从И.Г.布勃诺夫生平活动寻迹“船舶结构力学”的创建

本文内容分两部分.第1部分,简介I.G.布勃诺夫生平活动.第2部分,从I.G.布勃诺夫生平活动追寻他如何创建"船舶结构力学":接受优质的造船专业教育,攻读高水平数学力学课程;充分认识发展钢壳船面对的问题,以建立一门船舶结构强度计算学科为已任;为建立这一学科作充分的理论准备;在军舰结构设计实践中建立船舶结构强度计算方法;将计算方法的实践上升为理论,建立"船舶结构力学"学科;培养人才,使这一学科后继有人,不断发展.     

压电智能结构动力系统的伽辽金方法

币压电传感器、作动器和梁组成的机电耦合的动力系统，本文提出了一个计算机数值模拟的伽辽金方法。从哈密顿原理出发，导出其状态方程，采用有限维样条函数逼近该动力系统的运动。算便与实验结果比较表明，本文提出的方法，对于机电耦合梁的振动控制分析是有效的。此方法也容易进一步推广到其他更为复杂的智能结构。     

混合变换法在无网格伽辽金方法中的应用

移动最小二乘近似的非插值特征给无网格伽辽金方法的应用带来了一定的的困难，本文将再生核质点法中的混合变换法与无网格伽辽金方法相结合，通过对移动最小二乘近似进行局部修正，实现了无网格伽辽金方法中本质边界条件的精确施加。对权函数、影响半径、积分阶等对计算精度的影响进行了有益的探讨。数值计算结果表明了方法的可行性。     

无单元伽辽金法的并行计算

对无单元伽辽金法的并行计算进行了详细研究,并将其应用于弹性动力学问题。使用并行桶搜索算法进行节点搜索,使用并行几何搜索算法进行样点搜索,讨论了移动最小二乘MLS(Moving Least Squares)形函数及其导数的并行计算和方程组的并行求解,并利用多层图形划分实现负载平衡。最后给出了并行无单元伽辽金法应用于弹性动力学的计算流程和实例。计算结果表明无单元伽辽金法具有很高的并行性和很好的并行效率,对其进行并行计算具有非常重要的意义。     

利用无网格伽辽金法分析材料稳态蠕变问题

稳态蠕变是高温环境下材料的一个重要的考虑问题,它也是材料破坏的一种重要形式。由于存在划分网格,利用传统有限元法模拟稳态蠕变有一定的不足之处。作为一种新兴的数值模拟方法,无网格法不需要划分单元,只需将求解问题离散成独立的结点,计算过程可以局部细化。利用连续介质的虚功原理,将无网格伽辽金法应用于稳态蠕变的数值模拟,推导了稳态蠕变的无网格伽辽金法控制方程。利用罚参数来实现稳态蠕变的不可压缩条件和本质边界条件,能够保证求解过程中刚度矩阵的对称正定性。通过实例的计算结果表明,无网格伽辽金法在求解稳态蠕变时具有较高的计算精度,结果与理论解结果吻合,而且前后处理较为简单。     

几何非线性分析的无网格伽辽金算法

利用几何非线性的应变-位移关系,在小应变假设的条件下,推导出二维几何非线性问题中的无网格伽辽金法的计算格式。由于无网格方法中的形函数不具备Kronecker delta性质,文中采用罚方法来实现本质边界条件。数值实例表明,无网格伽辽金法在处理几何非线性问题时,具有较高的计算精度,是一种有效的数值计算方法。     

关于伽辽金法的一点注记

伽辽金法作为一种数值方法,广泛用于各种数学物理工程问题.教科书和一些文献关于伽辽金法试函数的选取存在一些争议,本文通过应用该法求解轴向力作用下悬臂梁的静动力学问题为例,证实仅选取满足位移而不满足力边界条件的试函数时,即使增加试函数的个数,可能也无法获得正确的计算结果.     

无单元伽辽金法在船体开孔板格弹性屈曲分析中的应用

针对船体开孔板格弹性屈曲问题,评估了无单元伽辽金法(EFG)的适用性。编程计算分别基于MLS近似和移动Kriging插值两种形函数构造方式进行,以ABAQUS有限元解为基准确定了两种算法最佳内置参数,对比分析了计算耗时和相对误差。结果表明:MLS-EFG算法在不同的板格尺寸、开孔位置、载荷条件下的结果都比较准确,具有较好的适用性;而MK-EFG算法的计算速度更优,但在纯剪切屈曲分析时计算结果存在一定程度的正偏差。本研究可为无网格法在船体结构设计中的推广应用提供参考。     

