薄壁杆侧向稳定分析有限杆元模型

根据位移变分原理,建立有限杆元模型,对薄壁杆进行侧向稳定分析。在考虑截面扭转、翘曲同时,特别考虑了反映剪力滞后现象的杆壁中面上剪应交的影响。推导出薄壁杆侧向屈曲能量方程可适用求解常用边界条件,任意棱形截面形状的薄壁杆的屈曲特征值问题。     

偏压薄壁杆稳定计算的有限杆元法

根据能量原理,综合三次B样条函数、有限单元法和经典Vlasov薄壁杆理论的优点,提出偏压薄壁杆稳定计算的有限杆元法．推导和求解过程中,同时考虑了截面扭转、翘曲和杆中面上剪应变的影响,可适用求解常用边界条件,任意截面形状的薄壁杆特征值问题．与经典方法比较显示着该文计算方法的有效性．     

开口薄壁梁的扭转理论与应用

以Vlasov薄壁构件理论为基础, 推导了开口薄壁构件一阶扭转理论. 该理论考虑了翘曲剪应力对截面转角的影响, 截面的转角分为自由翘曲转角和约束剪切转角, 在约束扭转中, St.Venant扭矩仅仅与自由翘曲转角有关, 而翘曲扭矩仅与约束剪切转角有关. 利用半逆解方法求出了约束扭转中薄壁构件的St.Venant扭矩表达公式; 依据能量方法, 建立了约束剪切转角和翘曲扭矩之间的关系, 并提出了翘曲剪切系数概念, 给出了一阶扭转理论的微分方程. 为了有效求解微分方程, 给出了求解微分方程的初参数法方程和相应的影响函数矩阵; 当St.Venant扭矩可以忽略时, 得到与一阶弯曲理论(Timoshenko梁理论)相似的一阶扭转理论简化形式. 最后利用算例证明了一阶扭转理论和简化理论的有效性.      

横截面变形对I形薄壁小曲率曲杆刚度的影响

本文应用对正交柱壳理论所作的假定推导了薄壁小曲率曲杆受力变形的方程,考虑了横截面变形的影响.对Ⅰ形曲杆作了具体分析,并指出只需修正刚度系数,就可以直接应用横截面不变形时的薄壁Ⅰ形曲杆理论.     

开口薄壁压杆考虑剪滞效应和几何非线性的临界荷载

针对上翼缘和下翼缘, 假设不同的剪力滞翘曲位移函数, 导出了薄壁压杆的能量泛函. 基于最小势能原理, 对开口薄壁压杆考虑剪力滞效应和几何非线性的稳定性进行了分析, 推导了压杆的特征方程, 并求出了简支压杆考虑剪力滞效应的临界荷载以及欧拉公式的修正系数, 讨论了翼缘宽度、厚度和压杆长度以及几何非线性对临界荷载修正系数的影响, 说明了欧拉临界荷载公式的适用条件.     

计算弯曲中心的理论公式及其应用

 使用弹性力学的Saint-Venant弯曲理论定义了一般截面的弯 曲中心并给出了精确的计算公式(对薄壁和非薄壁截面均适用)，在开口薄壁截面的情形， 由材料力学给出的关于不同截面的弯曲中心公式都可由本文的理论公式经近似分析获得.     

闭口薄壁曲杆的弯扭分析

本文利用 A·A·乌曼斯基对闭口薄壁直杆问题中截面轴向位移所作的假定推广到闭口薄壁曲杆的弯扭问题,导出了基本微分方程和对应边界条件,并给出了它的初参数解.当 J_p→∞时问题退化为开口薄壁曲杆弯扭问题的解.另外,从实例计算结果中看出:对闭口薄壁曲杆的边界条件需特别注意。     

开洞核芯筒结构动力特性的数值计算与分析

用等效剪力膜代替核芯筒洞口之间的连梁 ,把开洞的核芯筒结构模拟成为一个闭口的薄壁杆 ,利用有限杆元法提出开洞核芯筒结构动力特性分析的数值方法 ,考虑了扭转、翘曲、特别是筒壁中面上的剪应变对动力特征分析的影响 ,和其它数值方法比较显示着本文方法的有效性和可行性     

薄壁曲杆的有限元法

本文提出了开口和闭口截面薄壁曲杆的刚度矩阵.位移模式采用多项式逼近,并考虑了温度影响.对于闭口截面的薄壁曲杆,利用了乌曼斯基假设.文中还利用截面线元素,按线性分布规律逼近,讨论了圣维南翘曲函数的离散化计算.作了不同于藤谷义信的分析.     

