基于突变理论的弹性圆柱壳冲击扭转屈曲

本文将突变理论用于处理冲击载荷下弹性结构的屈曲问题,文中对无初缺陷的弹性圆柱壳给出了临界阶跃冲击扭矩.另外,本文还用数值方法求解了柱壳扭转时的非线性动力方程,并由B-R运动准则求得临界冲击扭矩。计算表明,这两个方法给出的结果是一致的。     

内爆炸条件下特种圆柱壳结构动力响应研究

针对有球形顶盖的圆型柱壳结构,基于弹性薄壳振动理论用相同边界梁振型函数近似柱壳振型轴向分布,提出内爆炸荷载作用下此类结构动力响应计算方法,分析长径比对柱壳振动影响,获得结构位移简化算法。通过算例与已有方法对比验证该方法的合理性,并研究顶盖对柱壳振动影响。结果表明,计算径向位移时由柱壳顶端侧向弹性铰支边界考虑顶盖约束,按内部静压条件确定的铰支系数对柱壳振动高阶振型计算时产生误差,在柱壳顶端加入顶盖等效集中质量可有效降低该误差,并使振动频率及顶端径向位移计算值较小;随长径比增大球形顶盖对柱壳振动影响逐渐减小。     

分析旋转薄壳的传递矩阵法

基于一般线弹性薄壳理论,首次导出了旋转壳体状态向量的一阶常微分矩阵方程,此方程是一般旋转壳的传递矩阵法分析所必需的.借助齐次扩容技术和精细积分,应用推广的传递矩阵法对旋转薄壳的静动力问题进行了数值求解.算例结果表明:提出的一套解法不仅精度良好,而且具有较高的计算效率;它为分析变厚度旋转壳的各类问题寻求一种半解析方法奠定了基础.     

柱面网壳结构动力性能分析

本文采用子空间迭代法系统地研究了双层柱网壳结构的自振特性，按反应谱法分析了竖向地震作用下柱面网壳结构的内力分布规律，并与相应的静内力作了比较，文中还对柱面网壳考虑支承竖向弹性刚度及法向弹性刚度的动力反应作了分析，文中所给出的结果对实际工程有参考价值。     

柱壳液力成形弹性稳定性分析

利用非线性弹性稳定性理论,分析研究了壳体液力成形工艺中的开口圆柱壳弹性稳定性问题。计算结果表明不仅非线性弹性临界载荷远低于线性弹性临界载荷,而且更重要的是内压很大程度上有助于提高柱壳轴向弹性临界屈曲载荷,这样为内高压成形工艺提供了弹性失稳理论依据。     

小比例柱面网壳振动台试验及动力响应概率模型

针对单层网壳实验费用高、周期长及地震变异性大等问题,开展了一小比例单层柱网壳振动台试验模型试验,并基于该模型试验统计了考虑地震动变异性时单层柱面网壳的动力响应概率模型。参考孔洞胶接节点装配式单层球面网壳模型制作方法制作了一小比例单层柱面网壳模型;在此基础上,分别选用TAFT波、人工地震波和简谐波对该单层柱面网壳模型开展一系列振动台试验研究,包括弹性阶段的动力特性测试和弹塑性状态下的动力倒塌测试;立足于现场实测数据,基于通用有限元分析软件ABAQUS建模、并开展相应数值仿真分析,总结分析单层柱面网壳模型动力特性与破坏特征;基于40组动力实测数据研究地震变异性对单层柱面网壳动力特性的影响,并初步拟合出地震动变异性与该结构动力响应的概率模型。该研究对开展系列单层网壳振动台试验定性研究及空间网壳结构抗震规范的修订提供参考。     

