卷积型GD半解析法及矩形薄板瞬态响应解

卷积型的Gurtin变分原理是目前在数学上唯一能和动力学初值问题完全等价的变分原理,它完全反映了有关初值问题的全部特征。GD法（General Differential Method）是从泰勒展开式出发,推出的一种求解偏微分方程的数值方法,本文系统地介绍了GD法的基本原理,以及权系数的推导。本文通过卷积将矩形薄板原始控...     

Dynamic response of elastic rectangular plates by spline state variable method

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Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

基于小波微分求积法的薄板弯曲分析

利用小波微分求积法(WDQM)对任意荷载作用下的薄板弯曲问题进行了求解分析。数值算例表明,小波微分求积法与一般的DQ法相比具有很好的适用性,特别是薄板受集中荷载或不连续分布荷载作用时,由于小波基函数的紧支撑特性与其对突变信号良好的描述能力,WDQ法的精度明显优于一般的DQ法,具有良好的应用前景。     

轴向均布载荷下压杆稳定问题的DQ解

叙述了微分求积法(differential quadrature method)的一般方法，研究用微分求积法求解在均布轴向载荷下细长杆的稳定问题．通过Newton-Raphson法求解非线性方程组，以及对问题进行线性假设后求解广义特征值方程，得到了精度很高的后屈曲挠度数值和临界载荷数值．与解析解和其他近似解相比，微分求积法具有较高的精度和简便性．     

Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression

In this paper, applving perturbation method to von Kármán nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments. The method suggested in this paper which has not been found in previous papers is rather simple and easy for the postbuckling analysis of rectangular plates.     

Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

Based on the Biot theory of porous media,the exact solutions to onedimensional transient response of incompressible saturated single-layer porous media under four types of boundary conditions are developed.In the procedure,a relation between the solid displacement u and the relative displacement w is derived,and the well-posed initial conditions and boundary conditions are proposed.The derivation of the solution for one type of boundary condition is then illustrated in detail.The exact solutions for the other three types of boundary conditions are given directly.The propagation of the compressional wave is investigated through numerical examples.It is verified that only one type of compressional wave exists in the incompressible saturated porous media.     

微分求积单元法在结构工程中的应用

微分求积法（Differential Quadrature Method）是求鳃偏微分方程和积分-微分方程的一种数值方法,该法具有计算简便、精度较高和易于实现等优点。微分求积单元法（Differential Quadrature Element Method）是在微分求积法的基础上结合区域分割和集成规则而形成的一种新的数值计算方法,能通过自适应地选取微分求积网点数目正确模拟构件的刚度和荷载性质,其精度可通过细分单元或增加离散点数目加以提高。微分求积单元法是一种可供选择的、性能优越的数值计算方法。本文将详细论述这一数值方法的基本原理,并通过数值算例说明该方法的应用过程及其优越性,为这一方法在结构工程中的推广应用提供参考。     

Early short time transient response of finite L-shaped Mindlin plate

The early short time transient response of an L-shaped plate is investigated by the method of reverberation ray matrix (MRRM) and the generalized ray method (GRM). The MRRM and GRM have been successfully used to study the transient elastic wave transmitting in the beams, planar trusses, space frames and infinite layered media. In the present paper, these two methods are extended to investigate the flexural wave propagation in a finite L-shaped Mindlin plate. The reverberation-ray matrix representing the multi-reflected and scattered waves in the L-shaped plate is presented. The rays in the GRM propagating in the L-shaped plate are determined by the shock source and the boundary conditions. From the numerical results, it indicates that the early short time transient responses of L-shaped plate calculated by the MRRM are the same as those by the GRM. The early short time transient acceleration responses are very large, while the early short time transient displacement responses are very small for the L-shaped plate subjected to the unit impulse. Furthermore, the effects of the different shock signals and the plate thickness on the early short time transient responses of the finite L-shaped Mindlin plates are also analyzed.     

