基于能量变化过程分析弹性力学总势能

当作用在弹性体上的外力的大小和方向在位移过程中均保持不变时,该弹性体定义的总势能的虚实常引起困惑.该文从能量变化过程角度对该外力作用下的弹性体进行了分析,认为该外力作用下的弹性体是一个从非平衡态到稳定平衡态的动态过程,在这个过程中应变势能、外力势能、动能和耗散能之间相互转换,当动能为零时,弹性体处于稳定平衡态,此时弹性体总势能达到最小值;由此认为,从真实状态和可能状态角度分析该外力作用下的弹性体时,总势能中应变势能和外力势能对应于可能应变和可能位移下的势能,但并不是虚势能.     

弹性机翼阵风响应数值计算方法

建立了求解弹性机翼阵风响应的计算方法.在计算中,通过采用数值方法求解三维非定常Euler方程来获得气动特性;采用模态叠加的方法考虑弹性影响,实现了流体力学和弹性力学的耦合计算.通过对刚性机翼在攻角突然增大的阵风作用下的响应历程计算和二维NLR7301翼型的极限环振荡计算,对计算方法进行了验证.此后在"1-cos"阵风响应的计算中考虑弹性效应影响,先是只考虑了结构变形的前三个基本模态,弹性机翼气动力响应的计算结果与刚性机翼的响应计算结果有比较大的区别,弹性机翼阵风响应的升力峰值低于刚性机翼,这与文献中的结果是一致的.最后在计算中考虑了高阶弹性模态,计算结果表明:考虑高阶模态后,机翼气动力计算结果的总体变化趋势与只考虑前三个模态时基本一致,但结果中出现了高频的波动,波动的频率与高阶模态本身的频率有关.     

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。     

一种求解弹性接触问题的缩减二次规划方法

基于势能原理以节点位移为设计变量、以接触条件为约束方程构建了无摩擦弹性接触问题的二次规划数学模型,在此基础之上利用力平衡线性约束方程的特解和由基础解向量构成的奇异模态矩阵,提出一种新的基于奇异坐标变换的自由度缩减方法,大大降低了二次规划的规模,并使得二次规划模型不再含显性等式约束;根据弹性接触力学体系的特点,通过人为假定接触自由度位移模式,提出了一种简单高效的奇异模态矩阵的计算方法。通过两圆柱接触、轴孔间隙配合接触两个数值算例的对比分析,验证了对于弹性接触问题的求解,缩减二次规划方法有效克服了传统方法计算量大、对求解参数设置敏感、收敛困难的问题。     

各向同性弹性损伤的双标量描述

损伤状态的描述是损伤力学中仍未完善解决的基本问题．我们旨在对此问题就最简单的一种情形——各向同性弹性损伤，进行较为全面的研究．首先，指出了古典各向同性损伤理论中，基于应变等效假设，用单个标量损伤变量描述损伤状态的局限性．然后，建立了一个用两个标量损伤变量描述的各向同性弹性损伤模型．此模型解除了古典理论的局限，能完全描述各向同性弹性损伤，并且得到本文数值实验的验证．最后，将本文模型与现有细观力学结果连接，给出了宏细观损伤变量之间的关系，使得细观量可以通过宏观量来反映，建立了一个用细观损伤材料常数描述细观缺陷特征的损伤本构模型     

极坐标下弹性力学的一个新解答

在极坐标下将Hamilton体系下的分离变量法应用到弹性力学的非齐次边界情况,得到了一个新解答,利用这个新解可以求解一类弹性力学问题。文中给出了具体例子。     

层状介质中多个非共面硬币形裂纹弹性波散射问题研究

本文在[1]的基础上,利用 Hankel 积分变换,进一步研究了层状介质中多个非共面硬币形裂纹的弹性波散射问题。从所得结果来看,虽然层状介质中多个非共面硬币形裂纹的弹性波散射问题在形式上与多个非共面穿透形裂纹问题[1]有惊人的相似之处,但两者之间有着质的差异。     

弹性力学的复变量数值流形方法

数值流形方法通过引入数学和物理双重网格,将插值域和积分域分别定义在两个不同的覆盖上来完成系统能量泛函积分运算. 当采用高阶函数构造位移函数时,广义节点自由度将大大增加. 在求解系统的平衡方程中,运算量是与自由度的三次方成正比的,因此数值流形方法的计算量是较大的. 为此,在复变量理论的基础上,采用一维基函数建立二维问题的逼近试函数,然后将其应用于弹性力学的数值流形方法,提出了复变量数值流形方法,推导了弹性力学的复变量数值流形方法的公式. 与传统的数值流形方法相比,复变量数值流形方法具有计算量小、精度高的优点.      

弹性屈曲大挠度杆纵横变形的计算

弹性屈曲大挠度杆纵横变形的计算刘传芬（兰州铁道学院,兰州７３００７０）两端铰支的弹性屈曲杆纵横变形的计算,根据压杆弹性稳定的大挠度理论,其中点最大挠度δ和两支座间距离Ｄ（见图１）的精确解为￣［１］上述３个公式中,ｐ为轴向载荷,ＥＩ为抗弯刚度;分别为第...     