稳定节点积分伽辽金无网格法的应力计算方法研究

应力计算是基于稳定节点积分的伽辽金无网格法的重要组成部分.该文着重研究稳定节点积分伽辽金无网格法的应力计算方法,对稳定节点积分方法的变分一致条件进行了讨论.证明当节点代表域内的应变采用非局郎光滑应变时,相应的应力在节点代表域内为常数,稳定节点积分伽辽金无网格离散方程是变分一致的.文中提出了三种节点应力计算方法,研究表明,基于位移梯度的节点应力计算方法不满足变分一致性要求,而采用光滑应变的节点应力计算方法和一致形心应力计算方法满足变分一致性要求.典型数值算例的误差分析表明,满足变分一致性不一定确保得到更为精确的结果.而基于光滑应变的一致形心应力计算方法总是较其它两种方法更为精确.     

一种适用于强非线性结构力学问题数值求解的修正小波伽辽金方法

论文通过对有限区间上的任一连续函数在边界处采用基于泰勒展开的延拓处理,构造了一种与任意边界条件相协调的改进小波尺度基函数及在此基础上建立了小波逼近格式,由此可有效避免小波逼近在求解微分方程时在边界处的跳跃或抖动问题.在此基础上,结合论文后两位作者提出的广义小波高斯积分法,关于未知函数的任意非线性项的小波展开可以显式地用原未知函数的展开系数表征,据此建立了一种可适用于求解任意强非线性的梁弯曲问题的小波伽辽金方法.该方法具有解的封闭性与计算简单等特点.通过定量求解包含幂次非线性与非幂次非线性项梁的两例大挠度弯曲问题,所得结果表明论文所建立的方法具有良好的数值精度.     

Buckling analysis of an elastic bar using the Bubnov-Galerkin method

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 148–156, January–February, 2008.     

Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach

Summary The Bubnov-Galerkin method is applied to reduce partial differential equations governing the dynamics of flexible plates and shells to a discrete system with finite degrees of freedom. Chaotic behaviour of systems with various degrees of freedom is analysed. It is shown that the attractor dimension of a system has no relationship with the attractor dimension of any of its subsystems.This work has been partially supported by Department of Mathematics of the Central European University in Budapest.     

Fundamental solution method for inverse source problem of plate equation

The elastic plate vibration model is studied under the external force. The size of the source term by the given mode of the source and some observations from the body of the plate is determined over a time interval, which is referred to be an inverse source problem of a plate equation. The uniqueness theorem for this problem is stated, and the fundamental solution to the plate equation is derived. In the case that the plate is driven by the harmonic load, the fundamental solution method (FSM) and the Tikhonov regularization technique are used to calculate the source term. Numerical experiments of the Euler-Bernoulli beam and the Kirchhoff-Love plate show that the FSM can work well for practical use, no matter the source term is smooth or piecewise.     

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.     

Uniquenes of solution of field point of singular source outside-region-distribution method

The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outsidergeion-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality. Examples of part ofthese singular sources such as Kelvin’s point force, Point-Ring-Couple (PRC) etc.are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.     

Improvement of mass source/sink for an immersed boundary method

An improved immersed boundary method using a mass source/sink as well as momentum forcing is developed for simulating flows over or inside complex geometries. The present method is based on the Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. A more accurate formulation of the mass source/sink is derived by considering mass conservation of the virtual cells in the fluid crossed by the immersed boundary. Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are used to validate the proposed formulation. The results indicate that the accuracy near the immersed boundary is improved by introducing the accurate mass source/sink. Copyright © 2006 John Wiley & Sons, Ltd.     

改进的平均源边界节点法模拟平面位势问题

平均源边界节点法ASBNM是一种最近提出的边界型无网格法。该方法仅使用边界节点不涉及任何单元和积分的概念,具有方法简单和程序设计容易等特点。但是,对于依赖于边界积分方程的边界型无网格法,关键问题是如何准确高效地估计影响矩阵的对角元。本文提出直接计算影响矩阵对角元的方法,是已有ASBNM法的改进,将对角元的计算转化为一个纯几何问题,因此适用于任何二维边值问题。数值算例证明了本文方法的有效性和准确性。     

水下爆炸爆源定位方法与误差分析

提出了一种采用最小误差逼近法对水下爆源进行定位计算的方法。通过验证性实验表明,在有效传感器观测数据不小于4个的情况下,该方法完全可以满足现场测量的要求;该方法在个别测量数据准确性较差的情况下,仍能得出较好的计算结果。最后分析了测点数据准确性、测点布置紊乱度、模型参数的准确性和测点数量对计算误差的影响,提出了定位计算实验所需要注意的问题。