竖向裂缝对功能梯度板的热响应影响

采用条单元法分析了竖向裂缝对功能梯度板的热响应影响。功能梯度板的材料属性沿板厚方向连续线性变化,温度变化热源作用于带竖向裂缝的功能梯度板上。通过研究得出了裂缝距离热源不同位置、不同长度裂缝及不同频率温度变化热源等状态时,功能梯度板上表面的热响应情况。采用条单元法研究带竖向裂缝的功能梯度板的热响应问题,为带裂缝的功能梯度板的热研究提供了一定的指导。     

横向裂缝对功能梯度板的热响应影响

采用条单元法分析了横向裂缝对功能梯度板热响应的影响。研究了功能梯度板的材料属性沿板厚方向连续线性变化时,温度变化热源作用于带横向裂缝的功能梯度板的问题（此热源沿板厚方向连续线性变化）。通过研究不同频率温度变化热源,得到了当量纲为一的温度变化热源频率为3.14时,功能梯度板上表面出现的位移响应比较均匀;通过研究裂缝长度取H、3H、5H时出现的位移响应,得到了根据位移响应特性判断裂缝长度的方法;通过对不同深度裂缝的研究表明：裂缝越深,上表面位移响应强度越小。本研究对带横向裂缝的功能梯度板的热响应问题具有一定的指导意义。     

Steady-shear viscosity and transient stress response for elasto-thixotropic fluids

A phenomenological model for dispersed systems which exhibit complex rheological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to different kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus functionG of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic ordersn=m=2.     

斜拉桥拉索-阻尼器系统非线性响应分析

考虑索的抗弯刚度、垂度及几何非线性的影响,得出了索一阻尼器系统的空间非线性振动偏微分方程,用中心差分法将微分方程在空间内离散,导出了系统的非线性振动常微分方程组。结合Newmark法及虚拟力法提出了一种用于求解非线性振动瞬态响应的杂交分析算法。并以典型的斜拉桥拉索为研究对象,给出了数值算例,并与Runge—Kutta直接积分法进行了比较,说明了杂交算法的准确性及有效性。     

Nonlinear transient response of stay cable with viscoelasticity damper in cable-stayed bridge

Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.     

可倾瓦径向滑动轴承支承的转子系统瞬态响应计算

研究了可倾瓦径向滑动轴承支承的转子系统瞬态响应的计算方法,提出了可倾瓦径向滑动轴承非线性滑膜力计算的数据库方法,将可倾瓦与轴颈的结构和运动参数归结到三个参数中,建立了起可倾瓦的非线性油膜力数据库,通过精确插值到每一运动参数组合下轴承提代的油力和轴瓦上所受的油膜力矩。     

计入膜力塑性耗散效应的矩形板塑性动力响应

从能量的观点在小挠度理论中引入表征膜力塑性耗散效应的修正因子,基于刚性板块的总体平衡给出矩形板大挠度塑性动力响应的完全运动方程组,分析了理想刚塑性简支和固支矩形板在矩形脉冲和冲击载荷下包括移行塑性铰相的完全大挠度响应过程。解决了当矩形板的挠度达到厚度量级时弯矩、膜力的联合作用问题,理论预报的结果在板的挠度为10倍板厚的量级与实验结果符合良好,改进了只考虑弯矩作用的小挠度理论结果和模态近似估计。     

Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.     

流固冲击载荷下弹性约束加筋板的非线性动力响应

本文在考虑大变形、忽略阻尼影响的情况下,基于高散加筋板模型,对具有弹性约束边界的加筋板在流固冲击载荷下的非线性瞬态响应进行了理论研究.取样条函数作为挠度试函数,运用加权残值法求得加筋板动力响应的控制方程,采用四阶Runge-Kutta法求解该方程,并用Fortran语言编制了相应的计算程序.构造的B样条函数能适应板侧边上的任意弹性转动约束.文中不仅分析了不同的冲击载荷形式对加筋板动力特性的影响,还讨论了载荷峰值、冲击栽荷持续时问、加强筋和弹性转动约束的影响.     

Dynamic response of plates due to moving vehicles using finite strip method

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A high accurate time-domain-advance integration method for transient elastodynamic problems

All step-by-step integration methods available at present for structural dynamic analysis use the displacement, velocity, and acceleration vectors computed at a previous interval for evaluating those at an advanced time step. Hence, an accumulated error will be definitely introduced after such integration. This paper presents a novel time-domain-advance integration method for transient elastodynamic problems in which the exact initial conditions are strictly satisfied for the solutions for each time step. In this way, the accumulated error can be eliminated and the approximate solutions will converge to the exact ones uniformly on the whole time domain. Therefore, the new method is more accurate. When applying to a structural dynamic problem, the present mehtod does not have to use the initial acceleration as is required by most other algorithms and the corresponding computation can be avoided. The present method is simple in representation, easy to be programmed, and especially suitable for accurate analyses of long-time problems. The comparison of numerical results with exact ones shows that the present method is much more accurate than some most widely used algorithms.