求解刚-柔组合结构的隐式-显式混合法

针对整体柔性、局部刚性的组合结构系统的动力反应分析,推出了一种隐式-显式混合算法的逐步积分方法.这种混合求解方法,在一个算法步中,对柔性部分采用显式方法求解,对刚性部分则采用隐式方法求解,充分利用了隐式算法无条件稳定的优点和显式算法计算高效的优点.混合法稳定域大小表达式中的频率为柔性部分的最高频率,而不是整体结构的最高频率,这就避开了局部刚性导致显式算法时间步长需要过于细化的缺点.这种方法可以作为一种高效的逐步积分方法,用来求解土-结构相互作用、液固耦合系统等的动力反应.算例表明了方法的正确性.     

基于动力特征分区的显式-精细混合积分法

大型动力系统中常因局部的高频振动及非线性等特性限制了系统的积分步长而导致整体计算量激增，针对此问题提出一种分区域异步长显式-精细混合积分方法。在特性复杂的局部区域采取显式积分法，根据精度和稳定性要求取较小的时间步长求解；在其余常规区域则应用精细积分方法，采取可以跨越显式积分区周期的大积分步长求解。对于精细积分区域边界荷载，提出一种基于离散FFT变换的线性项与主频谐波项的组合表示方法，并给出了此种荷载形式下的精细积分计算格式。数值算例结果表明该法能够明显提高计算效率，在显式积分区域和精细积分区域都有很高的精度。     

有阻尼动力方程显式积分方法的精度研究

在动力问题分析中,一种好的显式积分方法不仅要具有良好的稳定性,而且还要具有良好的计算精度。对几种有阻尼动力方程显式积分方法的精度问题进行了分析,研究了各自的局部截断误差、数值阻尼比和相对周期误差。这一研究将有助于更加全面地了解这些积分格式的性能。     

显式积分求解橡胶元件刚度的方法研究

应用显式积分与隐式积分两种求解方法计算橡胶元件的垂向静刚度,其中显式积分采用斜坡、正弦、光滑三种加载函数进行位移加载。通过对比分析计算结果与试验数据发现,其中斜坡加载的动能在计算初始时出现振荡,而光滑加载与正弦加载的动能整个过程均并没有出现振荡;在大变形时,隐式积分求解方法由于出现网格畸变从而导致程序收敛失败,此时显式积分求解体现出优势,并且三种加载函数的计算结果几乎无差别,并且与试验数据吻合度比较好,最大误差为5.7%。对于橡胶元件大变形问题,应用显式积分求解静刚度的方法是可行的,并且不同的加载函数会直接影响计算结果,尤其是在初始计算阶段的结果的准确性有很大的影响。     

采用粘弹性人工边界单元时显式算法稳定性分析

在土-结构地震反应或近场地震波动问题的分析中,常采用粘弹性人工边界单元将无限域问题转化为近场有限域问题进行计算。由于粘弹性人工边界单元的材料参数和单元尺寸与内部介质单元不同,采用显式时域逐步积分算法时,人工边界区与内部系统的数值稳定条件存在差异,但目前尚未有针对性的分析方法和研究成果,影响了显式数值稳定条件的确定和稳定积分时间步长的正确选取。针对二维粘弹性人工边界单元,该文提出一种分析显式时域逐步积分算法稳定性的方法:建立可代表人工边界区域特征的,包含人工边界单元的若干局部子系统,对各子系统的传递矩阵进行分析,给出采用显式时域逐步积分算法时各子系统的稳定条件解析解。通过对各子系统的稳定条件进行对比分析,获得了采用粘弹性人工边界单元时,显式时域逐步积分算法的统一稳定性条件。当内部介质区也满足该稳定条件时,这一条件成为使整体系统数值计算稳定的充分条件,可用于指导数值分析中离散时间步长的选取。     