薄壁杆系结构的梁元分析模型

本文导出了用于薄壁杆系结构弹性分析的薄壁梁元分析模型，在空间梁元分析模型^[3]的基础上，采用了一种改进的位移模式，考察了薄壁杆件可能发生的拉压，剪切，弯曲，扭转和翘曲等各变形形式以及它们的耦合效应，得出了相应的单元形函数，同时从工程应变的定义出发，采用Taylor级数展开的方法，建立了单元的五阶近似正交变表达式，并建立了相应的薄壁单元刚度方程，从而得出了局部坐标系下单元刚度矩阵的显式，根据本文所导出的薄壁梁元分析模型，编制了相应的结构计算程序，通过算例验证了本文所推导的单元刚度矩阵，同时通过与传统空间梁元计算模型计算结果的比较，阐述了截面翘曲对薄壁杆系结构的影响。     

Correspondence between de Saint-Venant and Boussinesq. 1: Birth of the Shallow–Water Equations

The Shallow–Water Equations (SWEs), also referred to as the de Saint-Venant equations, constitute the current governing mathematical tool for free-surface water flows. These include, e.g., flood flows in rivers and in urban zones, flows across hydraulic structures as dams or wastewater facilities, flows in the environmental fields, glaciology, or meteorology. Despite this attractiveness, the system of two partial differential equations has an exact mathematical solution only for a limited number of problems of practical relevance.This historical work on the SWEs is based on a correspondence between two 19th-century scientists, de Saint-Venant and Boussinesq. Their well-known papers are thus commented from the point of development of their theory; the input of both scientists is evidenced by their writings, and comments of both to each other that led to what is commonly known as the SWEs. Given the age difference of the two of 45 years, the experienced engineer de Saint-Venant, and the mathematician Boussinesq, two eminent researchers, met to discuss not only problems in hydraulics, but in physics generally. In addition, their correspondence embraced also questions in ethics, religion, history of sciences, and personal news.The results of the SWEs cease to hold if streamline curvature effects dominate; this includes breaking waves, solitary and cnoidal waves, or non-linear waves in general. In most other cases, however, the SWEs perfectly apply to typical flows in engineering practice; they are considered the fundamental system of equations describing open channel flows. This work thus provides a background to its birth, including lots of comments as to its improvement, physical meanings, methods of solution, and a discussion of the results. This paper also deals with the steady flow equations, gives a short account on the main persons mentioned in the Correspondence, and provides a summary of further developments of the SWEs until 1920.     

Spatial Decay Estimates for a Coupled System of Second-Order Quasilinear Partial Differential Equations Arising in Thermoelastic Finite Anti-plane Shear

The spatial decay behavior of solutions of a coupled system of second-order quasilinear partial differential equations, in divergence form, defined on a two-dimensional semi-infinite strip, is investigated. Such equations arise in the theory of anti-plane shear deformations for isotropic nonlinearly thermoelastic solids. Differential inequality techniques are employed to obtain exponential decay estimates. The results are illustrated by several examples. The results are relevant to Saint-Venant principles for nonlinear thermoelasticity as well as to theorems of Phragmen-Lindelof type. This revised version was published online in August 2006 with corrections to the Cover Date.     

A reciprocity theorem in linear gradient elasticity and the corresponding Saint-Venant principle

In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be used as test specimens for measuring the lengths that enter the constitutive equations of gradient elasticity. It is then useful to be able to apply approximate solutions for the extension, shear and flexure of slender bodies. Such approach requires the existence of some form of the Saint-Venant principle. The present work presents a statement of the Saint-Venant principle in the context of linear strain gradient elasticity. A reciprocity theorem analogous to Betti’s theorem in classic elasticity is provided first, together with necessary restrictions on the constitutive equations and the body forces. It is shown that the order of magnitude of displacements are in accord with the Sternberg’s statement of the Saint-Venant principle. The cases of stretching, shearing and bending of a beam were examined in detail, using two-dimensional finite elements. The numerical examples confirmed the theoretical results.     

