含直觉模糊弹性约束的广义模糊变量线性规划

本文基于模糊结构元方法建立并讨论了一类含有直觉模糊弹性约束的广义模糊变量线性 规划问题。首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析。然后,通过选取风险中立型决策态度来定义序关系并拓展Verdegay模糊线性规划方法,将新型模糊变量线性规划问题转化为两个含一般模糊弹性约束的模糊变量线性规划模型,给出了此类规划最优直觉模糊解的求法。最后,通过数值算例进一步说明该方法的有效性。     

On the optimal design of plates for a given deflection

The optimum design problem of an elastic plate for a given deflection is considered. The design variable is chosen to be the thickness of the plate. Using the principle of stationary mutual potential energy first introduced by Shield and Prager, a sufficient optimality condition (which makes the volume stationary) is derived for plates under bending caused by general loading conditions. As an example, the optimum profile of a simply supported circular plate under a given rotationally symmetric loading is obtained.     

两种材料组成的弹性楔的佯谬解

从Hellinger-Reissner变分原理出发,通过引入适当的变换可以将两种材料组成的弹性楔问题导入极坐标哈密顿体系,从而可以在由原变量和其对偶变量组成的辛几何空间,利用分离变量法和辛本征向量展开法求解该问题的解。在极坐标哈密顿体系下的所有辛本征值中,本征值-1是一个特殊的本征值。一般情况下本征值-1为单本征值,求解其对应的基本本征函数向量就直接给出了顶端受有集中力偶的经典弹性力学解。但当两种材料的顶角和弹性模量满足特殊关系时,本征值-1成为重本征值,同时经典弹性力学解的应力分量变成无穷大,即出现佯谬。此时重本征值-1存在约当型本征解,通过对该特殊约当型本征解的直接求解就给出了两种材料组成的弹性楔顶端受有集中力偶的佯谬问题的解。结果进一步表明经典弹性力学中弹性楔的佯谬解对应的就是极坐标哈密顿体系的约当型解。     

A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate

In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner’s principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given.     

3D elastic scattering theorems for point-generated dyadic fields

The problem of scattering of elastic spherical waves by a rigid body, cavity or a penetrable obstacle in 3D linear elasticity is considered. For two point sources, dyadic far-field pattern generators are defined, which are used for the formulation of a general scattering theorem. The main reciprocity principle and mixed scattering relations are also established. We provide the necessary energy considerations, presenting relative energy functionals and expressions for the differential and the scattering cross section due to point-source dyadic incidence. Finally, an application of the general scattering theorem for appropriate locations of the point source leads to an optical theorem. Copyright © 2007 John Wiley & Sons, Ltd.     

Unique solvability and exponential stability of differential hemivariational inequalities

ABSTRACT

In this paper, we study a differential hemivariational inequality (DHVI, for short) in the framework of reflexive Banach spaces. Our aim is three fold. The first one is to investigate the existence and the uniqueness of mild solution, by applying a general fixed-point principle. The second one is to study its exponential stability, by employing the formula for the variation of parameters and inequality techniques. Finally, the third aim is to illustrate an application of our abstract results in the study of an initial and boundary value problem which describes the contact of an elastic rod with an obstacle.     

连续介质中杆件系统的振动问题

弹性连续介质中杆件系统的振动问题,是工程中经常遇到的,这是弹性动力学和结构动力学的混合求解问题。按照一般的方法进行求解,似乎有很多困难,且很复杂。本文采用Lagrange乘子法,给出了这种类型平面问题的广义泛函。并通过实例说明本文方法的应用。     

弹性基上锥壳一般弯曲问题的精确解

本文应用Donnell的简化假定,从弹性基上锥壳位移型微分方程组出发,通过引入一个位移函数U(s,θ)(在极限情况下就退化成V.S.Vlasov对于圆柱壳所引的位移函数[5]),将基本微分方程组化成为一个八阶可解偏微分方程.这个方程的一般解用级数形式给出.对于在实际中有广泛应用价值的Winkler弹性基上锥壳的轴对称弯曲问题,本文给出了详细的数值结果,并求出了边缘荷载作用下的影响系数,这对计算弹性基上锥壳组合结构有着重要的意义.     