工程结构非线性动力响应数值分析显式积分格式的研究

工程结构非线性动力响应数值分析中时间积分的处理是其难点之一,它关系到此类动力响应分析程序的运算效率及分析精度。本文详细介绍了有限元直接积分法中显式积分格式及其稳定性条件。通过分析可看出,对于求解强冲击载荷作用下的非线性结构动力响应及波传播等问题,显式算法是一种好的选择。文中给出了各种类型单元稳定性条件下临界时间步长△tcrit的计算公式,并以数值算例给出了实现的步骤。     

基于ANSYS二次开发的轮轨耦合模型及应用研究

基于ANSYS的二次开发技术,首先利用APDL语言提出一种具有广泛适用性的轮轨耦合相互作用计算方 法。在该计算方法中,车辆部分基于多体动力学理论建模,并通过APDL语言编程到ANSYS中,再根据有限元理论对 轨道部分进行仿真,充分考虑轮轨非线性接触,车辆系统和轨道系统分别采用显式积分和隐式积分求解。然后,通过 与文献中采用交叉迭代算法计算得到的车辆-轨道垂向耦合系统动力响应对比,验证模型和计算方法的正确性。最后, 以高速列车-CRTSⅡ型板式无砟轨道为例,利用该方法分析扣件失效数量对耦合系统动力响应的影响。研究结果表 明：单个扣件失效对车辆系统的动力响应影响有限,对于钢轨的动力响应影响较大;扣件失效数量的增加会显著增大 车轨系统的动力响应,加剧轮轨的磨耗和相邻钢轨扣件的失效。提出的计算方法可以对不同型式的轨道结构和轨下 基础进行分析,对于轮轨耦合动力特性的研究具有很好的适用性。     

结构体系动力方程求解的显式积分格式的能耗特性

针对作者提出的结构体系动力方程求解的一种显式积分格式,探讨其数值计算能耗特性即算法阻尼特性,导出了其算法阻尼值随体系的物理阻尼和结构体系振动频率值变化的关系,并进一步讨论了该积分格式用于无限介质波动的数值模拟中抑制或消除透射边界引起的计算高频失稳问题,给出了该积分格式与中心差分格式的对比分析算例。     

一种半隐式的气动弹性时域求解方法

针对结构小幅运动、流动强非线性的气动弹性问题,基于Adams 隐式方法发展了一种半隐式的线性多步法(SILMS)。将隐式的广义气动力项采用显式插值求解,结构项仍采用隐式格式计算,该方法融合了显式方法耦合简单和隐式方法稳定性好的特点。结构运动采用模态坐标描述,流动方程应用计算流体力学(CFD)技术求解,二者采用松耦合方法进行时域推进。算例计算了一个标准气动弹性模型(Isogai wing)的颤振结果,并与几种经典的时域模拟方法进行了比较,证明该方法具有效率高、稳定性好、精度高的优点。     

基于显式摩擦摆单元的大规模复杂连体结构非线性时程分析

为克服复杂摩擦摆减隔震结构隐式非线性动力分析收敛困难且计算效率低的技术瓶颈;基于经典的摩擦摆力学模型,该文构造了一种2节点12自由度的显式摩擦摆单元,利用修正的向前Euler方法实现了此单元的内力计算;在自主研发的非线性有限元软件中完成开发,通过与SAP2000隐式摩擦摆单元对比,验证了开发内容的正确性。利用自主研发软件对某三塔连体结构进行了整体动力时程分析,研究了结构非线性、连廊支座类型及参数对结构动力响应的影响。     

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. © 1998 John Wiley & Sons, Ltd.     

Partitioned rational Runge Kutta for parabolic systems

A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit–explicit or mixed time implicit–explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.     

Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method

An implicit integration strategy was developed and implemented for use with the material point method (MPM). An incremental‐iterative solution strategy was developed around Newton's method to solve the equations of motion with Newmark integration to update the kinematic variables. Test problems directly compared the implicit MPM solutions with those obtained using an explicit MPM code and implicit finite element (FE) code. Results demonstrated very good agreement with FE predictions and also illustrated several advantages in comparison to calculations using the explicit MPM code. In particular, the accuracy of the implicit solution was superior to the explicit MPM when compared to validated FE solutions, and by definition the implicit time integration is unconditionally stable. Similarities between the assembly of the implicit MPM equations and those of the FE method were identified and should allow further algorithmic improvement. Copyright © 2003 John Wiley & Sons, Ltd.     