On the Flexure of a Saint-Venant Cylinder

The flexure of a Saint-Venant cylinder is defined from a kinematic point of view. A complete solution for the field equations is provided and the gauge choices to define the center of shear and rotation are made consequently. This seems to eliminate some ambiguities present in the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Saint-Venant problem of plane bar under an axial force

I.PrefaceAsweknow,theSaint-Venanttheoryisawell-knownanduniversallyacceptedtheory.Butasoneofthegeneraltheoriesofelasticmechanics,itisnotprovedperfectely,althoughitistestedbyexperiments.Infact,onlyforthesimplestproblemofelasticity,itisnoteasytofindanalytics…     

Saint-Venant problem for solids with helical anisotropy

We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters.     

Resonant dynamics in a rotordynamic system with nonlinear inertial coupling and shaft anisotropy

The response of a nonlinear, damped Jeffcott rotor with anisotropic stiffness is considered in the presence of an imbalance. For sufficiently small external torque or large imbalance, resonance capture or rotordynamic stall can occur, whereby the rotational velocity of the shaft is unable to increase beyond the fundamental resonance between the rotational and translational motion. This phenomena provides a mechanism for energy transfer from the rotational to the translational mode. Using the method of averaging a reduced-order model is developed, valid near the resonance, that describes this resonant behavior. The equilibrium points of these averaged equations, which correspond to stationary solutions of the original equations and rotordynamic stall, are described as the applied torque, damping, and anisotropy vary. As the anisotropy increases, assumed to arise from increasing shaft cracks, the torque required to eliminate the possibility of stall increases. However, when the system is started with zero initial conditions, the minimum torque required to pass through the resonance is approximately constant as the anisotropy increases. The predictions from the reduced-order model are verified against numerical simulations of the original equations of motion.     

Dynamic Saint-Venant region in a semi-infinite elastic strip

This paper presents a formulation for the solution of the steady state rosponse of a semi-infinite strip with atress-free semi-infinite edges and a time-harmonie shear and normal stress applied to the end. If the end stresses form a self-equilibrated stress state, the presence or absence of a dynainic Saint-Venant region may be examined. The mathematical analysis is based on the linear equations for generalized plane stress and are solved by a biorthogonal eigenfunction expansion. The formulation is in terms of stresses and a displacement related auxiliary variable of the same differential order as the stress. Numerical solutions are presented as an indication of frequency and stress mode shape dependency.     

厚板的高阶剪切变形理论研究

已有多种厚板理论和高阶剪切变形模型,但仍需要进一步研究以更加完善.首先根据平均转角及上下表面剪应力自由这两个条件,提出了具有统一高阶剪切变形模型的中面位移模式,并将之表示为正交分解形式.根据正交特性,定义了板的广义应力;运用板问题应变能密度表示的等价性,提出了与广义应力功共轭的广义应变表示形式,建立了板的本构关系.证明了不同转角定义时虚功原理板理论表示的客观性,以及与三维弹性理论表示的等价性.运用虚功原理,建立了变分自洽的高阶厚板理论和变分渐近的低阶厚板理论,推导了相应的平衡方程及边界条件,分析了与已有板理论的异同.以广义应力形式建立了厚板理论的平衡方程,厘清了不同转角表示时板理论间的关系、低阶厚板理论与高阶厚板理论间的关系以及剪切系数计算等若干基本问题.对圣维南扭转问题的求解证明了该理论的正确性.      

Saint-Venant decay rates for an anisotropic and non-homogeneous mixture of elastic solids in anti-plane shear

The purpose of this research is to investigate the influence of material inhomogeneity and anisotropy on the decay of Saint-Venant end effects in anti-plane shear deformations of linear mixtures of elastic solids. The spatial decay of solutions of a boundary value problem with variable coefficients on a semi-infinite strip is investigated. The results may be interpreted in terms of a Saint-Venant principle for anti-plane shear deformations of linear anisotropic mixtures of elastic solids. As our first results have a very general point of view, we study some examples in detail.