微分求积法处理轴向变速黏弹性梁混杂边界条件

给出了一种利用微分求积法处理非线性轴向变速黏弹性梁的混杂边界条件的方法。利用微分求积法数值求解具有混杂边界轴向变速黏弹性梁的控制微分方程,将混杂边界条件直接引入到控制微分方程高阶导数的微分求积解权系数矩阵中。使用这种方法研究了非线性轴向变速黏弹性梁主参数共振的稳态幅频响应,并对算例的微分求积解和解析近似解做了比较。     

用GDQ空-时半解析法分析圆弧拱强迫振动

从圆弧拱的强迫振动控制方程出发,在空间域采用广义微分求积法,将广义微分求积法中的节点参数在时域内取为响应的时间级数,通过时域配点求解该六阶偏微分方程得到全域内的响应位移场,分析了圆弧拱的平面内强迫振动问题。运用Matlab语言编制圆弧拱强迫振动时程分析的计算程序,并进行了相应的算例分析,数值计算结果表明该方法对于求圆弧拱的强迫振动问题具有较高的精度和效率。     

用微分求积法求解梁的弹塑性问题

根据梁塑性弯曲的工程理论,采用微分求积法进行了梁的弹塑性平面弯曲分析。微分求积法是一种直接求解微分方程(组)的数值方法,不依赖于变分原理,且能以较少的网格点求得微分方程的高精度数值解。与有限元分析结果的比较,表明了微分求积法求解梁的弹塑性问题的计算效率和精度。微分求积法的计算结果不受荷载步长的限制,也不需要迭代求解,特别对于承受非线性分布荷载作用的梁的弹塑性分析具有很大的优越性。通过选用不同的网格点数目,分析了微分求积法的稳定性和收敛性。     

轴向变速黏弹性Rayleigh梁非线性参数振动稳态响应

研究非线性轴向运动黏弹性Rayleigh梁因速度周期变化产生的亚谐波共振。轴向运动速度在平均速度附近做简谐周期性脉动。通过取物质导数的Kelvin本构关系描述Rayleigh梁的黏弹性。运用多尺度近似解析方法,构建轴向运动Rayleigh梁的非线性偏微分方程的可解性条件,分析参数振动稳态响应的振幅与扰动速度频率关系。并运用微分求积方法直接离散非线性Rayleigh梁的控制方程,以验证近似解析方法分析。通过数值算例,分析了系统参数对稳态响应曲线的影响。     

波谱单元法在空间桁架地震响应分析中的应用

摘 要：针对传统波谱单元法（SEM）只能用于求解节点集中荷载作用下结构动力响应问题的不足,提出了一种通过计算地震等效波谱节点荷载求解桁架结构地震响应的方法。基于虚功原理,利用波谱形函数积分得到地震等效波谱节点荷载的显式表达式,通过修改波谱单元法中单元刚度矩阵的波数,考虑了阻尼对结构动力特征的影响,采用数值拉普拉斯（Laplace）变换替换快速傅立叶（FFT）变换,回避了传统波谱单元法中FFT的周期性问题。利用地震荷载等效后的波谱节点荷载对三维空间桁架结构进行地震响应分析,结果表明,采用本文的方法能方便的计算桁架结构的地震等效波谱节点荷载,精确求解结构的地震响应,与传统有限元法（FEM）相比,大大减少计算单元数量,提高计算精度,且便于编程计算。     

混杂边界轴向运动Timoshenko梁固有频率数值解

运用微分求积方法求解两端带有扭转弹簧且弹簧系数均可任意变化的非对称下的轴向运动Timoshenko梁的固有频率。以权系数修改法处理轴向运动Timoshenko梁的混杂边界。研究系统的前两阶固有频率随轴向速度、刚度系数以及弹簧弹性系数变化的情况,并将数值计算结果与半解析半数值的研究结果进行比较,结果表明,数值计算结果与半解析半数值结果基本吻合。     

计及非齐次边界条件的面内变速运动黏弹性板的稳态响应

研究非齐次边界条件和1∶3内共振下面内平动黏弹性板的横向非线性1∶2主参数振动的稳态响应。考虑黏弹性对边界条件的影响,建立了面内平动板的偏微分运动方程和相应的非齐次边界条件。采用直接多尺度法建立了次谐波参数共振时的可解性条件,并根据Routh-Hurvitz判据判别了系统幅频响应的稳定性。讨论了速度扰动幅值和黏弹性系数对幅频响应的影响,对比了齐次和非齐次边界条件下稳态响应的差异。最后,引入微分求积法验证直接多尺度法的近似解析结果。     

