弹性压杆稳定问题的精确解法

对于杆系结构的静力问题能够通过有限单元法得到精确解答,但是对于稳定问题常规有限元法则很难得到精确解答。本文提出一种新的有限元列式,能够精确求解弹性压杆稳定问题。即通过对弹性压杆稳定问题控制微分方程进行分析,建立了新的精确单元形函数,提出一种新的弹性压杆稳定有限单元,利用迭代算法来确定压杆的临界荷载及相应的失稳模态。最后通过数值算例验证了本文方法的正确性及有效性。     

250m特高型塔式起重机塔身整体稳定性分析

本文用解析法和有限元法分析了连续多支承压杆的稳定性及其近似解与精确解。解析解与有限元解之间的误差,取得了较好的一致性,并通过250m特高型塔式起重机的实例进行了计算与验证。     

修正的VN方程组的对称、约化和精确解

为了得到修正的VN方程组的精确解,利用改进的CK直接方法研究该方程组,建立了该方程组新、旧解之间的关系,基于此关系推广了方程组的解;同时,得到了该方程组的对称,通过求解约化方程,得到修正的VN方程组的许多新的精确解,包括幂级数解、艾米尔函数解、雅克比椭圆函数解等。结果表明,改进的CK直接方法对于求解此类非线性发展方程的精确解是有效的。     

一个材料力学压杆稳定问题的精确解

本文详细地推导一个两端铰支承等截面细长压杆弹性曲线微分方程式的精确解,并说明解的最后结果及与近解的区别。     

新辅助函数法及(2+1)维Burgers方程的精确解

给出了一种新的辅助函数法,并给出了该辅助函数的一些精确解。作为例子,求解了(2+1)维Burgers方程。显然,该辅助函数法也可以解其它类型的非线性发展方程。     

考虑锚固体不均匀及杆体脱黏效应的GFRP抗浮锚杆杆体荷载分布函数

基于荷载传递理论及Kelvin位移解,推导得出理想条件下GFRP抗浮锚杆杆体与锚固体的剪应力、轴力沿锚固深度的分布函数,并通过对2根同型号GFRP抗浮锚杆的拉拔试验进行验证。试验结果表明:试验锚杆杆体轴力及剪应力分布曲线与理论值形式相似,证明提出理论方法应用于求解GFRP锚杆杆体荷载分布函数的可行性。但由于锚固体成型后的不均匀性及杆体的脱黏效应,导致试验剪应力值低于理论值且实际曲线主要分布范围较深,同时造成轴力下降较慢,消失深度较深的现象。通过固定脱黏长度下的平均剪应力衰减法及下移弹性段起点的方法对理想条件下的杆体剪应力分布函数进行修正,并利用杆体轴力分布与剪应力分布之间的函数关系,对理想条件下的轴力分布函数进行修正,修正后剪应力及轴力分布曲线精度大大提高。     

高层杆系结构的解析解

杆系结构本质上是一种离散体系，一般不存在封闭形式的解析解。本文拟通过若干高层结构说明，在“等劲式”条件下，这类离散性结构的静力、动力和稳定分析问题的解析解还是存在的，并且给出了相应的具体计算公式。对于非等劲式体系，则辅以摄动分析，仍可获得问题的精确解。     

悬索结构动力特征的研究与伽辽金法求解

悬索结构按对称振型振动时索力将发生变化，因此用单项正弦函数来描述对称振型是相当不精确的，尤其对前几阶振型。本文用多项正弦函数来逼近振型函数，并用伽辽金法求解振型与频率。为实际应用，按上述解给出了简化计算公式。为了证实上述解的精确性，将计算结果与连续化的超越函数解、非线性有限元的切线刚度法进行了数值比较。最后对悬索结构的动力特征进行了讨论，并给出了几个有用的结论。     

利用插值函数求解基础隔震结构的地震响应

利用插值函数逼近地面加速度并结合复数振型叠加法,提出了一种新方法用于求解多层基础隔震结构的动态响应,该求解方法能够得出精确解,由精确解作为基础,采用该法可大大减少了计算工作量,避免数值方法所常遇到的精确性、收敛性和稳定性问题。     

