And then the brief description of the researches in micro - mechanics is presented . ( see chapter 1 ) 2 . the basic conception of the homogenization theory is given , and then by laplace transforming , the formulae for predicting the viscoelastic relaxation moduli in laplace transformed domain are obtained from the governing equation of the problem of composite materials (详见第一章) 2 、在简要介绍细观多尺度均匀化方法的基本理论的基础上，通过复合材料粘弹性问题的控制方程的laplace变换，并利用对应原理，在像空间中导出了利用均匀化理论预测宏观松弛模量的laplace变换泛函形式。
The work in this dissertation mainly consists of two parts . in the first part , the dynamic response of nonlinear structures with uncertain physical parameters is studied by means of subsection linearization method and equivalent random systems method , separately . in the second part , a method for analyzing the response of viscoelastic structures with uncertain physical parameters is proposed , with fem in space domain and discrete method in time domain 本文的研究工作主要由两个部分组成；第一部分是分别用分段线性化方法和等效随机系统方法对含随机参数非线性结构动态响应统计量的求解；第二部分是建立了用扩阶随机有限元方法求解含随机参数粘弹性问题的计算模型。
The boundary integral equation for elasticity is derived through the general green ’ s formula and the corresponding fundamental solution . the paper represents the contact conditions , which are essential for the coupling of the boundary integral equations of the two different elastic contact bodies , in a local coordinate system properly chosen 利用广义格林公式和基本解得出弹性问题的边界积分方程,采用循环迭代的方法,通过寻求与接触条件相协调的接触边界位移及面力增量来确定接触区域的大小。
A homogenization - based method for predicting the viscoelastic property of multi - layered composite material is presented . by laplace transforming the governing equation of the viscoellastic problem of jointed rock , the dependent relation of the laplace transformation of the effective relaxation modulus of jointed rock on the joint distribution was derived by applying the homogenization method in laplace transformed domain . then , the effective relaxation modulus was obtained from the inverse transformation 首先对层状复合材料粘弹性问题的控制方程进行laplace变换，在像空间中利用均匀化理论建立宏观松弛模量的laplace变化与各层形式的依赖关系解析表达式，通过laplace逆变换可获得等效松弛模量预测的解析表达式，并给出了体积变形为弹性、剪切变形符合三元件模型的单向节理岩石的粘弹性松弛模量预测的数值算例。
The governing equations of the problem are derived in hamiltonian form by using variable substitution and variational principle . then the methods of separation of variables and conjugate symplectic eigenfunction expansion are developed to solve the equations of plate bending problem . the result can be derived by analytical method 在平面弹性问题中，由变量代换及变分原理，方程可导向哈密顿体系，从而通过分离变量法及共轭辛本征函数向量展开法，以解析的方法来进行求解。
In order to reduce the computing time and improve efficiency , the procedure has been paralleled and the distributed parallel computation is accomplished in a net with four pcs . the parallel computation of static aeroelasticity and flutter has been initiated at home . on this basis , the work includes four parts 通过对单机串行程序进行分布式并行化改造，在国内首次实现了基于微机网络上的静气动弹性和颤振分布式并行计算，解决了数值求解气动弹性问题难以避免的耗时巨大的问题。
Based on g - w contact model , two rough surfaces in contact were simplified to a smooth one and a rough one which has regular rectangular asperities , and a three - dimensional transient thermal and stress coupled fem model was established using thermal - structure sequential coupling . the course of the sliding with friction was simulated using the nonlinear multiphysics field fem , meanwhile considering thermal - elastic problems of the two bodies , to calculate and analyze the temperature , contact pressure and stress of the sliding contact surfaces with frictional heating 基于g - w接触模型，将两个粗糙表面简化为一个有规则排列的长方体微凸体的粗糙表面与一光滑表面，利用热结构顺序耦合建立三维瞬态有限元计算模型，考虑两个物体摩擦接触的热弹性问题，采用非线性有限元多物理场来实现，对粗糙表面接触模型的瞬时摩擦温度场、压力场和应力场进行了计算分析。
A new analytical method for the plane elastic or thermoelastic problem on complex multiply connected region based upon the complex potential theory of elastic mechanics built by muskhelishvili . n . i . by combining the theory of sectionally holomorphic function , cauchy model integral , the analysis of the singularity of complex function and riemann boundary problem , the analysis relation between the complex potentials is obtained , and then the problem is transformed into solving an elementary complex potentials equation I弹性力学复势理论的基础上提出一种处理复杂多连通域平面弹性与热弹性问题新的分析方法，将复变函数的分区全纯函数理论，复势奇性分析， riemann边值问题与cauchy型积分相结合，求得各分区复势的解析关系，将问题归结为一个初等复势函数方程的求解。
The vertical pile group loaded laterally has extensively used , so the researches on the bearing and deforming behaviour pile group under lateral loads are very important . previous researches of pile group loaded laterally are carried out mainly by experimental and theoretical analysis . though a lot of experimental data and researching achievements have been obtained , many problems remain unsolved for the complex nature of pile group loaded laterally 在实验研究方面，由于做桩体流变实验耗资大，时间长，国内外还没有相关的报道；在理论上，人们对桩的流变的认识也非常有限，主要是利用遗传理论、模型理论、或者把粘弹性问题转化为弹性问题进行解答，但研究的都是桩的线性流变问题。
The equivalent random systems method that is clear in principle , simple in plan , and high in precision of example , will be developed in the 2 disposal of dynamic response of structures with uncertain physical parameters . 4 . developments of study on stochastic finite element method ( sfem ) are introduced . for the linear elastic problem , the seem is to mature 介绍了随机有限元方法的研究现状，对于线弹性问题，方法趋于成熟，但是用随机的思想来进行粘弹性结构的分析的研究工作迄今少有见诸报导；本文在空间上采用有限元法，在时域上采用差分的方法，首次建立了用扩阶随机有限元方法求解含随机参数粘弹性问题的计算模型，推导了相应的有限元公式，给出了算法，编制了有限元程序。
