Lode角对应力张量的导数的基本性质

为计及岩土类材料塑性力学行为的中主应力影响或应力路径相关性,通常将应力张量Lode角/Lode数引入屈服函数与塑性势函数。由此在计算塑性应变增量时必然涉及Lode角/Lode数对应力的导数张量（记为 ）。然而,应力张量主值有重根时 的计算存在困难。本文给出了 的主值计算方法及谱分解表达式并详细讨论了张量 的基本性质。     

Lode参数的物理实质及其对塑性流动的影响

回顾了1926年Lode在做屈服准则实验验证时,为了考虑中间主应力的影响而提出的参数μσ,指明其在应力Mohr圆中的几何意义,推证了μσ与应力偏张量第三不变量J3和应变增量比d2ε/d1ε及d3ε/d1ε的定量关系,进而指明μσ给实际成形工序在Mises圆柱上的定位提供了依据,作为工程上的定性分析,μσ值的符号(正或负)可以作为应变类型的判据.     

修正的厚壁筒初屈公式

符号表P_y=内压厚壁筒的初屈压力; σ_y=材料的拉伸屈服强度; K=ba=半径比; a、b=圆筒的内、外半径; μ_a=Lode参数; σ_(yt)=材料的扭转屈服限; α=考虑应力球张量对材料屈服限的影响系数; ...     

Mohr-Coulomb准则主应力回映算法及在地基问题的应用

针对Mohr-Coulomb准则在应力空间中存在奇异点的问题,提出了主应力空间应力回映算法。分析了多屈服面下塑性流动法则,给出了应力更新过程中应力回映区域的判定方法,推导了不同映射区域下塑性因子的Newton-Raphson迭代求解式和应力更新方程,建立了对应的一致切线模量表达式。利用C++语言,编制了弹塑性有限元求解程序,并对岩土地基问题进行求解,计算结果的比对证明了所编程序的可行性和精确性。     

一种考虑静水压力和偏应力共同作用的相变临界准则

同时考虑静水压力和偏应力的影响,分别建立了“应力诱发”和“形变诱发”相变的临界准则．准则在主应力空间中给出的相变临界曲面呈现明显的拉压不对称性．在弹性阶段,偏应力对相变总是起促进作用．塑性屈服后,偏应力通过塑性功产生的温升影响相变临界面,从而对高温相到低温相转变起阻碍作用,反之起促进作用．静水压力对相变可能起促进作用,也可能起阻碍作用,取决于相变时材料的体积是膨胀还是收缩．建立的相变临界准则对准静态加载条件下的Fe-20％Ni-0．5％合金和Fe-30％Ni合金和一维应变冲击条件下的Fe-32％Ni-0．035％。C合金中的γ-α相变进行了拟合和预测,预测与实验结果有较好的吻合。在主应力空间中柱形屈服面可能与锥形相变临界面相交,从而在一定条件下将发生“形变诱发”相变和“应力诱发”相变间的转变,这一推论有待实验的验证。     

圣维南原理的应用及屈服面形状大小的确定

在第1 部分,讨论弹性力学的圣维南原理在线弹性断裂力学中的应用,举例说明它的误用会引起很大的误差. 在第2 部分,讨论塑性力学中的Tresca 屈服面和Mises 屈服面的形状和大小,并推广到对Mohr-Coulomb 屈服面和Drucker-Prager 屈服面的描述,给出主应力空间中Mises 屈服面和Tresca 屈服面的形状和大小的三维图象,并以此更正和补充现有的弹塑性力学教材.     

