约束位置的小修改对固有频率的影响

利用固有频率的瑞利商变分原理和广义变分原理，给出了约束位置的小修改对固有频率的影响表达式。约束位置的小修改，要分两种情况来讨论，第一种情况是修改导致了自变函数选择域发生变化，另一种是不是导致自变函数域的变化。     

一类广义边值问题的含参广义变分原理

针对一类广义边值问题，本文提出了推广Ｇａｕｓｓ－Ｇｒｅｅｎ定理的数学恒等式和含参广义变分原理，导出了一些新的广义变分原理，并讨论了其特殊形式。     

科学出版社有关图书介绍

<正> 《高等材料力学》,[美]A.P.博雷西等著,定价5.75元本书论述理工院校一般材料力学课程中通常不讲授的主要内容和重要专题,侧重于理论在工程设计和工程研究方面的应用,各章列有例题和习题。《弹性力学的变分原理及其应用》,胡海昌著,定价5.25元本书系统地介绍了弹性力学中的各种变分原理,尤其是广义变分原理以及这些变分原理在理论方面和近似计算方面的应用,讨论到的物体形式有梁、板、扁壳和一般弹性体,     

弹性动力学Gurtin型广义变分原理

本文按照Gurtin方法提出了含有两个任意参数的弹性动力学广义变分原理.参数的不同取值以及附加不同的约束条件,可以得到多种弹性动力学Gurtin型变分原理。     

对称斜交铺层复合材料层板在平面变形情况下分层问题的解析-广义变解法

本文采用弹性力学的位移解法研究对称斜交铺层复合材升层板在平面变形情况下的分层问题,得到了满足所有基本方程,层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式.然后利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定裂纹尖端附近奇异应力场的控制量--广义应力强度因子.由于所有基本方程预先得以满足,在变分方程中只有线积分而无面积分.计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速.     

高层建筑结构力学分析

目前,高层建筑结构力学分析还是停留在利用现有的计算理论进行被动设计的阶段,不能从根本上满足未来高层建筑朝着技术功能先进和艺术完美相结合的方向发展。因此,对高层建筑的结构力学分析需要实践来改进和发展,并以此促进高层建筑结构的不断完善。本文分析了现代几种高层建筑结构力学的分析方法,包括常微分方程求解器法、有限条法和样条函数法、基于分区广义变分原理与分区混合。     

一种基于Hamilton型拟变分原理的时间子域法

本文首先给出有阻尼线弹性动力学的一类变量广义Ｈａｍｉｌｔｏｎ型拟变分原理,它能反映动力学初值一边值问题的全部特征。然后,以这类Ｈａｍｉｌｔｏｎ型拟变分原理为基础,提出一种时间子域以五次Ｂ样条函数插值的时间子域法。算例表明,这种动力响应分析新方法的精度和计算效率都明显高于国际上常用的Ｗｉｌｓｏｎ－法和Ｎｅｗｍａｒｋ－β法。     

光弹性力学的分区相似耗联势能原理及有限元法

本文建立了光弹性力学的分区相似耦联势能原理及相似耦联有限元法和广义分区相似耦联势能原理及广义相似耦联有限元法，这些分区相似耦联势能原理及相似耦联有限元法的建立，为解决光弹性力学中泊松比对冻结应力法精度的影响奠定了理论基础和提供了从模型供体应力场向原型体应力场转换的计算手段。     

对称角铺层复合材料层板在反平面变形情况下分层问题的解析—广义变分解法

本文采用弹性力学的位移解法研究对称角铺层复合材料层板在反平面变形情况下的分层问题,得到了满足所有基本方程、层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。再利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定应力强度因子。由于所有基本方程预先得以满足,变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。     

对称角铺层复合材料层板在反平面变形情况下分层问题的解析—广义变分解法

本文采用弹性力学的位移解法研究对称角铺层复合材料层板在反平面变形情况下的分层问题,得到了满足所有基本方程、层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。再利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定应力强度因子。由于所有基本方程预先得以满足,变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。     