滚动摩擦力计算中弹性滞后系数的确定

采用两种材料碰撞时的恢复系数κ解决滚动摩擦力计算公式中ε的粗略确定问题．同时介绍弹性滞后系数的较精确的测定方法．     

POINT FORCE SOLUTION FOR A TRANSVERSELY ISOTROPIC ELASTIC LAYER

ＰＯＩＮＴＦＯＲＣＥＳＯＬＵＴＩＯＮＦＯＲＡＴＲＡＮＳＶＥＲＳＥＬＹＩＳＯＴＲＯＰＩＣＥＬＡＳＴＩＣＬＡＹＥＲＰＯＩＮＴＦＯＲＣＥＳＯＬＵＴＩＯＮＦＯＲＡＴＲＡＮＳＶＥＲＳＥＬＹＩＳＯＴＲＯＰＩＣＥＬＡＳＴＩＣＬＡＹＥＲ￥ＤｉｎｇＨａｏｊｉａｎｇ（丁...     

APPROXIMATE FORMULASOF IMPACT FORCE FOR NORMAL IMPACT OF A FINITE ELASTIC BEAM OF ELASTIC FOUNDATION BY A FINITE ROD

ＲｅｎＷｅｎｍｉｎ（任文敏）；ＨｕａｎｇＪｉａｎｍｉｎ（黄剑敏）；ＣｈｅｎＷｅｎ（陈文）（ＲｅｃｅｉｖｅｄＤｅｃ．２５，１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＹａｎｇＧｕｉｔｏｎｇ）ＡＰＰＲＯＸＩＭＡＴＥＦＯＲＭＵＬＡＳＯＦＩＭＰＡＣＴＦＯＲＣＥＦＯ...     

Elastic dynamics variational principle for nonlinear elastic body

Based on paper, the variational principle and generalized variational principle of elastic dynamics for elastic body with nonlinear stress-strain relations are introduced in this paper. The generalized instantaneous variational principle is also raised for the mixed harmonious displacement element and the mixed harmonious stress element.     

基面力元法(BFEM)的研究及应用进展

从高玉臣院士提出的基面力概念出发,针对一种基于基面力概念的新型有限元法—基面力元法BFEM(Base Force Element Method)的研究及应用进行综述.分析结果表明:基面力元法的计算所得结果与理论解吻合较好,基于余能原理的基面力元法较传统平面4节点等参元(Q4单元)具有较高的计算性能;在高度几何非线性分析中,基于余能原理的基面力元法较平面4节点减缩积分单元(Q4R单元)也具有一些优势;基面力元法列式推导简单,是有限元方法的一种新思路,具有较好的应用前景.     

A computational method on process optimal control for finite deformation problems

On the principle of non-incremental algorithm, some basic ideas of process optimal control iterative algorithm, based on the Optimal Control Variational Principle in Mechanics, is proposed in this paper. Then the essential governing equations are presented. This work provides a new method to achieve the numerical solutions of the mechanic of finite deformation. Project supported by the National Natural Science Foundation of China (Grant No. 594305050).     

Physical mechanics calculations for the cohesive energies and elastic constants of alkali-halide crystals

The Gordon-Kim method of calculating the interatomic potentials is modified with corrections to the exchange and dispersion interactions, and the interionic potentials in alkali-halide crystals are calculated from Roothaan-Hartree-Fock ionic wavefunctions. The lattice constants, cohesive energies and elastic constants of NaCl, NaF, NaBr, KCl, KF, KBr, RbCl, RbF and RbBr crystals are evaluated using the calculated interionic potentials. The agreement of the results with the experimental data is good.     

Calculations of elastic constants for noble metals with pseudopotential method

The third order elastic constants and the pressure derivatives of the second order elastic constants for noble metals (Cu, Ag and Au) at OK are calculated using the pseudopotential model and the overlap energy of noble metals proposed by us in Ref [1]. Five undeter mined parameters are determined by experimental data of the total energy, three second order elastic constants and the lattice constant of the crystal at OK and zero pressure. The comparisons between theoretical calculations and experiments show that the present results for gold are closer to the experimental data than those obtained by other authors.     

PI force feedback control for large flexible structure vibration with active tendons

Active tendon, consisting of a displacement actuator and a collocated force sensor, was first presented by Preumont and his co-workers to attenuate the vibration of large flexible space structures, and the control algorithm adopted by them was integral force feedback. This paper presents a new proportional-integral （PI） force feedback algorithm to achieve larger damping ratios for the structure without the requirement of structure model. Stability of the control system is shown, and simulations of a structure similar to JPL-MPI demonstrate the effectiveness of the proposed algorithm for vibration control of space structures.     

线接触弹性接触变形的解析算法

以一般光滑性体接触理论为基础,结合有限长弹性体接触的特点,求出线接触弹性接蟹变形的解析公式,并发现其解析解与数值解具有很好的一致性,所得公式可以对赫兹线接触理论加以补充,与经验公式相比,它能够确切反映材料、载荷以及曲率半径等对接触变形的影响,为工程中的精确计算提供了方便。     

Precise method to control elastic waves by conformal mapping

The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier's equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier's equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.