压电体中T应力项

探讨了横观各向同性压电体平面问题中裂尖的非奇异应力项．利用叠加原理和Plemelj公式，通过求解Rieman-Hilbert问题得到非奇异应力项．结果表明弹性常数，压电及介电常数影响着非奇异应力项的值．当压电材料退化为各向异性材料时，该值与在各向异性材料时所得结果一致．     

弹性基上的薄板在侧向动载荷、中面力和外场联合作用下的小挠度弯曲

本文借用量子电动力学中的知识,将小挠度弹性薄板的一般Euler方程降阶成Schr?dinger方程型的形式,进而求得了弹性基上的薄板在侧向动载荷、中面力和外场联合作用下的小挠度弯曲的一般解.     

The equations of elastostatics in a Riemannian manifold

To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts that the deformation of the elastic body arising in response to given loads minimizes over a specific set of admissible deformations the total energy of the elastic body, defined as the difference between the strain energy and the potential of the loads. Assuming that the strain energy is a function of the metric tensor field induced by the deformation, we first derive the principle of virtual work and the associated nonlinear boundary value problem of nonlinear elasticity from the expression of the total energy of the elastic body. We then show that this boundary value problem possesses a solution if the loads are sufficiently small (in a sense we specify).     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

夹杂和裂纹的相互作用及端点相交的奇性性态分析

利用单根裂纹和单根夹杂的基本解,通过弹性力学的线性叠加原理,将平面裂纹和夹杂相互作用的问题归结为解一组带有柯西型奇异积分的积分方程组,计算了裂纹和夹杂端点的应力强度因子,给出了一些数值例子,并对夹杂和裂纹水平接触时的情形作了奇性分析,结果可作为研究夹杂尖端引起的裂纹及其扩展的工程分析的计算模型。     

Forced nonlinear vibrations of a viscoelastic body

An approximate solution of the problem of the forced, geometrically nonlinear vibrations of an arbitrary viscoelastic body is found in the form of an expansion in eigenfunctions of the corresponding linear elastic problem. With the aid of the virtual displacement principle the problem is reduced to a system of nonlinear integro-differential equations whose periodic solution is constructed by the small-parameter method.     

Transient elastodynamic three-dimensional problems in cracked bodies

The general formulation of the transient elastodynamic second boundary value problem in an isotropic linear elastic body with a crack of arbitrary shape by combining the boundary integral equation method and the Laplace transform with respect to time is presented in this paper. Both finite and infinite elastic bodies are considered. A numerical solution of the transformed boundary integral equations is proposed.     

工程中一类拼接问题的复变方法

讨论工程中一类含边裂缝弹性材料补强的拼接问题 .根据平面弹性复变方法 ,问题归结为一类解析函数的边值问题 ,通过有效的分析方法和积分变换 ,进一步将问题简化为一类奇异积分方程 ,证明了方程解的存在唯一 ,并对方程解的简化进行了研究 ,得到了弹性材料体内应力分布的封闭形式解 ,并导出一直裂缝情况裂缝尖端应力强度因子的表达式     

Minimum Principle of Complementary Energy for Nonlinear Elastic Cable Networks with Geometrical Nonlinearities

A minimum principle of complementary energy is established for cable networks involving only the stress components as variables with geometrical nonlinearities and nonlinear elastic materials. The minimization problem of total potential energy is reformulated as a variational problem with a convex objective functional and an infinite number of second-order cone constraints; its Fenchel dual problem is shown to coincide with the minimization problem of the complementary energy. It is of interest to note that the obtained complementary energy attains always its minimum value at the equilibrium state irrespective of the stability of the cable networks, contrary to the fact that only stationary principles have been presented for elastic trusses and continua, even in the case of a stable equilibrium state.     

On the minimum principle for dipolar materials with stretch

In the present paper we generalize the results obtained by Iesan and Quintanilla for microstretch elastic bodies in order to cover dipolar elastic materials with stretch. For the boundary value problem considered in this context, we prove a generalized existence result and, also, an extension of the principle of minimum potential energy.     

The realization of unilateral constraints

The problem of realizing a one-sided constraint by means of an elastic force is considered. A limit theorem is established for more general assumptions on the non-potential generalized forces than in [1].