屈服条件由应力张量的二次齐次函数与一次齐次函数之和来表达的极限分析定理

本文建立了由应力张量σ_ij的二次齐次函数与一次齐次函数的和来表达其屈服条件的刚理想塑性体的极限分析变分原理,它可用于岩土力学的极限分析问题,并把屈服条件为应力张量σ_ij 的二次齐次函数或一次齐次函数来表达的情况作为其特例.     

用张量导数法求横观各向同性弹性材料的弹性张量的一般形式

用对张量函数求导的方法导出了横观各向同性材料和各向同性材料的弹性张量的一般形式与应力-应变关系式.从推导过程可更清楚地看出为什么横观各向同性材料和各向同性材料分别有五个和两个独立的弹性常数,即材料有几个独立的弹性常数是由其应变能函数的形式所决定的.     

微分形式,守恒律和单调公式

利用一般微分形式应力-能量张量的基本公式推出了相当一般的单调性公式,据此,在一定的几何条件下可得到Liouville型的消没定理。本文还顺便说明了应力-能量张量的一些性质。     

应力函数一般解的补充

本文指出平面问题极坐标形式应力函数一般解并不完备,不能处理曲杆受任意边界分布力的问题.为此,提出两个新的应力函数,将一般解作若干补充之后,能解曲杆r=a,b上受任意分布力的问题.这是包含区域边界几何参数的新的应力函数.     

具有一致精度的薄壳方程的线性有限元方法

对Naghdi壳的弯曲问题提出一种混合有限元方法.该方法采用连续分片线性函数逼近切向延压应力张量和横向剪切应力向量,并采用间断线性函数来逼近壳的中面位移和法向纤维旋转.建立了适用于任意几何形状的壳的一般性的误差估计.分析表明如果壳中面的几何系数是分片常数,该方法对主要变量具有最优阶的,与壳的厚度无关的一致的精度.在一般情况下,在壳体几何形状快速变化的区域中适当细化有限元网格是必要的.无论如何,当有限元网格尺寸不超过壳的厚度的平方根时,最优阶的一致精度可得到保证.     

一类非对称各向同性张量函数导数的不变表示

将Dui和Chen于2004年提出的求解对称各向同性张量函数导数的方法推广到一类满足可交换条件的非对称各向同性张量函数情况,此类函数比以往研究的更具一般性．在有3个不同特征根时,由可交换性引进张量函数相对应的标量函数,进而求得此类非对称各向同性张量函数及其导数的不变表示形式．在2或3重特征根时,利用求极限的办法给出此类张量函数及其导数的表示形式．     

考虑损伤的修正梯度弹性理论

梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来.     

静止平面应力裂纹尖端的静水应力相关理想塑性应力场

在裂纹尖端的应力分量都只是θ的函数的条件下,利用平衡方程和静水应力相关屈服条件,本文导出了静止平面应力裂纹尖端的静水应力相关理想塑性应力场的一般解析表达式.将这些一般解析表达式用于具体裂纹,我们就得到Ⅰ型和Ⅱ型裂纹尖端的静水应力相关理想塑性应力场的解析表达式.     

含内裂纹的有限圆盘的平面问题

本文用弹性理论复变函数方法讨论了在内部任意位置含直线裂纹的有限圆盘在一般载荷作用下的平面问题,得到了复应力函数和应力强度因子用级数表示的一般表达式,并对此问题讨论了三种特殊情形,即裂纹受均布压应力,均布剪应力和圆盘匀速旋转的情形,其中还给出了计算应力强度因子的近似式.计算结果表明,对位于圆盘内部且不靠近外边界的中、小裂纹,这些近似式给出好的或较好的近似.     

各向同性超对称Descartes张量

各向同性张量在构造各向同性弹性固体的本构方程时有着极其重要的作用.基于各向同性Descartes张量的表达式并结合超对称张量的性质,探讨了各向同性Descartes张量各标量之间的关系,进而得出了二到六阶各向同性超对称Descartes张量的一般表达式.     

