一种新的有限域动力刚度改进连分式求解算法

比例边界有限元法仅需离散边界,网格划分灵活,且易于采用高阶单元,是结构动力分析的理想方法。针对有限域动力问题,基于广义特征值分解对动力刚度表示的比例边界有限元方程进行模态变换。通过选取特定的因子矩阵,简化了改进连分式算法的求解流程,提出了一种新的有限域动力刚度改进连分式求解算法。在动力刚度连分式渐近解的基础上引入辅助变量,建立了有限域动力问题的运动方程,其系数矩阵对称稀疏,可以利用现有的有限元求解器求解。正八边形板和重力坝算例表明,新算法具有良好的数值稳定性和计算精度,适用于实际工程问题的动力响应分析。     

三维一致粘弹性人工边界及等效粘弹性边界单元

基于粘弹性人工边界推导了三维一致粘弹性人工边界单元的刚度及阻尼矩阵,利用单元矩阵等效原理采用普通有限单元构造了等效粘弹性边界单元来模拟三维粘弹性边界。均匀半空间算例与成层半空间算例证明三维粘弹性边界单元具有与集中粘弹性人工边界相近的精度,并且施加更为简便。     

求解无限域动力刚度矩阵的双渐近算法

采用连分式算法可以有效地求解无限域动力刚度表示的比例边界有限元方程, 它具有收敛范围广、收敛速度快等优点. 该文在高频渐近连分式算法的基础上考虑了低频渐近, 发展了一种针对矢量波动方程的双渐近算法. 随着展开阶数的增加, 双渐近算法可以在全频域范围内快速逼近准确解. 引入了系数矩阵?X(i)来增强连分式算法的数值稳定性. 通过在高频极限、低频极限时满足动力刚度表示的比例边界有限元方程, 建立了递推关系以求得动力刚度矩阵. 通过二维半无限楔形体、三维均质弹性半空间数值算例表明, 双渐近算法比单渐近算法更稳定、优越.     

液化场地中Timoshenko桩自由振动与屈曲的精确数值解

基于单桩的Timoshenko梁模型和桩-土相互作用的Winkler模型,建立考虑轴力效应的具有分布参数的Timoshenko梁模型微分控制方程,确定对应的齐次方程的通解,并以此作为有限单元的基函数。推导得精确形函数矩阵,建立分布参数Timoshenko梁的精确有限单元,根据拉格朗日方程得到有限元离散方程和单元刚度矩阵、几何刚度矩阵和一致质量矩阵。应用建立的精确Timoshenko梁单元于分层液化土中单桩-土-结构系统的自由振动与屈曲模态分析,通过与对应解析解以及常规有限元解的对比,表明精确Timoshenko桩基础单元的可靠性与较常规有限元法的优势。     

基于界面单元的子结构协调技术

该文提出一种用于协调子结构的界面单元方法。基于广义变分原理,将两子域的刚度与界面单元刚度组装成耦合结构的整体刚度矩阵,求解新的平衡方程即可得到各个耦合子域的位移。界面单元的意义是对子域引入边界力,并建立边界上平衡关系和位移协调关系。该文利用悬臂梁单轴受拉案例验证了界面单元方法的精确性。为了使得界面单元能够应用到子结构混合试验中,引入静力凝聚与BFGS方法,这样只需通过提取边界上的力与位移即可实现多子域不共节点的边界协调问题。该文最终以悬臂梁案例验证了界面单元在解决非线性静、动力加载工况下的正确性。     

考虑频变阻尼的黏弹性阻尼层板结构模态分析方法

结构动力中的模态分析可归结为数学上矩阵特征值问题的求解。研究了一种求解有限元非线性特征值问题的数值方法,即RSRR,该方法通过对系统矩阵逆矩阵的采样,构造可靠的特征空间用于非线性特征值问题的求解,比现有基于围道积分的非线性特征值解法稳定性更好、精度更高。采用基于Layerwise离散层理论的Layerwise板单元建立黏弹性阻尼结构有限元模型比混合单元建模方法简单方便,结合Layerwise板单元建模方法,将RSRR拓展应用于黏弹性阻尼结构的模态分析,算例结果表明RSRR求解精度高、稳定性好,是黏弹性阻尼结构模态分析的有效数值方法。     

一种新型的时域动力无穷单元

针对频域动力无穷元不便与时域有限元结合的缺陷,采用时域的波传函数,推导出一种新型的时域动力无穷单元,并采用UPFs工具对ANSYS进行二次开发,将其嵌入到ANSYS当中。然后采用经典算例对所提出的新型动力无穷单元进行验证,并将其结果与远置边界、粘性边界、粘弹性边界的结果进行比较。验证结果表明,所提出的新型时域动力无穷单元是成功的,并可方便地实现与时域的有限单元结合。     

