弹性

Based on the current development of VED in structural control and its fractional derivative model, the finite element formula of VED is erected by using three different assumptions of the shear strain.

针对粘弹性材料的分数导数模型，采用不同的剪应变的假设，推导了粘弹性阻尼器的有限元计算公式，通过粘弹性阻尼器在一单自由度系统的控制上的应用，确定了其计算模型。

After introducing the generalized strain energy function with fractional order, the constitutive equation of biological visco-elastic material was obtained by means of the fractional calculus.

摘 要：对生物粘弹性材料，引入广义分数阶应变能函数以后，应用分数阶微积分分别给出了粘弹性固体和粘弹性流体的本构关系式。

The coupling effect between elastic deformation and the rigid motion was concerned in the dynamic equations. At the same time, the flexible manipulators were assumed as Euler-Bernoulli beams, the elastic deformation of the manipulator was represented by modality truncation equations, both elastic and gravitational potential energy were considered to calculate the total energy for whole system, therefore the finial dynamic modeling is more accurate and simple than others published.

该方法考虑了柔性机械臂刚体运动和弹性变形之间的耦合影响，并将柔性机械臂假设为一段Euler-Bernoulli梁处理，将弹性变形用截断模态方程表示，同时考虑了弹性势能和重力势能的影响，得到的双连杆柔性机械臂的动力学模型具有模型准确、结构简单等特点。

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method, where the problem is formulated by distributions of fictitions fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically.

弹性半空间；本文用线载荷积分方程法研究嵌在弹性半空间的刚性变直径圆轴的轴对称扭转。利用将"半空间的点环力偶"这一虚的基本载荷沿对称轴的圆轴区间中分布就能使本问题归结为一个一维的非奇异的Ferdholm第一种积分方程，且很易用数值求解。文中给出刚性圆锥，圆柱，圆锥柱嵌在弹性半空间的扭转的数值计算的例并和他人的已知结果相比较。

The discriminant is derived using the above theory wether gear profile need to modify and the formula using to calculate precisely modify measment of gear is derived. An elastic curve of the harmonic drive that the profile of the rigid gear and elastic gear are involute is studied.

利用本文建立的弹性啮合理论推导出齿轮齿面是否需要修形的判别式和修形量精确计算的公式；利用本文弹性啮合理论研究了谐波齿轮传动中的弹性曲线求解问题。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

The analytic expressions for the displacement components and stresses at any point of an infinite micropolar orthotropic elastic medium with an overlying elastic half space as a result of moving inclined load of arbitrary orientation were obtained.

在无限大微极正交各向异性弹性介质上覆盖弹性介质的弹性半空间的任意点上，作用着任意方向倾斜的移动荷载，给出了位移分量和应力的解析表达式·假设倾斜荷载是法向荷载和切向荷载的线性组合·利用Fourier变换采用特征值方法，并利用数值技术反演了Fourier变换·给出了铝环氧树脂复合材料的数值结果图形

Based on the three dimensional viscoelastic integral constitutive relation of a propellant grain with the finite element method, the analysis about the thermo-viscoelasticity of solid propulsive agent column is presented.

基于药柱的三维线性热粘弹性积分本构关系，采用有限元法，对固体火箭推进剂药柱进行热粘弹性有限元分析，得出药柱在轴向过载作用下的变形结果和药柱内危险部位的位置，表明药柱具有明显的粘弹性特点。

Using LaGrange theorem on base of analyzing the elastic prop model tension system of band saw machine, the dynamics model of elastic prop tension system of band saw machine has been established and converted to mathematics model applying the modern control theory.

本文以MJ317型木工杠杆压砣张紧系统的带锯机改造成弹性挺杆张紧系统的带锯机为研究对象，通过对带锯机弹性挺杆式张紧系统的弹性动力学分析，运用拉格朗日定理建立了张紧系统的动力学模型，并应用现代控制理论将模型转换成数学模型。

The propagation matrix method used widely in stratified media is extended to laterally inho-mogeneous media,and a numerical method known as generalized propagation matrix method for simulating elastic seismic wave propagation in inhomogeneous media is presented by using mixed variable elastic wave equation and matrix exponent solution of system of linear ordinary differential equations.

应用混合变量弹性动力学方程和线性常微分方程组的矩阵指数解法，将层状介质中广泛应用的弹性波传播矩阵解法推广至横向非均匀介质，给出了一种可计算复杂地质体中弹性波传播的广义传播矩阵数值解法。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。