Large deformations of a new class of incompressible elastic bodies

The consequences of the constraint of incompressibility is studied for a new class of constitutive relation for elastic bodies, for which the left Cauchy–Green tensor is a function of the Cauchy stress tensor. The requirement of incompressibility is imposed directly in the constitutive relation, and it is not necessary to assume a priori that the stress tensor should be divided into two parts, a constraint stress and a constitutively specified part, as in the classical theory of nonlinear elasticity.     

A variant of the theory of local strains

A variant of the theory of local strains giving the stress tensor as a function of a given strain tensor is formulated. The stresses in an orthogonal coordinate system are established by means of a functional that averages the local stresses expressed by the local stress function. This function is determined by the given strain program. It is shown that in certain practical problems these relations are more convenient than those previously proposed.Mekhanika Polimerov, Vol. 3, No. 5, pp. 800–802, 1967     

A possible approach to the construction of a relation between the stress and strain tensors and temperature in rheonomic media

So-called averaging functionals have been determined and used to extend and generalize the local strains theory in relation to the solution of a problem of the mechanics of rheonomic media-the construction of the strain tensor as a function of the stress tensor and temperature in time.Mekhanika Polimerov, Vol. 3, No. 1, pp. 104–110, 1967     

Problems of the anisotropy of strength

The concept of a strength tensor, analogous to the tensor of elastic constants, has been introduced with a view to using its components for approximate determination of laws governing the variation of strength of anisotropic materials in uniaxial tension or pure shear as a function of the orientation of the stress state. It has been shown that the plasticity condition postulated by Mises can be used as a criterion of strength of many "weakly" anisotropic materials, if one rejects the hypothesis according to which the condition is invariant in respect to hydrostatic pressure. In the case of "strongly" anisotropic materials, wood in particular, the Mises condition is at variance with the results obtained for variously oriented specimens tested in uniaxial tension. A strength condition in the form of a fourth-degree polynomial, based on the assumed existence of a strength tensor analogous to the tensor of elastic constants, has been postulated for these materials. The validity of this criterion has been demonstrated by constructing surfaces of equicritical plane stress states from experimental data obtained for pine wood, plywood, and glass-reinforced plastic laminates.Mekhanika Polimerov, Vol 1, No. 2, pp. 79–92, 1965     

“A new approach to formulate the general strength theories for anisotropic discontinuous materials” Part B General form of polynomial to describe the strength of anisotropic discontinuous materials

A new approach to describe the failure hypersurface on the basis of assumptions presented in Part A reveals the new form of failure stress polynomial. In the presented theory new terms such as: unit tensor object, object formed on the basis of unit tensor object, the first, second and third form of the anisotropy failure function, and the first and the second type of object axis, were defined. On the basis of these terms the coefficients of their polynomials were formulated as values of the appropriate objects. The presented theory divides the six dimensional hyperspace of stresses into eight parts in which eight intersected hypersurfaces constitute the failure hypersurface. Six hypersurfaces may be assigned to two of three mutually coupled sets of elements. In general cases the theory may be used to describe the failure hypersurface for anisotropic structures where tensorial relationships do not occur. The obtained polynomial is transformed to tensor polynomial on the assumption that the failure stress tensorial relationships describe the failure hypersurface of anisotropic materials.     

Effect of combined loading on the components of the compliance tensor in shell stability problems

The local strains theory is used to establish relations for determining the components of the compliance tensor in shell buckling with allowance for combined loading of the material at the buckling point and as a function of the precritical loading path in stress space.Mekhanika Polimerov, Vol. 2, No. 3, pp. 387–391, 1966     

Die Elementararbeit in einem Kontinuum und die Zuordnung von Spannungs- und Verzerrungstensoren

Summary This paper is concerned with the calculation of the elementary work in a continuum. Whence follows a method of associating a definite stress tensor with a given strain tensor. This association is intimately connected with the choice of the definition of the rate of change of the strain tensor. It turns out that very few of the well-known stress and strain tensors are associated. However, additional associations are possible when the material is isotropic in the initial state.