Development of mixed time partition procedures for thermal analysis of structures

The computational methods used to predict and optimize the thermal-structural behaviour of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.     

An adaptive time integration strategy based on displacement history curvature

This work introduces a time‐adaptive strategy that uses a refinement estimator on the basis of the first Frenet curvature. In dynamics, a time‐adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative methods of solution. These changes aim to improve the relation between quality of response and computational cost. The method here proposed is suitable for a variety of numerical time integration problems, for example, in the study of bodies subjected to dynamical loads. The motion equation in its space‐discrete form is used as reference to derive the formulation presented in this paper. Our method is contrasted with other ones based on local error estimator and apparent frequencies. We check the performance of our proposal when employed with the central difference, the explicit generalized‐ α and the Chung‐Lee integration methods. The proposed refinement estimator demands low computational resources, being easily applied to several direct integration methods. Copyright © 2012 John Wiley & Sons, Ltd.     

非线性精细积分方法及其在拟动力试验中的应用

将精细积分方法和预估-校正Adams-Bashforth-Moulton多步法相结合,构造了一种避免状态矩阵求逆、隐式预估-校正、四阶精度的精细积分多步法,可用于多自由度结构体系的非线性地震反应分析。基于精细积分多步法,构造了一种实用的显式拟动力试验数值积分方法,该方法在成倍地增大时间步长后的计算精度比中心差分法高,稳定性较好,试验工作可大量减少。最后,将本文显式方法应用于组合筒体结构拟动力试验中。     

Trust‐region based return mapping algorithm for implicit integration of elastic‐plastic constitutive models

A new method for the solution of the non‐linear equations forming the core of constitutive model integration is proposed. Specifically, the trust‐region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic‐plastic models. Although attention here is restricted to these rate‐independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non‐quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared with other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared with existing algorithms. Through these efforts, it is shown that the utilization of a trust‐region approach leads to superior performance versus a traditional closest‐point projection Newton–Raphson method and comparable speed and robustness to a line search augmented scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Segregated Runge–Kutta methods for the incompressible Navier–Stokes equations

In this work, we propose Runge–Kutta time integration schemes for the incompressible Navier–Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both velocities and pressures. The segregated Runge–Kutta methods are motivated as an implicit–explicit Runge–Kutta time integration of the projected Navier–Stokes system onto the discrete divergence‐free space, and its re‐statement in a velocity–pressure setting using a discrete pressure Poisson equation. We have analysed the preservation of the discrete divergence constraint for segregated Runge–Kutta methods and their relation (in their fully explicit version) with existing half‐explicit methods. We have performed a detailed numerical experimentation for a wide set of schemes (from first to third order), including implicit and IMEX integration of viscous and convective terms, for incompressible laminar and turbulent flows. Further, segregated Runge–Kutta schemes with adaptive time stepping are proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

Investigation of integration algorithms for rate-dependent crystal plasticity using explicit finite element codes

The work presented here concerns the use of rate-dependent crystal plasticity into explicit dynamic finite element codes for structural analysis. Different integration or stress update algorithms for the numerical implementation of crystal plasticity, two explicit algorithms and a fully-implicit one, are described in detail and compared in terms of convergence, accuracy and computation time. The results show that the implicit time integration is very robust and stable, provided low enough convergence tolerance is used for low strain-rate sensitivity coefficients, while being the slowest in terms of CPU time. Explicit methods prove to be fast, stable and accurate. The algorithms are then applied to two structural analyses, one concerning flat rolling of a polycrystalline slab and another on the response of a multicrystalline sample under uniaxial tensile condition. The results show that the explicit algorithms perform well with simulation times much smaller compared to their implicit counterpart. Finally, mesh sensitivity for the second structural analysis is investigated and shows to slightly affect the global response of the structure.