应用功的互等定理计算矩形弹性薄板的自然频率

在文[1]的基础上,本文进一步推广功的互等定理的应用于计算矩形弹性薄板的自然频率.应用本法无需求解控制微分方程,只需在基本系统与实际系统之间应用功的互等定理后求解一简单的积分方程即可.使用了广义简支边的概念并且引入了频率矩阵,从而一并得到了两对边简支、另两对边为各种支持的矩形板的所有频率方程.这是计算矩形板自然频率的一个简便通用的方法.     

集中载荷作用各边上任一点被支承的矩形板弯曲

应用功的互等定理求解在集中载荷作用下各边上任一点被支承的矩形板弯曲,给出了其精确解及算例.     

关于求解弹性力学平面问题的功的互等定理法

本文推广功的互等定理法于求解具有复杂边界条件矩形板的弹性力学平面问题.首先,我们给出了作为基本系统的四边固定矩形板平面问题的基本解,然后基于在具有复杂边界条件的实际系统与基本系统之间应用功的互等定理,从而求得实际系统的位移表达式.当只存在位移边界条件时,用功的互等定理法求得的位移表达式就是真实的.但是在另一些情况下,当有静力边界条件或混合边界条件时,所求得的位移是容许的.为求得真实位移.必须应用最小势能原理.一些计算表明.对于求解具有复杂边界条件的矩形板弹性力学平面问题,功的互等定理法是一简便通用的方法.显然,这是一个新方法.     

弹性厚矩形板受迫振动的功的互等定理法

本文将功的互等定理法（ＲＴＭ）推广应用于求解基于Ｒｅｉｓｓｎｅｒ理论的厚矩形板受迫振动问题·本文导出了厚矩形板动力基本解；给出了三边固定一边自由厚矩形板在均布简谐干挠力作用下稳态响应的精确解析解·这是计算厚矩形板受振动稳态响应的一个简便通用的方法·     

应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲

悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.     

直边上具有混合支撑段薄矩形板的弯曲

在本文中,应用功的互等定理法首次给出了直边上具有简支段与自由段混合支撑的矩形板的精确解析解.作为比较,我们用有限元法计算了同一问题.比较表明,该解析解是正确的.     

求解厚矩形板弯曲问题的功的互等定理法

在本文中,功的互等定理法(RTM)被推广于求解基于Reissner理论的厚矩形板弯曲问题。首先,本文绘出了厚矩形板弯曲的基本解;其次,给出了三边固定一边自由在均布载荷作用下厚矩形板弯曲的精确解析解;最后,我们分析了本文解的数值结果。     

直边上具有混合支撑段薄砑矩形板的弯曲

在本文中，应用功的互等定理法首次给出直边上具有简支段与自由段混合支撑的矩形板的精确解析解。作为比较，我们用有限元法计算了同一问题，比较表明，该解析解是正确的。     

半圆形弹性薄板弯曲的功的互等定理法

半圆形弹性薄板的弯曲问题,由于其边界条件的复杂性,给求解带来一定困难.本文应用功的互等定理,提出一种计算此板挠曲面方程的简便、通用的算法.     

再论在一集中载荷作用下悬臂矩形板的弯曲

在本文中,我们应用功的互等定理[1]进一步研究了在一集中载荷作用下悬臂矩形板的弯曲问题.该法更为简单和通用.     

复杂构造地震数据叠前逆时偏移方法

叠前逆时偏移方法可以精确成像复杂地下构造,利用高阶有限差分方法求解声波方程,并给出了满足稳定性条件的采样间隔的选取方式.利用GPU/CPU加速技术实现地震资料的叠前逆时偏移算法,极大地提高了计算效率,算法也采用随机边界条件,节约了大量存储空间.分析了速度模型变化对成像结果的影响.复杂地震数据成像的测试结果表明,所述的叠前逆时偏移算法可清晰成像陡倾角成像清晰,对盐丘边界和内部构造成像效果也较好.     

Linearized inverse scattering based on seismic reverse time migration

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse time migration (RTM). In the process, the explicit evaluation of the so-called normal operator is avoided, while other differential and pseudodifferential operator factors are introduced. We prove that, under certain conditions, the transform yields a partial inverse, and support this with numerical simulations. In addition, we explain the recently discussed ‘low-frequency artifacts’ in RTM, which are naturally removed by the new method.     

海冰弯曲破坏下的破坏准则数值模拟方法研究

海冰的弯曲破坏进程的研究已经称为冰工程界的一项重要课题.通过理论分析结合数值计算对海冰弯曲破坏数值模拟方法进行探索:探讨适合于海冰弯曲应力状态下的本构模型和破坏准则;在LS-DYNA中模拟圆环形冰排弯曲破坏和冰排与锥体结构相互作用的进程,提出了一种对海冰破坏准则验证的技术思路;通过所提出的技术思路对基于三轴压缩试验的Derradji破坏准则进行了修正,使其能够适用于海冰的弯曲破坏.     

黄金分割算法在简支桥梁设计计算中的应用

移动荷载作用下,简支桥梁横截面上弯矩的变化为二元函数Z=f(x,y),本文给出了绝对最大弯矩Zm ax的极值点x*、y*的判别方法:利用数学中的黄金分割算法搜索梁的绝对最大弯矩对应的最危险横截面位置x*;利用力学中的影响线理论判别该截面发生最大弯矩时的最危险荷载位置y*,计算该横截面的最大弯矩得到梁的绝对最大弯矩.该算法易于编写计算程序,以计算机为工具,适用于任意有限多个平行移动荷载在桥梁上移动,对于桥梁的设计计算与安全评估,有一定的实用价值.     

Application of Daubechies wavelets approximation to plate bending

In this paper a new wavelet-based approach is presented for solving two-dimensional boundary-value mechanical problems on the example of plate bending. The deflection equation of a bending plate is approximated by two-dimensional Daubechies wavelets using a least-squares Galerkin method. Due to the order of the differential equation in mechanics of plate structures is four, a way to perform the calculations of high order connection coefficients (that is, integrals of products of basis functions with their high order derivatives) is suggested. The implementation of two-dimensional Daubechies scaling functions approximation to plate bending is exhibited numerically in some examples. The results show that this method has good precision and reliability. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of layer geometry and stiffness on the fields of normal stresses in multilayer beams under asymmetric bending

A mathematical model is suggested for calculating the bending stiffness and fields of normal stresses (strength) at any point in the cross section of a multilayer beam. It is found that the structure of the scalar field of normal stresses allows one to solve some optimization problems with multivariant parameters. The method is illustrated with an example of two-layer beams. The results of an investigation into the strength and stiffness of two-layer beams, with a geometric and (or) stiffness asymmetry, in asymmetric bending are presented. The kinetics of bending stiffness and strength in relation to variations in the geometric parameters of cross sections and in the ratio of elastic moduli of layers is examined. It is established that the normal stresses in multilayer beams under asymmetric bending considerably depend on the location of the flexural center, neutral plane, and bending stiffnesses relative to the principal axes of cross sections of the beams.     

Bilevel aggregator-prosumers' optimization problem in real-time: A convex optimization approach

This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem where the aggregator and the prosumers are considered as self-interested agents. We present a convex optimization problem which can capture a subset of the set of global optima of the bilevel problem as its optimal solution.     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.