关于双剪强度理论的教学探讨

<正> 在我国的材料力学教材和教学中,多数只讲授最大拉伸正应力理论、最大伸长线应变理论、最大剪应力理论、歪形能理论,以及莫尔强度理论.在讲授最大剪应力理论,即屈服准则 τ_(max)=(σ_1-σ_3)/2=c,亦即σ_1-σ_3=σ_s,时都要讲到,这个理论由于未考虑中间主应力σ_2对材料强度的影响而对材料在复杂应力状     

关于双剪强度理论的教学探讨

在我国的材料力学教材和教学中,多数只讲授最大拉伸正应力理论、最大伸长线应变理论、最大剪应力理论、歪形能理论,以及莫尔强度理论.在讲授最大剪应力理论,即屈服准则 τ_(max)=(σ_1-σ_3)/2=c,亦即σ_1-σ_3=σ_s,时都要讲到,这个理论由于未考虑中间主应力σ_2对材料强度的影响而对材料在复杂应力状     

基于有限元模拟的SUS304奥氏体不锈钢摩擦耦合变形过程的应力分析

采用ANSYS/LS-DYNA软件对SUS 304奥氏体不锈钢薄板的摩擦耦合变形过程进行了数值模拟.采用隐式-显式序列求解法和分段线性塑性材料模型,分析了钢带摩擦耦合变形时的应力分布规律及载荷、下压量和滑动速度等因素对钢带剪应力、主应力及等效应力的影响.结果表明:摩擦耦合变形的试验参数显著影响钢带的应力分布,验证了钢带在低于其屈服强度的应力条件下发生塑性变形的摩擦诱发效应.对奥氏体不锈钢摩擦诱发马氏体转变行为的研究及其摩擦学性能的改善具有一定的指导意义.     

半无限空间重力隧洞洞室临塑状态分析

利用Mindlin给出的、半无限空间重力隧洞初始应力场下的完整应力解分析了洞室周边的应力分布规律,用数值方法计算出了最大压应力的位置;结合Mohr-Coulomb屈服条件,研究了洞室周边出现塑性点时洞室直径、围岩粘聚力、内摩擦角与相对埋深的关系,以便工程设计应用。     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

Development and design of new methods of measurement of state of strain of structures

The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect.     

Method of constructing estimates of the solution of equations of filtration of an aerated liquid

The exact solutions of the nonlinear equations of filtration of an aerated liquid have been obtained in [1–3]. In [4] the system of equations of an aerated liquid have been reduced to the heat-conduction equation under certain assumptions. An approximate method of computing the nonsteady flow of an aerated liquid is given in [5], where the real flow pattern is replaced by a computational scheme of successive change of stationary states. In [6] the same problem is solved by the method of averaging. In the present article estimates of the solution of the equations for nonstationary filtration of an aerated liquid in one-dimensional layer are constructed under certain conditions imposed on the desired functions. These estimates can be used as approximate solutions with known error or for the verification of the accuracy of different approximate methods. We note that the use of comparison theorem for the estimate of solutions of equations of nonlinear filtration is discussed in [7–9]. The methods of constructing estimates of solutions of various problems of heat conduction are given in [10, 11]     

Calculation of aerodynamic characteristics of arrays of profiles of arbitrary shape

It is well known that the problem on nonseparating potential flow of an incompressible fluid about an array of profiles reduces to an integral equation for a certain real function, determined on the contours of the profiles of the array. As such a function one can take, as was done, for instance, in [1–5], the relative velocity of the fluid on the profiles of the array. For arrays of profiles of arbitrary shape it is necessary to solve the corresponding integral equation numerically. In the particular examples of the calculation of aerodynamic arrays that are available [1–3] the numerical methods used were based on the approximate evaluation of contour integrals by rectangle formulas. As investigations showed, sizeable errors arose thereby in the approximate solution obtained, these being especially significant in the case of curved profiles of relatively small bulk. In the present paper a method for the numerical solution of the integral equation obtained in [5] is proposed. The method is based on the replacement of a profile of the array with an inscribed N polygon, the length of whose sides is of the order N^–1 and whose internal angles are close to . Convergence with increasing N of the numerical solution to an exact solution of the integral equations at the reference points is demonstrated. Examples of the calculation are given.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–112, March–April, 1972.