偏心圆柱薄壳输入功率流特性研究

根据偏心圆柱薄壳截面的几何特性,将偏心圆柱薄壳问题转化为周向变厚度圆柱壳问题。基于Flügge薄壳理论推导出偏心圆柱薄壳的受迫振动方程,采用波传播的思想将偏心柱壳位移以双Fourier级数形式展开,周向变厚度表示为周向角度坐标的函数,通过三角函数变换将变系数的偏微分方程组转换为周向模态阶数相互耦合的有限阶线性方程组,通过对耦合方程进行求解得到偏心柱壳的位移响应,进而计算壳体的输入功率流。通过与文献及FEM结果进行对比,验证了所建立的偏心柱壳振动理论模型及计算方法的准确性。同时,详细计算并分析了激励力位置、偏心率、壳体厚度和材料阻尼等参数对偏心柱壳输入功率流的影响。     

改进傅里叶级数法求解封口锥柱球组合壳的自由振动

提出了一种改进傅里叶级数的半解析方法分析封口锥柱球组合壳的自由振动特性.基于能量泛函,结合经典薄板理论和Love壳体理论,建立了组合结构的理论模型,研究了不同柱壳长度,不同锥球半角以及不同厚度端板下锥柱球组合壳的固有频率.该方法下的各子壳结构位移由标准的傅里叶级数和辅助收敛函数组成,既克服了传统傅里叶级数在子壳结构交接...     

柱壳结构自振频率计算的精化传递矩阵法

本文建立了弹性柱壳结构自由振动问题的一般数学模型。通过引入指数矩阵的精化数值算法,发展一个计算柱壳的自振频率的新的传递矩阵法。数值算例表明本文新的数值算法具有较高的计算精度,较好的数值稳定性和简单实用性。     

弹性薄壳的大变形分析

本文给出了弹性薄壳大变形时应变与位移之间的精确关系。经过合理的简化,给出了壳的挠度与厚度同级的大变形基本公式。当薄壳为柱形且作柱状弯曲时,精确地求得了壳的挠度与长度同级的大变形基本公式。这些公式符合实际和便于应用。用解析法求得了无限长园柱壳一边固定,另一边受力偶作用的精确解。用能量法求得了无限长条板的近似解。     

A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.     

Flexural-Torsional Buckling and Vibration Analysis of Composite Beams

In this paper the general flexural-torsional buckling and vibration problems of composite Euler-Bernoulli beams of arbitrarily shaped cross section are solved using a boundary element method. The general character of the proposed method is verified from the formulation of all basic equations with respect to an arbitrary coordinate system, which is not restricted to the principal one. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. It is subjected to a compressive centrally applied load together with arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting problems are (i) the flexural-torsional buckling problem, which is described by three coupled ordinary differential equations and (ii) the flexural-torsional vibration problem, which is described by three coupled partial differential equations. Both problems are solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the method can treat composite beams of both thin and thick walled cross sections taking into account the warping along the thickness of the walls. The proposed method overcomes the shortcoming of possible thin tube theory (TTT) solution, which its utilization has been proven to be prohibitive even in thin walled homogeneous sections. Example problems of composite beams are analysed, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. Moreover, useful conclusions are drawn from the buckling and dynamic response of the beam.     

A model for forced vibrations of ceramic/metallic thick rings

In this paper a general model for transient dynamic analysis of functionally graded material (FGM) thick arch/ring is introduced. The material is arbitrarily distributed between metal (aluminium or steel) and ceramic (Alumnina or Silicon carbide) phases, according to several types of functional distributions, including exponential law, power law, sigmoid law, among others. The model, developed within the context of strength-of-materials theory, includes many others theories as particular cases. For example, Timoshenko beam and other first-order shear deformation theories. The material properties such as Young’s modulus, shear modulus, density, can arbitrarily vary along the generally-shaped cross-section (that can be a multiply connected region), however holding symmetry with respect to the motion plane. The tangential stresses are consistently featured by the classical internal equilibrium equations in polar coordinates. This allows the proper calculation of the shear coefficient, which is crucial in this class of theories. The three fully coupled motion equations are solved in order to carry out studies of natural vibrations as well as transient dynamics under a general type of applied loads. The transient solution is reached by means of a modal superposition method appealing to “ad hoc” orthogonality conditions. Numerical studies are presented to show qualitatively and quantitatively the vibratory features of ceramic/metallic thick arches/rings with graded properties.     

