由结构力学的平面问题例说最小势能原理

最小势能原理作为结构力学的提高部分,很少在该课程中看到关于它的完整介绍。本文以等刚度连续梁为研究对象,在只考虑弯曲变形的情况下,讨论了位移法典型方程的适用条件。在此基础上,分析了势能法和位移法之间的对偶关系。得出：等刚度连续梁在平面载荷与支座反力构成的平衡力系作用下,可能的小位移状态由虚力方程控制。若真实位移还能利用叠加原理进行求解,则可能位移状态下的总势能在真实位移处取极小值。等刚度连续梁弯曲变形的分析验证了最小势能原理,有助于对一般情况下最小势能原理的深刻认识。

     

二维边坡稳定性分析的最小势能法新解

针对最小势能法研究的不足,通过条块虚位移方向的静力平衡方程确定滑面上剪应力的解析解,构建了一种新的剪切势能计算模型.同时,提出了一种多地层边坡稳定性分析方法.算例结果表明：剪切势能对边坡稳定性系数会产生影响,使得计算结果更为合理;运用文中方法计算得到边坡稳定性系数与极限平衡法的结果较为一致,表明文中的计算方法是可行且合理的;文中多地层边坡的计算模型,考虑了土层滑面长度以及法向力对边坡抗剪强度的贡献,且计算简便,易于工程人员使用.     

从受拉杆变形浅析弹性力学中的最小势能原理

最小势能原理是弹性力学中较难理解的知识点。本文通过对弹性杆轴向受拉时的弹性势能、外力势能和总势能的变分分析,得出总势能变分是位移变分或应变变分的二阶无穷小量,并在位移变分或应变变分为零时,总势能取得极小值。弹性杆轴向受力变形的分析应验了最小势能原理,有助于对一般情况下最小势能原理的深刻理解。     

圆截面杆在曲线井中的屈曲问题

本文研究了线弹性的圆截面压杆在刚性井壁的曲线井中的屈曲问题。压杆两端为铰支，杆和井壁之间的摩擦力忽略不计，失稳前假设压杆位于曲线井的较低侧。分析了压杆屈曲时的几何变形条件，导出了压杆的曲率，变形能和各项外力势的表达式，用最小势能原理导出压杆失稳的微分方程和边界条件。引入梁单元，用有限单元法求得了压杆失稳时的临界压力和杆轴线状态。结果显示，临界压力随着压杆自重和曲线井半径的增加而增加。自重为零时，杆轴线为半个正弦曲线；自重不为零时，杆轴线为振荡的曲线，且振荡主要集中在压杆顶部。     

考虑接触界面材料微观结构与势能参数的滑动摩擦计算研究

根据独立振子模型的能量耗散机理,提出了在无磨损界面摩擦中,利用通用界面粘附能量函数计算滑动时接触界面势能的变化从而计算摩擦力和摩擦系数的方法,建立摩擦力和摩擦系数与金属材料表面能与微观结构参数的关系,并利用已有的实验数据进行计算.结果表明,摩擦力与金属材料的表面能基本呈线性关系,与比例参数呈线性负相关关系,与晶格常数基本无关.计算结果与粘附理论公式以及超高真空原子力显微镜试验结果吻合较好.     

逆迭代法的一种变通应用

本文利用逆迭代法与共轭梯度法配合使用时的“广义力”一致出现之规律,将大型结构动力分析的有限元(条)网格以族排列,然后将单元族分批集于“广义力”向量之中,从而避开了传统的结构刚度阵与质量阵的集成过程,大大节约了计算机内存。整个过程极为简明、有效。     

空间杆系结构优化设计的修正 Goldfarb法

提出了一种用于空间杆系结构优化的快捷、有效的算法．该算法吸取文[１］的松弛方法通过对Ｇｏｌｄ－ｆａｒｂ提出的共轭梯度投影算法进行修正和完善，扩大了其应用范围和应用效率．通过对结构优化算例的计算，证明了这种修正 Ｇｏｌｄｆａｒｂ方法的有效性．     

大挠度弯曲直梁混合变量最小势能原理的应用

应用大挠度弯曲直梁混合变量最小势能原理,求解均载两端固定大挠度柱面弯曲板条的轴向挠度分布和轴向弯矩分布．实例计算表明:该方法简单实用、精度高,是一种计算大挠度柱面弯曲板条变形的有效方法．     

一维杆与结构接触冲击问题的计算

一维杆与结构接触冲击问题的计算黄剑敏，任文敏（清华大学工程力学系，北京１０００８４）１引言工程中大量存在着杆与结构的接触冲击问题，对这类问题的研究极为重要，但这方面的论著甚少，理论所能解决的问题更少，仅在极个别的情况下有精确解。Ｔ．Ｔ．Ｒ．Ｈｕｇｈｅ...     

