iterative scheme based on the generalized displacement control method because of its general numerical stability and efficiency. The accuracy of the proposed procedure is verified by comparisons of the obtained results with experimental data and existing solutions. The proposed numerical procedure proves to be a reliable tool for the nonlinear analysis of concrete-filled steel tubular structures.     

Nonlinear inelastic time-history analysis of truss structures

This paper presents a reliable numerical procedure for the nonlinear inelastic analysis of concrete-filled steel tubular frames. Geometric nonlinearities are taken into account by the use of stability functions derived from the exact stability solution of a beam–column subjected to axial force and bending moments. The spread of plasticity over the cross section and along the member length is captured by tracing the uniaxial stress–strain relationships of each fiber on the cross sections located at the selected integration points along the member length. The nonlinear equilibrium equations are solved using an incremental-iterative scheme based on the generalized displacement control method because of its general numerical stability and efficiency. The accuracy of the proposed procedure is verified by comparisons of the obtained results with experimental data and existing solutions. The proposed numerical procedure proves to be a reliable tool for the nonlinear analysis of concrete-filled steel tubular structures.     

钢管混凝土框架的非线性分析

建立数值程序,对钢管混凝土框架进行非线性分析。通过采用轴力和弯矩共同作用下梁柱结构稳定求解中的稳定函数,考虑几何非线性。通过追踪沿杆件长度方向选定的横截面上的纤维单轴应力-应变关系,描述横截面上及杆件长度方向的塑性发展。由于位移控制方法具有数值稳定性和有效性,基于此,采用增量迭代法,求解非线性平衡方程。通过与试验和已有求解结果的比较,验证了本方法的准确性。对于钢管混凝土结构的非线性分析,数值分析是有效的。     

利用Birkhoff多项式求解结构动力响应的新方向

结合解析方法和数值方法优点，提出了一种求解动力响应的新方法。在求解动力响应的Duhamel积分中，利用分段Birkhoff插值多项式逼近任意动力荷载，并推导了相关公式。由于分段Birkhoff多项式的Duhamel积分有精确解，因而和现在常用的逐步积分法相比，本文方法不但具有高得多的计算精度，避免了收敛性和稳定性的问题，而且大大减少了计算工作量。     

An efficient solution method for predicting indoor environment of buildings with complex geometric configuration

An efficient solution method has been developed to solve two-dimensional steady flow in complex domain. The study is based on a control-volume formulation with Cartesian physical velocity components as the dependent variables in momentum equations. The strategies for implementing the hybrid convection schemes, maintaining the diagonal dominance and decoupling the pressure–velocity in irregular grid system have been presented. Comparing the results with other numerical results available in the literature has assessed the accuracy of the proposed algorithm. The ability of the method to handle complex geometry is illustrated through an example of airflow distribution in a large and complex geometric cinema hall.     

Algorithms for seismic analysis of MDOF systems with fractional derivatives

Viscoelastic dampers are often considered for use in structural systems to reduce their dynamic response. The frequency dependent storage and loss moduli of the viscoelastic material are sometimes modeled using the fractional derivatives. This introduces fractional derivatives in the equations of motion. Herein, several schemes, specialized for arbitrary inputs such as earthquake induced ground motions, are presented for direct numerical integration of such equations to obtain the dynamic response of multi-degrees-of-freedom damper-structure systems. Relative numerical accuracies of the proposed schemes are examined. The numerical analyses with fractional derivatives require that all previous time response values be used, but this is invariably time consuming. The possibility of discarding some early time response values without compromising the accuracy of the calculations is, thus, of natural interest. It is shown that such truncations are, indeed, possible but a straightforward omission of preceding time values can introduce unacceptable errors in the calculated responses. To reduce such errors a new algorithm is proposed.     

层状地基三维问题的解析层元解

从弹性力学三维问题的基本控制方程出发,通过双重 Fourier 变换及解耦变换技术,推导出相应问题在积分变换域的解析解;根据该解析解,进而推导出三维弹性地基问题的精确刚度矩阵,即解析层元;然后根据有限层法原理,组装得到总体刚度矩阵;通过求解总体刚度矩阵形成的代数方程,得到三维层状地基问题在变换域内的解答;最后应用 Fourier 逆变换 技术,得到其物理域内的解。与经典 Bounsinesq 解及有限元软件 ABAQUS 的结果进行比较,验证了本文理论及数值计算方法的正确性;计算分析结果还表明：土体的分层特性对地基沉降具有较显著的影响。