A variational formulation in fracture mechanics

A variational approach to linear elasticity problems is considered. The family of variational principles is proposed based on the linear theory of elasticity and the method of integrodifferential relations. The idea of this approach is that the constitutive relation is specified by an integral equality instead of the local Hooke’s law and the modified boundary value problem is reduced to the minimization of a nonnegative functional over all admissible displacements and equilibrium stresses. The conditions of decomposition on two separated problems with respect to displacements and stresses are found for the variational problems formulated and the relation between the approach under consideration and the minimum principles for potential and complementary energies is shown. The effective local and integral criteria of solution quality are proposed. A numerical algorithm based on the piecewise polynomial approximations of displacement and stress fields over an arbitrary domain triangulation are worked out to obtained numerical solutions and estimate their convergence rates. Numerical results for 2D linear elasticity problems with cracks are presented and discussed.     

弹性膜结构静力学的各类变分原理

通过罗恩早已提出的一条简单而统一的新途径,系统地建立了弹性膜结构静力学的各类变分原理。首先给出膜结构静力学的广义虚功原理的表式,然后从该式出发,不仅能得到膜结构静力学的虚功原理,而且通过所给出的广义Legendre变换,还能系统地成对导出弹性膜结构静力学的3类变量、2类变量变分原理以及总势能驻值原理和总余能驻值原理的互补泛函。同时,通过这条新途径还能清楚地阐明这些原理的内在联系。     

从Levinson高阶梁理论的一致变分到高次翘曲梁理论

将矩形截面梁的截面翘曲位移设定为3次Legendre多项式的形式,利用弹性力学平面应力问题分项的不完全的广义变分原理,导出高次翘曲梁理论,得到形式简单易求解的方程。由于引入轴向拉伸的情况,使梁的平面内变形问题得以统一;计及了梁表面剪切荷载的作用,并严格满足表面剪应力边界条件;通过引入轴向位移约束参考点间距离的概念对梁端翘曲约束作更精致地描述,且使得该理论包含了变分一致或者不一致的高阶剪切梁理论。该理论的推导还表明,Levinson梁理论的变分不一致仅仅局限于有转角约束的梁端。通过算例,将高次翘曲梁理论与弹性力学平面应力问题以及Timoshenko梁理论、Levinson梁理论进行比较,初步显示出该理论的优越性。     

On the micromechanics theory of Reissner-Mindlin plates

Summary A micromechanics model is developed for the Reissner-Mindlin plate. A generalized eigenstrain formulation, i.e., an eigencurvature/eigen-rotation formulation, is proposed, which is the analogue or counterpart of the eigenstrain formulation in linear elasticity. The micromechanics model of the Reissner-Mindlin plate is useful in the study of mechanical behavior of composite plates that contain randomly distributed inhomogeneities, whose sizes are close to the order of thickness of the plate; under those circumstances, the use of micromechanics of linear elasticity is not justified, and moreover, it is inconsistent with structural theories, such as the Reissner-Mindlin plate theory, that are actually used in engineering design.In this paper, the analytical solution of an elliptical inclusion embedded in an infinite thick plate is sought. In particular, the first order asymptotic (or approximated) solution of the elliptical inclusion problem is obtained in explicit form. Accordingly, the Eshelby tensors of the Reissner-Mindlin plate are derived, which relate eigencurvature and eigen-rotation to the induced curvature and shear deformation fields. Several variational inequalities of the Reissner-Mindlin plate are discussed and derived, including the comparison variational principles of Hashin-Shtrikman/Talbot-Willis, type. As an application, variational bounds are derived to estimate the effective elastic stiffness of Reissner-Mindlin plates, specifically, the flexural rigidity and transverse shear modulus. The newly derived bounds are congruous with the Reissner-Mindlin plate theory, and they provide an optimal estimation on effective rigidity as well as effective transverse shear modulus for unstructured composite thick plates.     