考虑螺栓球节点半刚性的网格结构有限元模型修正研究

为获取用于螺栓球节点网格结构健康监测准确有限元模型,用具有刚度可调节点单元描述节点半刚性;采用神经网络技术,利用有限测点模态信息构造网络输入参数CPFM,提出对螺栓球节点单元刚度折减系数进行分步修正新方法。以单层柱面网壳振动台试验模型为例,在螺栓球节点精细化模型基础上,基于实测模态数据对其进行有限元模型修正。结果表明,修正后有限元模型能较好反映该网壳结构的真实动力特性,采用分步修正算法能精简神经网络结构,可有效用于螺栓球节点网格结构有限元模型修正,具有一定实用价值。     

多边形比例边界有限元非线性高效分析方法

比例边界有限元法作为一种高精度的半解析数值求解方法,特别适合于求解无限域与应力奇异性等问题,多边形比例边界单元在模拟裂纹扩展过程、处理局部网格重剖分等方面相较于有限单元法具有明显优势。目前,比例边界有限元法更多关注的是线弹性问题的求解,而非线性比例边界单元的研究则处于起步阶段。该文将高效的隔离非线性有限元法用于比例边界单元的非线性分析,提出了一种高效的隔离非线性比例边界有限元法。该方法认为每个边界线单元覆盖的区域为相互独立的扇形子单元,其形函数以及应变-位移矩阵可通过半解析的弹性解获得;每个扇形区的非线性应变场通过设置非线性应变插值点来表达,引入非线性本构关系即可实现多边形比例边界单元高效非线性分析。多边形比例边界单元的刚度通过集成每个扇形子单元的刚度获取,扇形子单元的刚度可采用高斯积分方案进行求解,其精度保持不变。由于引入了较多的非线性应变插值点,舒尔补矩阵维数较大,该文采用Woodbury近似法对隔离非线性比例边界单元的控制方程进行求解。该方法对大规模非线性问题的计算具有较高的计算效率,数值算例验证了算法的正确性以及高效性,将该方法进行推广,对实际工程分析具有重要意义。     

地震作用下水-轴对称柱体相互作用的子结构分析方法

针对水-轴对称柱体动力相互作用问题,提出了一种地震作用下水-结构相互作用的时域子结构分析方法.基于三维不可压缩水体的波动方程和边界条件,利用分离变量法将其转换为环向解析、竖向和径向数值的二维模型;基于比例边界有限元推导了截断边界处无限域水体的动力刚度方程,并将水体内域有限元方程和人工边界处的动水压力进行耦合,从而得到结...     

Finite elements for piezoelectric vibrations with open electricboundaries

The problem of a piezoelectric body vibrating in the free space of infinite extent has been posed as a problem with open electric boundaries. A three-dimensional finite element analysis of piezoelectric vibrations has been complemented by the modeling of the external electrostatic field. The infinite exterior region that adheres to Laplace's equation is represented as a single “superelement” obtained by the ballooning of the outer boundary. The spectral transformation Lanczos method is used to find approximations to some solutions of the generalized eigenvalue problem arising from the finite element discretization of interior and exterior regions. The proposed approach was tested on simple vibrators with different mesh discretization and element order. The method produces numerically stable results, and was used to estimate the influence of the exterior leakage field on electromechanical properties of free piezoelectric vibrations. Numerical tests show that for some materials, vibrator geometries and modes, favorable to the coupling with the exterior field, the resonant frequency and electrical parameter shifts due to open electric boundaries may be as great as several percent     

Evaluation of added mass by a cloning algorithm

In problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force-displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.     

Lamb Wave Interaction with Delaminations in CFRP Laminates

In this paper, we investigate Lamb wave interaction with delamination in an infinite carbon fiber reinforced plastics (CFRP) laminate by a hybrid method. The infinite CFRP laminate is divided into an exterior zone and an interior zone. In the exterior zone, the wave fields are expressed by wave mode expansion. In the interior zone, the wave fields are modeled by the finite element method (FEM). Considering the continuity condition at the boundary between the exterior and interior zones, the global wave fields can be calculated. Lastly, numerical examples show how a delamination in the laminate influences the mode conversion of different incident wave modes.     

Viscoplastic plane‐strain analysis of infinite solids using elastic supports

A highly efficient novel Finite Element Boundary Element Method (FEBEM) is proposed for the elasto‐viscoplastic plane‐strain analysis of displacements and stresses in infinite solids. The proposed method takes advantage of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) to achieve higher efficiency and accuracy by using the concept of elastic supports to simulate the effects of unbounded solid mass surrounding the region of interest. The BEM is used to compute the stiffnesses of elastic supports and to estimate the location of the truncation boundary for the finite element model. As compared to the conventional coupled FEBEM, the proposed method has three main computational advantages. Firstly, the symmetrical and highly banded form of the standard finite element stiffness matrix is not disturbed. Secondly, the proposed technique may be implemented simply by using standard codes for elasto‐viscoplastic finite element analysis and elastic boundary element analysis. Thirdly, the yielded zone is approximately located in advance by using the BEM and hence, an unnecessarily large extent of the domain does not have to be discretized for the finite element modelling. The efficiency and accuracy of the proposed method are demonstrated by computing elastic and elasto‐plastic displacements and stresses around ‘deep’ underground openings in rock mass subject to hydrostatic and non‐hydrostatic in situ stresses. Results obtained by the proposed method are compared with ‘exact’ solutions and with those obtained by using a BEM and a coupled FEBEM. Copyright © 1999 John Wiley & Sons, Ltd.     