加腋梁的简化计算模型及其解析解

将横截面沿梁轴线连续变化的加腋梁简化为以截面形心的连线为中性轴的空间曲梁,推导出线弹性状态下加腋梁内力和挠度的精确解。同理可类推,任何沿梁轴线连续变化的变截面杆件都可简化成以横截面形心的连线为中性轴的空间曲杆,从而可得到其精确解。给出了对称直线加腋梁在均布荷载作用下的精确解和可供查表计算的表格,并将实例和三维有限元的数值解进行了对比,结果非常吻合。根据精确解得到了在横向荷载作用下加腋梁内产生轴力是其不同于等截面直梁的重要特性。     

Coupled flexural and torsional vibrations of ship-like girders

The paper is related to investigation of coupled horizontal flexural and torsional vibrations of container vessels. Differential equations of coupled vibrations of a prismatic beam with open cross-section are derived. The equations are solved analytically by direct integration and by variational method. In the former case, the frequency equation is reduced to a polynomial of the fourth order. In the latter case, beam deflection and twist angle are assumed in the form of series of natural modes of uncoupled vibrations of free beam with suspended warping. The variational method manifests very fast convergence and high accuracy. Application of the developed methods is illustrated in the case of a prismatic pontoon with cross-section of a container vessel. The same numerical example is used for checking 1D FEM mathematical model and code developed for analyses of real structures of container vessels with variable cross-sections. In addition, correlation analysis of 1D and 3D FEM results is done to validate the accuracy of the former.     

Free longitudinal vibrations of tall buildings and high-rise structures

In this paper, tall buildings and high-rise structures are considered as cantilever bars with variable cross-section for the analysis of their free vibrations. The differential equations of free longitudinal vibrations of bars with variable cross-section are reduced to Bessel's equations by selecting suitable expressions, such as power functions and exponential functions, for the distribution of stiffness and mass. An approach is proposed for determining the natural frequencies and mode shapes in the vertical direction for tall buildings and high-rise structures with variably distributed stiffness and variably distributed mass. The derived solutions are expressed in terms of Bessel functions. A numerical example shows that the value of the natural frequency computed by the proposed method is close to full scale measured data. It is shown that the selected expressions are suitable for describing the distributions of stiffness and mass of tall buildings and high-rise structures. It is demonstrated that the proposed method has practical significance for free longitudinal vibration analysis. © 1998 John Wiley & Sons, Ltd.     

Vibration characteristics of tall buildings braced by shear walls and thin‐walled open‐section structures

An analytical method is presented for the three‐dimensional frequency analysis of buildings braced by shear walls and thin‐walled open‐section structures. Owing to the asymmetry of the structure, the centre of gravity and the centre of flexural rigidity of the floor plan do not coincide, and hence the flexural vibration in two mutually perpendicular directions and the warping torsional vibrations are all coupled. Based on the continuum approach and D'Alembert's principle, the governing differential equation of free vibration and its corresponding eigenvalue problem for asymmetric shear walls and thin‐walled open‐section structures are derived. Based on the theory of differential equations, an analytical method of solution is proposed to solve the eigenvalue problem and a general solution is derived for determining the natural frequencies of the structures. Results obtained from the proposed method for the example structure show good agreement with those of finite element analysis. It is also shown that the proposed analysis is efficient and accurate enough to be used both at the concept design stage and for final analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Vibration analysis of tall buildings with narrow rectangular plane configuration

In this paper, tall buildings of narrow rectangular plane configuration are treated as one-step or multi-step cantilever flexural-shear plates for the analysis of their free vibrations. The governing differential equations for the vibration of flexural-shear plates considering the effects of both flexural and shear deformation are established. The general solutions for one-step flexural-shear plates are derived and used to obtain the eigenvalue equation for multi-step cantilever flexural-shear plates. A new exact approach is presented which combines the transfer matrix method and a closed-form solution for a uniform flexural-shear plate. A numerical example demonstrates that the calculated natural frequencies and mode shapes of a tall building are in good agreement with the experimentally measured data. It is also shown that the effect of shear deformation on the fundamental natural frequency can be ignored, but its effect on the higher natural frequencies should be considered. Copyright © 1998 John Wiley & Sons, Ltd.     