可视化杆系结构分析程序设计

利用可视化编程语言将杆系优化计算封装为动态连接库 (DLL) ,采用面向对象的方法描述了杆系结构分析所需的类 ,并用数据库技术和三维图形模式对杆系结构分析进行格式化输入输出。通过对杆系结构的特点分析 ,将程序分为三个主要的设计模块 :显示模块、数据管理模块和结构分析模块 ,实现了程序的模块化设计。通过对实例的测试 ,说明该程序已达到对一般多工况杆系可视化设计的目的     

A combined programming and iteration algorithm for finite element analysis of three-dimensional contact problems

Comparing with two-dimensional contact problems, three-dimensional frictional contact problems are more difficult to deal with, because of the unknown slip direction of the tangential force and enormous computing time. In order to overcome these difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is derived in this paper. The iteration algorithm, which alleviates the difficulty of unknown slip direction, is used along with the PQP method to cut down computing costs. Numerical example is given to demonstrate the validity of the present algorithm. The project supported by the Machinary and Electronics Ministry of China     

Linear and non-linear iterative methods for the incompressible Navier-Stokes equations

In this study, the discretized finite volume form of the two-dimensional, incompressible Navier-Stokes equations is solved using both a frozen coefficient and a full Newton non-linear iteration. The optimal method is a combination of these two techniques. The linearized equations are solved using a conjugate-gradient-like method (CGSTAB). Various types of preconditioning are developed. Completely general sparse matrix methods are used. Investigations are carried out to determine the effect of finite volume cell anisotropy on the preconditioner. Numerical results are given for several test problems.     

微机网络并行环境下杆壳组合结构动力特性并行计算

回顾了有限元并行计算发展的历史,阐述了微机网络并行计算环境的意义,给出了基于微机网络并行环境的杆壳组合结构动力分析并行算法,该算法包括杆壳组合结构总刚度矩阵和总质量矩阵的并行计算以及求解广义特征值问题的并行子空间迭代法的并行计算,在多台微机上安装PVM．使用Linux操作系统．构成分布式微机网络并行计算环境,将上述算法用于某型号飞机机翼及某型号挂架动力特性的并行计算,在该并行环境下的教值试验表明所给算法是非常有效的。     

A form function method for form finding of tension structure

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STATIC ANALYSIS OF CABLE STRUCTURE

Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.     

An asymptotic iteration method for the numerical analysis of near-critical free-surface flows

Satisfying the boundary conditions at the free surface may impose severe difficulties to the computation of turbulent open-channel flows with finite-volume or finite-element methods, in particular, when the flow conditions are nearly critical. It is proposed to apply an iteration procedure that is based on an asymptotic expansion for large Reynolds numbers and Froude numbers close to the critical value 1.The iteration procedure starts by prescribing a first approximation for the free surface as it is obtained from solving an ODE that has been derived previously by means of an asymptotic expansion (Grillhofer and Schneider, 2003). The numerical solution of the full equations of motion then gives a surface pressure distribution that differs from the constant value required by the dynamic boundary condition. To determine a correction to the elevation of the free surface we next solve an ODE that is obtained from the asymptotic analysis of the flow with a prescribed pressure disturbance at the free surface. The full equations of motion are then solved for the corrected surface, and the procedure is repeated until criteria of accuracy for surface elevation and surface pressure, respectively, are satisfied.The method is applied to an undular hydraulic jump as a test case.     

Application of the modified iteration method to nonlinear postbuckling analysis of thin circular plates

In this paper,the modified iteration method is further generalized to the study ofaxisymmetrical postbuckling of thin circular plates and hereby a new approximate analyticsolution of the problem is obtained.Further utilizations of this method to postbucklinganalyses of plates of more complicated structure are expected.     

销钉耳片连接件接触应力分析的能量解法

针对光滑无间隙的钉孔接触情况,根据圣维南原理,以耳片孔为中心取出一圆形区域,采用叠加原理将受力状态分解为对称和反对称状态,利用正交完备的三角级数和勒让德级数构造这两种受力状态的位移场.假设接触表面的载荷分布模态,由最小势能原理确定位移函数中的待定系数,得到耳片孔边的位移场和应力场.本文计算结果与有限元数值解比较显示:两...     

非对称势阱对三稳态压电俘能器性能的影响分析

为了探讨具有非对称势能函数的三稳态压电俘能器的优点,提出了一种具有不对称势能函数的三稳态结构.基于广义Hamilton变分原理,考虑梁端磁铁偏心距和转动惯量的影响,建立了非对称三稳态压电悬臂梁俘能系统的动力学方程,利用龙格-库塔法和多尺度法分析了初始振动点、外界激励等对存在非对称势阱的磁力式三稳态压电俘能系统响应的影响...     

复合材料周期结构数学均匀化方法的一种新型单胞边界条件

数学均匀化方法是计算周期复合材料结构的有效方法之一,单胞边界条件施加的合理性直接决定了影响函数控制方程的计算效率和精度,进而影响均匀化弹性参数和摄动位移的计算精度.本文首先将单胞影响函数作为虚拟位移处理,给出了单胞在结构中真实的边界条件,结果表明,四边固支适合作为二维结构单胞边界条件;其次,针对二维结构提出了超单胞周期边界条件,有效提高了影响函数的计算精度,并使用与虚拟位移相对应的虚拟势能泛函验证超单胞周期边界条件的有效性;最后,利用数值分析验证多尺度渐进展开方法的计算精度,强调了二阶摄动的必要性.