Accurate H-shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half-space

An accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half-space. The proposed ABC is H-shaped line that consists of two parts: a new ABC at horizontal bottom boundary of finite domain to replace semiinfinite strip below horizontal boundary and between two vertical boundaries, and a general consistent ABC at vertical lateral boundary to replace semiinfinite layered half-space outside vertical boundary. The key point for constructing the ABC is that a new continued fraction (CF) is presented to expand dynamic stiffness of underlying half-space, and the CF-based stress-displacement relationship is then transformed into an auxiliary variable system with square of horizontal wavenumber. The ABC has only one undetermined real parameter that is the CF-order independent of frequency and incidence angle of propagating outgoing waves. The parameter can be chosen relatively small value to achieve an accurate ABC. Moreover, the ABC can couple seamlessly with finite element method of finite domain. The finite domain can be chosen very small size due to high accuracy of the ABC. Numerical examples are finally given to demonstrate the effectiveness of the ABC.     

Influence functions of the displacement discontinuity method for anisotropic bodies

In this study, the boundary element equations are obtained from the influence functions of a displacement discontinuity in an anisotropic elastic medium. For this purpose, Kelvin fundamental solutions for anisotropic media on infinite and semi-infinite planes are used to form dipoles from singular loads. Various combinations of these dipoles are used to obtain the influence functions of the displacement discontinuity. Boundary element equations are then derived analytically by the integration of these influence functions on a constant element which results in a linear system for unknown displacement discontinuities. The boundary integrals are calculated in closed form over constant elements. The obtained formulation is applied to a number of classical engineering problems.Tel.: +90-212-285-65-85, 90-212-285-37-07     

Transient analysis of three-dimensional dynamic interaction between multilayered soil and rigid foundation

The study of dynamic soil-structure interaction is significant to civil engineering applications, such as machine foundation vibration, traffic-induced vibration, and seismic dynamic response. The scaled boundary finite element method (SBFEM) is a semi-analytical algorithm, which is used to solve the dynamic response of a three-dimensional infinite soil. It can automatically satisfy the radiation boundary condition at infinity. Based on the dynamic stiffness matrix equation obtained by the modified SBFEM, a continued fraction algorithm is proposed to solve the dynamic stiffness matrix of layered soil in the frequency-domain. Then, the SBFEM was coupled with the finite element method (FEM) at the interface to solve the dynamic stiffness matrices of the rigid surface/buried foundation. Finally, the mixed-variable algorithm was used to solve the three-dimensional transient dynamic response of the foundation in the time domain. Numerical examples were performed to verify the accuracy of the proposed algorithm in solving the dynamic stiffness matrix of the infinite domain in the frequency domain and the dynamic transient displacement response of the foundation in the time domain. Compared with the previous numerical integration technique, the dynamic stiffness matrix in the frequency domain calculated by using the proposed algorithm has higher accuracy and higher efficiency.     

BOUNDARY ELEMENT–FINITE ELEMENT COUPLED EIGENANALYSIS OF FLUID–STRUCTURE SYSTEMS

The eigenanalysis of acoustical cavities with flexible structure boundaries, such as a fluid-filled container or an automobile cabin enclosure, is considered. An algebraic eigenvalue problem formulation for the fluid–structure problem is presented by combining the acoustic fluid boundary element eigenvalue analysis method and the structural finite elements. For many practical eigenproblems, use of finite elements to discretize the fluid domain leads to large stiffness and mass matrices. Since the acoustic boundary element discretization requires putting nodes only on the wetted surface of the structure, the size of the eigenproblem is reduced considerably, thus reducing the eigenvalue extraction effort. Futhermore, unlike in ordinary cases, the finite element discretization of pressure–displacement based fluid–structure problem gives rise to unsymmetric matrices. Therefore, the fact that the boundary element formulation produces unsymmetric matrices does not introduce additional difficulties here compared to the finite element case in the choice of an eigenvalue extraction procedure. Examples are included to demonstrate the fluid–structure eigenanalysis using boundary elements for the fluid domain and finite elements for the structure.     

离散高阶Higdon-like透射边界

基于比例边界有限元法(SBFEM)半离散思想和Higdon透射微分算子提出了一种用于模拟二维层状介质标量波传播的高效离散高阶Higdon-like透射边界。对无限介质边界进行迦辽金有限元离散后,描述标量波的偏微分方程转换为局部坐标系下半离散矩阵方程组;然后使用高阶Higdon透射算子和辅助变量,在时域内得到了一个阶数不超过2阶的离散高阶透射边界。透射边界是由一组常微分方程构成,可以采用通常的时步积分方法求解,它在截断边界上非局部,在时间域局部。算例表明:该文提出的透射边界的计算精度可以随着辅助变量的增加而提高,但计算量却呈线性化增加,因而计算效率较全局方法有了显著提高。另外,由于该文的边界条件是直接建立在离散节点上的,所以它很方便与近场有限单元法耦合。