Numerical solution to a sideways parabolic equation

The inverse heat conduction problem can be considered to be a sideways parabolic equation in the quarter plane. This is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but one side is inaccessible to measurements. A numerical procedure for this severely ill‐posed problem is suggested, which consists of two steps, namely a mollification of the data and a marching difference scheme. The numerical method is proved to be stable. Several computational results are presented and discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

厚板哈密顿求解体系及其变分原理与正交关系

将哈密顿求解体系推广应用于Reissner-Mindlin厚板问题。首先导出了厚板哈密顿对偶微分方程,然后采用换元乘子法导出了厚板哈密顿变分原理的泛函表示式,最后提出并证明了厚板理论的两个正交关系。厚板哈密顿体系的理论成果将为研究厚板解析解和有限元解提供新的有效工具。     

Laplace-transform analytic-element method for transient porous-media flow

A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.     

Method for specific heat measurement of thick film layers

A method of simple implementation is presented for the measurement of the specific heat of thick film layers. It has to do with a system, operating at room temperature in accordance with a dynamic non-adiabatic technique, whose function regards the transient phase of a heating process between two steady states. It consists of a compact ensemble of three elements: a small plate thermistor serving as a heater, an alumina disk as a sample support and a tiny calibrated thermistor as a temperature sensor. The voltage across the heater and temperature from the sensor are monitored. An accurate evaluation of the dissipated energy allows the absorbed energy, responsible for the temperature variation, to be brought out. That makes possible the determination of thermal capacity of a small mass material deposited on a substrate. The achievement of the result simply involves the recording of a voltage and temperature during the transient phase, a fitting procedure with given analytical functions and a mathematical elaboration. The measuring system, its calibration procedure together with the transient operation are described. An application concerning screenprinted ferroelectric thick films on alumina substrate is presented and the results discussed.     

A simple method for including shear deformations in thin plate elements

A method is described for including the effect of shear deformations in existing thin plate finite elements, and thereby extending their range of application to include moderately thick plates. The method does not add extra degrees of freedom to the final element, so the thick and thin plate elements can be used interchangeably, and the thick plate solution is not appreciably more expensive than the thin plate solution. It is assumed that the shear deformations are constant over the element and, to account for this, two extra internal shear strain variables are added to the element. Various methods for eliminating these internal variables are examined but it is shown to be impossible to simultaneously satisfy both the constant bending moment and constant shear patch tests, except for parallelograms. However, one method gives elements which pass the constant shear patch test and, although failing the constant bending moment patch test for arbitrary geometries, gives errors which are small enough to be neglected in most engineering applications. This method has been applied to a triangular plate element and it is shown that the results obtained with this element converge (for all practical purposes) to the correct thick plate results.     

正交各向异性厚板振动分析的边界积分方程法

本文采用正交各向异性厚板静力问题的基本解作为边界积分方程的核函数,利用加权残数法建立了正交各向异性厚板振动分析的边界积分方程。文中详细地讨论了边界积分方程的数值处理过程并给出了若干数值算例以论证本文方法的正确性。      

矩形悬臂厚板的解析解

首先把胡海昌提出的弹性厚板弯曲问题的简化方程表示成为Hamilton正则方程,然后利用辛几何方法对全状态相变量进行分离变量,求出其本征值后,再按本征函数展开的方法求出矩形悬臂厚板的解析解。由于在求解过程中不需要事先人为地选取挠度函数,而是从厚板弯曲的基本方程出发,直接利用数学的方法求出可以满足其边界条件的这类问题的解析解,使得问题的求解更加合理论化。最后还给出了计算实例来验证所采用的方法以及所推导出的公式的正确性。