Electroelastic plate equations for high frequency vibrations of thermopiezoelectric materials

In relation to high frequency vibrations of ceramic materials subject to strong electric fields and large deflections, a system of plate equations is deduced from the three-dimensional equations of thermopiezoelectricity with second sound. The system of two-dimensional approximate equations is derived in differential and variational forms by means of a unified variational principle together with the series expansions of field variables, and it governs the extensional, thickness-shear and flexural as well as coupled vibrations of electroelastic plates of uniform thickness. Certain cases involving special motions, geometry and material properties are indicated and, in particular, the linearised system of plate equations is recorded and the uniqueness of its solutions is also pointed out.     

Free vibrations of orthotropic spherical shells

The equations of motion for the free vibrations of orthotropically stiffened open spherical shells are developed and solved using a suitable finite difference model. Variations in both flexural and extensional orthotropic stiffness properties are investigated by means of carefully selected parametric studies. A systematic examination of the contribution to strain energy in each mode, arising from the various components of orthotropic shell stiffness, is shown to assist the interpretation of the effects of orthotropic stiffness changes, and to allow prediction of approximate frequency spectra. Based on the analysis of a related isotropic spherical shell it is shown how a modified form of Rayleigh's method provides approximations of frequency spectra sufficiently accurate to assist the conceptual dynamic design process.     

大跨径连续梁构件刚度最小二乘识别方法

提出了一种利用低阶模态测试对桥梁构件抗弯刚度进行有限权量平差的最小二乘解识别方法。通过对主跨110m的3跨变截面连续箱梁广州大桥实桥梁体抗弯刚度进行数值模拟识别及结合桥梁现场动静载试验进行识别,表明此方法利用现有的测试技术对大跨径连续梁桥进行抗弯刚度识别,可获得较好的工程精度。     

Local and global instability and vibrations of a slender system consisting of two coaxial elements

The stability and free vibrations of a geometrically non-linear system built of a pipe and a rod are discussed in the paper. The pipe and the rod were connected between the mountings by an elastic element and the whole system was subjected to Euler’s load by external force whose direction is unchanging. The boundary problem (static and free vibrations) was formulated and solved, and numerical computations connected to the bifurcation load and natural frequency were carried out. The boundary problem was formulated using Hamilton’s principle and the straightforward expansion method. The calculations were carried out for different characteristic parameters of the considered system, such as rigidity, the placement of the elastic element, pre-stressing of the system as well as the flexural rigidity asymmetry factor of a column.     

两片弯剪型抗侧力体系的相互作用

推导了在水平荷载作用下共同工作的两个弯剪型抗侧力结构的基本微分方程组及其解析解。与传统框架-剪力墙结构可以一次求解不同,两个弯剪型结构共同作用的分析必须分两步求解。算例分析表明,一个结构的抗弯刚度参与另一个结构共同工作的能力受到自身抗剪刚度的影响,一个结构的抗剪刚度参与另一个结构共同作用的能力也受到自身抗弯刚度的影响。     

锈蚀钢筋混凝土梁正截面受弯破坏模式及承载力简化计算方法

为快速准确评估受拉纵筋锈蚀对钢筋混凝土梁正截面受弯承载力的影响,采用解析方法计算受弯破坏时锈蚀钢筋混凝土梁正截面应力和应变分布,识别并定义锈蚀钢筋混凝土梁的3个界限锈蚀率和6种正截面受弯破坏模式,提出预判破坏模式再计算承载力的锈蚀钢筋混凝土梁正截面受弯承载力简化计算方法。采用该简化方法,计算相关文献中235根锈蚀钢筋混凝土梁的正截面受弯承载力,并与试验结果对比,验证该简化方法的准确性。通过两个算例,分别研究初始超筋梁和初始适筋梁的正截面受弯破坏模式及承载力随受拉纵筋锈蚀率的变化规律。研究结果表明：随着受拉纵筋锈蚀率的增大,初始超筋钢筋混凝土梁的正截面受弯破坏模式按照从“类似超筋”、“类似适筋”、“类似超筋”到“类似少筋”依次转变;初始适筋钢筋混凝土梁的正截面受弯破坏模式按照从“类似适筋”、“类似超筋”到“类似少筋”依次转变;钢筋混凝土梁正截面受弯承载力近似呈多段线性降低,最终退化为素混凝土梁的开裂弯矩,转折点位置为界限及临界锈蚀率。