基于微分求积法及V-变换的大规模动力系统快速数值计算方法

针对大规模动力系统动态响应的数值计算,传统的微分求积法通常在时间域上逐步离散、整体求解,存在“维数灾”问题。在多级高阶时域微分求积法的基础上,提出了基于V-变换的大规模动力系统动态响应的快速数值计算方法。利用微分求积法的加权系数矩阵满足V-变换这一重要特性,将离散后的雅可比矩阵方程进行解耦分块,推导形成了多级分块递推计算方法。数值算例表明,即使采用相当于Newmark方法2s倍的步长,微分求积法的计算精度仍比Newmark方法要高出2~3个数量级。进一步对3个不同规模的算例系统进行了测试,结果表明：相对于传统的数值计算方法,多级分块递推计算方法可以获得较大的加速比,能够显著提高大规模动力系统动态响应的计算效率。     

橡胶支座与柱串联体系的动力特性分析

针对工程界比较关注的橡胶隔震支座与柱串联的隔震体系,研究了串联隔震体系横向振动的固有频率,探讨了轴向压力和不同隔震支座等效弯曲刚度对串联隔震系统固有频率的影响。考虑横截面转动和剪切变形以及轴向压力的影响,建立了串联隔震系统横向自由振动的数学模型;采用微分求积单元法（DQEM）对所得控制方程和边界条件进行离散处理,避免了繁琐的偏微分方程求解;数值求解固支—自由边界条件下串联隔震体系的横向固有频率,并得到该系统横向固有频率参数随压力变化的曲线。数值结果表明：轴向力的增加将显著降低串联隔震系统的低阶固有频率;在总高度一定的情况下,隔震支座尺寸的增大对串联隔震体系的力学特性也有显著的影响。     

应用动力单元法进行空间索网结构自由振动分析

索网结构具有成型跨度大而结构重量轻的优点,因此在空间航天领域得到了广泛应用。目前对索网结构的动力学分析主要是采用集中质量法或有限单元法进行低阶模态的分析,这些方法得到的较高阶频率和模态,其精度和实用性都不理想。动力单元法采用含有固有频率的动态形函数作为动力学分析离散单元中的插值函数,该形函数由单元动力学控制微分方程导出,因此能给出比有限元法更高的求解精度。在总结研究动力单元法理论的基础上,推导了张紧索单元的动力单元矩阵。采用动力单元法对几个典型的空间张紧索网结构进行动力学特性的分析,并将分析结果与传统有限元分析结果进行比较。     

DQEM for analyzing dynamic characteristics of layered fluid-saturated porous elastic media

Based on the Porous Media Theory presented by de Boer, the governing differential equations for a layered space-axisymmetrical fluid-saturated porous elastic body are firstly established, in which the suitable interface conditions between layers are presented. Then, a differential quadrature element method (DQEM) is developed, and the DQEM and the second-order backward difference scheme are applied to discretize the governing differential equations of the problem in the spatial and temporal domain, respectively. In order to show the validity of the present analysis, the dynamic response of a fluid-saturated porous medium is analyzed, and the obtained numerical results are directly compared with the existing analytical results. The effects of the numbers of the elements and grid points on the convergence of the numerical results are considered. Finally, the dynamic characteristics of a layered fluid-saturated elastic soil cylinder subjected to a water pressure or a dynamic loading are studied, and the effects of material parameters are considered in detail. From the above numerical results, it can be found that the DQEM has advantages, such as little amount in computation, good stability and convergence as well as high accuracy, so it is a very efficient method for solving the problems in soil mechanics, especially such problems with discontinuities.     

Dynamic response of shear-deformable axisymmetric orthotropic circular plate structures solved by the DQEM and EDQ based time integration schemes

The dynamic response of shear-deformable axisymmetric orthotropic circular plate structures is solved by using the DQEM to the spacial discretization and EDQ to the temporal discretization. In the DQEM discretization, DQ is used to define the discrete element model. Discrete dynamic equilibrium equations defined at interior nodes in all elements, transition conditions defined on the inter-element boundary of two adjacent elements and boundary conditions at the structural boundary form a dynamic equation system at a specified time stage. The dynamic equilibrium equation system is solved by the direct time integration schemes of time-element by time-element method and stages by stages method which are developed by using EDQ and DQ. Numerical results obtained by the developed numerical algorithms are presented. They demonstrate the developed numerical solution procedure.     

On non‐linear behaviour of spherical shallow shells bonded with piezoelectric actuators by the differential quadrature element method (DQEM)

The static behaviour of spherical shallow shells bonded with piezoelectric actuators and subjected to electrical loading are studied in this paper by using the differential quadrature element method (DQEM). Geometrical non‐linear effects are considered. Detailed formulations for the DQ circular spherical shallow shell element and the DQ annular spherical shallow shell element are given for the first time. Numerical studies are performed to evaluate the effects of actuator size, thickness and boundary conditions. Very accurate results are obtained by the DQEM. Based on the results reported in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions for smart materials and structures exhibiting geometric non‐linear behaviours. Thickness effects cannot be neglected when the actuator thickness is comparable to that of the base material. Snap‐through may occur when the applied voltage reaches a critical value even without mechanical loading for certain geometric configurations. Copyright © 2001 John Wiley & Sons, Ltd.     