弹性力学求解体系的研究与进展 第十三届全国结构工程学术会议特邀报告

本文介绍弹性力学对偶求解体系的近期研究和进展:(1)提出一种新的正交关系。不用辛几何的概念,直接导出对偶微分方程组;(2)基于新正交关系,建立二维弹性力学特征函数展开直接解法,求得含可对角化边界条件下的显式封闭解:(3)将对偶求解体系推广到多坐标方向,建立多坐标方向的对偶微分方程和求解体系。(4)采用偏微分方程的算子解法,建立了板状弹性体的弯曲理论,把它的解分解为弯曲齐次解、特解、和衰减解:(5)将对偶求解体系推广应用于厚板和薄板问题,建立了有关的对偶微分方程,正交关系和变分原理。     

On the positive definiteness of the operator of the micropolar elasticity

Summary The present paper is concerned with the static theory of anisotropic and inhomogeneous micropolar elastic solids. The operator of micropolar elasticity is considered and the positive definiteness of this operator for the first boundary value problem is proved. This fact leads to the existence of a generalized solution and to the applicability of the variational method [1] to this problem.     

On Eshelby tensors in the context of the thermodynamics of open systems: Application to volumetric growth

The connections between the notion of Eshelby tensor and the variation of Hamiltonian like action integrals are investigated, in connection with the thermodynamics of continuous open bodies exchanging mass, heat and work with their surrounding. Considering first a homogeneous representative volume element (RVE), it is shown that a possible choice of the Lagrangian density is the material derivative of a suitable thermodynamic potential. The Euler equations of the so built action integral are the state laws written in rate form. As the consequence of the optimality conditions of the resulting Jacobi action, the vanishing of the surface contribution resulting from the general variation of this Hamiltonian action leads to the well-known Gibbs–Duhem condition. A general three-field variational principle describing the equilibrium of heterogeneous systems is next written, based on the zero potential, the stationarity of which delivers a balance law for a generalized Eshelby tensor in a thermodynamic context. Adopting the rate of the grand potential as the lagrangian density, a generalized Gibbs–Duhem condition is obtained as the transversality condition of the thermodynamic action integral, considering a solid body with a movable boundary. The stationnarity condition of the surface part of the thermodynamic action traduces a relationship between the virtual work of the field variables and the virtual work of the material forces at the moving boundary. This framework is applied to the volumetric growth of spherical tissue elements due to the diffusion of nutrients, whereby a growth model relating the growth velocity gradient to a growth like Eshelby stress built from the grand potential is set up.     

广义集值混合变分不等式的一类单调算法

本文利用一个新的技巧建立了广义集值混合变分不等式与新的不动点问题的等价性。利用这个等价性,我们提出和分析了一类解集值混合变分不等式和相关的优化问题的新算法。我们的结果统一和改进了该领域内的一些最新结果。     

Exact solution of Eshelby–Christensen problem in gradient elasticity for composites with spherical inclusions

The gradient elasticity theory is employed to solve exactly the problem of Eshelby–Christensen for filled composites with spherical inclusions across length scales. Relying on the fundamental symmetry considerations and using Lagrange’s variational formalism, we derive the governing relations of linear isotropic gradient elasticity. We demonstrate that to avoid spurious solutions, one should necessarily impose some additional symmetry restrictions on the operational strain gradient elastic constants that can be considered as a new correctness condition. By enforcing the “strain gradient” symmetry condition, we offer the variant of the correct applied one-parametric gradient theory of interfacial layer model. To solve the Eshelby–Christensen problem, we employ the generalized Eshelby’s integral representations for the gradient elasticity models that allow to formulate the closing equations in a self-consistent three-phase method, and we also use the generalized Papkovich–Neuber representation to determine the general form of the gradient solution and the structure of the scale effects. As a result, we obtained for the first time an exact solution of Eshelby–Christensen problem for composites reinforced with spherical inclusions in framework of the gradient interfacial layer model. There are known analogs of fundamental results for gradient models related to closed solution for composites with spherical inclusions obtained by R.M. Christensen and K.H. Lo in 1976. The obtained analytical solution of Eshelby–Christensen problem for correct gradient theory is used to determine the stress–strain state and the effective properties of dispersed composites. The analysis of the effect of scale factors is given; the error associated with the use of gradient theories that do not obey the proposed condition of correctness is estimated.