任意非亏损矩阵特征灵敏度分析的模态展开法

把特征向量的各阶导数表示成所有模态的线性组合，并利用左模态与右模态间的双正交性，首先导出了任意非亏损矩阵的重特征值的一阶导数所满足的特征值问题，然后根据此特征值问题无、看重根的情况，再导出了异导重特征值和等导重特征值对应的可微特征向量、特征值和特征向量各阶导数的一般计算公式。算例显示了方法的正确性。     

The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach

After recalling the constitutive equations of finite strain poroelasticity formulated at the macroscopic level, we adopt a microscopic point of view which consists of describing the fluid-saturated porous medium at a space scale on which the fluid and solid phases are geometrically distinct. The constitutive equations of poroelasticity are recovered from the analysis conducted on a representative elementary volume of porous material open to fluid mass exchange. The procedure relies upon the solution of a boundary value problem defined on the solid domain of the representative volume undergoing large elastic strains. The macroscopic potential, computed as the integral of the free energy density over the solid domain, is shown to depend on the macroscopic deformation gradient and the porous space volume as relevant variables. The corresponding stress-type variables obtained through the differentiation of this potential turn out to be the macroscopic Boussinesq stress tensor and the pore pressure. Furthermore, such a procedure makes it possible to establish the necessary and sufficient conditions to ensure the validity of an ‘effective stress’ formulation of the constitutive equations of finite strain poroelasticity. Such conditions are notably satisfied in the important case of an incompressible solid matrix.     

离散时间系统Ляпунов函数的构造与稳定性判定

本文旨在以矩阵的相似变换理论为基础,以电子计算机为工具,提供一种无需求解离散?矩阵方程,而直接由系统矩阵来构造离散时间系统?函数和判定系统稳定性的方法.     

Cavity nucleation, growth and stress field in elastic-plastic medium

A finite element method is used to study the cavity nucleation and growth in an elastic-plastic medium. The critical cohesion strength, _c at IPM (interface between second phase particle and matrix) is employed as the criterion of cavity formation. Three different values of _c are taken to examine their influence on the overall mechanical behaviour and process of cavity formation.     

轴对称薄壁结构自由振动的边界元分析

采用双互易法分析薄壁轴对称结构自由振动的特征频率以及特征模态.首先,采用径向基函数插值域积分里的位移,利用双互易法将域积分转化为子午面边界的积分.然后,将边界物理量、基本解和特解展开为傅里叶级数,沿环向积分后得到的边界积分方程可用于轴对称结构带体积力问题和受非对称载荷的动力学分析,其积分域为轴对称结构子午面边界上的线积分,进一步降低了问题的维度和离散的难度.文章详细探讨了源点处于对称轴的特殊情况,根据基本解和特解的退化形式,针对无体积力和有体积力分别给出了处理奇异矩阵的方案.对于薄壁结构,采用双曲正弦变换处理近奇异积分有效提高积分精度.最后将双互易法和双曲正弦变化应用于薄壁轴对称结构带体积力的静力学和自由振动分析.数值结果表明,文章提出的处理奇异矩阵的方法能够有效处理源点处于对称轴的情况;当圆筒厚高比为$10^{-3}$,边界元计算的特征频率的相对误差为$10^{-3}$,且优于有限元的结果.      

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation effectiveness and precision, is presented for solving the acoustic radiation from a submerged infinite non-circular cylindrical shell stiffened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work,besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The effects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efficient than the existing mixed FE-BE method.     

半刚性钢框架的内力分析

采用二阶非线性分析方法分析和设计半刚性钢框架，包括连接的柔性以及构件的几何非线性的影响，提出了半刚性钢框架中梁柱单元刚度矩阵和半刚性梁的单元刚度矩阵；推导了半刚性梁在集中荷载，均布荷载，线性荷载作用下的固端弯矩的求解公式；连接的柔性对无支撑框架的侧移有很大的影响，设计时通过变化连接的刚度以平衡梁的跨中和端弯矩。     

充液层合压电圆柱壳的自由振动

推导得到轴向极化的圆柱型正交各向异性压电弹性力学的三维状态方程，采用细分近似方法，得到了状态方程的解，并建立了圆柱壳内外表面边界量之间的传递关系，分析了内充可压缩流体的层合压电圆柱壳的自由振动问题，给出了频率方程的精确形式，并作了具体计算。     

金属基复合材料单向和循环变形行为的数值模拟研究

利用晶体细观力学模型，依据组元材料的单晶体变形性质，以Ａｌ－Ａｌ２Ｃｕ自生复合材料为模型材料，用数值法模拟其拉伸和循环拉伸变形过程，得到了与有关实验结果相符的应力－应变曲线，研究了增强相间距和循环加载过程对复合材料变形行为的影响，通过考虑变形过程中组元相及其界面的应力分布规律，分析研究了循环变形过程中基体Ｂａｕｓｃｈｉｎｇｅｒ效应对于复合材料微观变形与损伤机制的作用，结果表明，晶体细观力学模拟计算     

容量矩阵法在涡方法中的应用

本文将容量矩阵技术与快速Fourier变换相结合求解非矩形域的Poisson方程,再与格子涡方法相结合,发展了一套求解复杂外形的快速涡方法。作为算例,计算了有厚度平板和楔形体的分离流动,得到了满意的结果。特别是在垂直平板绕流中,模拟出了由于剪切层不稳定性引起的小涡结构。