The Timoshenko beam model of the differential quadrature element method

A new numerical approach for solving Timoshenko beam problems is proposed. The approach uses the differential quadrature method (DQM) to discretize the Timoshenko beam equations defined on all elements, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of Timoshenko beam structures. The resulting overall discrete equation can be solved by using a solver of the linear algebra. Numerical results of the DQEM Timoshenko beam model are presented. They demonstrate the DQEM numerical method.     

DQEM for free vibration analysis of Timoshenko beams on elastic foundations

 A differential quadrature element method (DQEM) based on first order shear deformation theory is developed for free vibration analysis of non-uniform beams on elastic foundations. By decomposing the system into a series of sub-domains or elements, any discontinuity in loading, geometry, material properties, and even elastic foundations can be considered conveniently. Using this method, the vibration analysis of general beam-like structures is to be studied. The governing equations of each element, natural compatibility conditions at the interface of two adjacent elements and the external boundary conditions are developed in a systematic manner, using Hamilton's principle. The present DQEM is to be implemented to Timoshenko beams resting on partially supported elastic foundations with various types of boundary conditions under the action of axial loading. The general versality, accuracy, and efficiency of the presented DQEM are demonstrated having solved different examples and compared to the exact or other numerical procedure solutions. Received: 11 October 2002/Accepted: 26 November 2002     

Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor

Abstract

This paper is concerned with evaluating stress intensity factors (SIFs), for a cracked curved beam of rectangular cross section, applying an approach which allows us to estimate the strain energy release rate. The beam is located on an elastic foundation. The out-of-plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach, namely differential quadrature element method (DQEM), to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.     

Differential quadrature element method for static analysis of shear deformable cross‐ply laminates

In this paper, the two‐dimensional differential quadrature element method (DQEM) is developed for the static analysis of symmetric cross‐ply laminates using the first‐order shear deformation plate theory. In this study, the laminated plate, which may contain different discontinuities in loading, geometry, material, and boundary conditions, is first divided into several simple plate elements and then the differential quadrature method (DQM) is applied to each simple element. Compatibility conditions are derived to connect the plate elements so that the overall matrix equation system for the whole plate is obtained and solved. The reliability of the DQEM for solving the titled problems is examined carefully through convergence and accuracy studies and finally some numerical test examples are given to demonstrate the applicability and flexibility of this method for practical use. The methodology presented here has overcome some critical drawbacks of the global DQM but is different from the Quadrature Element Method (QEM) since only one grid point is employed to represent the interface point. Copyright © 1999 John Wiley & Sons, Ltd.     

A micromechanics based analysis of hollow fiber composites using DQEM

In this study, a generalized plane strain micromechanical model is presented to obtain micro-stress/strain fields within the unidirectional (UD) hollow fiber reinforced composites. In addition, the thermally induced residual stresses during cooling down process, overall elastic properties and energy absorption capability of hollow reinforced composite are studied. The representative volume element (RVE) of the composite consists of a quarter of the fiber surrounded by matrix to represent the real composite with repeating square array of fibers. Fully bonded fiber–matrix interface condition is considered and the displacement continuity and traction reciprocity are properly imposed to the interface. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain. A Least-squares based differential quadrature element method (DQEM) is used to obtain solutions for the governing partial differential equations of the problem. Results of the presented method for various stress and displacement components and thermal residual stresses show excellent agreement with finite element analysis. Furthermore, predicted overall properties also show good agreement with other available analytical and finite element results. Moreover, results also revealed that the presented model can provide highly accurate predictions with a few number of elements and grid points within each element.     

索杆式伸展臂的结构设计与分析

 对国内外伸展臂的研究现状进行了总结，说明了索杆式伸展臂具有的高精度、高刚性、高收纳率的特点．结合一种索杆式伸展臂的模型制作，介绍了该类伸展臂的技术要求，其中包括：高收纳率、高刚性、展开的高可靠性、轻质量、高重复展开精度以及满足空间环境要求等．同时，总结了伸展臂展开与收纳机理和设计方法．最后，对伸展臂展开后的结构进行了动力分析，包括模态、频率响应和冲击响应分析．动力学分析的结果可以作为伸展臂实际应用时的参考．     

Time-Resolved Characterization of Ferroelectrics Using High-Energy X-Ray Diffraction

Diffraction provides an effective means to characterize ferroelectric materials under the application of dynamic and cyclic electric fields. This paper describes a typical timeresolved diffraction setup at a synchrotron facility using high X-ray energies. Such a setup is capable of measuring the structural response of ferroelectric ceramics to electric fields of various frequencies, amplitudes, and waveforms. The use of high energies also allows the response of the sample to be measured at various angles to the applied load. The results of 3 different types of electric loading are presented and discussed: the structural response of ferroelectric ceramics to a single electric field step function, a cyclic electric field of square waveform, and a cyclic electric field of sinusoidal waveform. Each type of electric field loading provides unique information about the material behavior.