风力发电塔的自振特性分析

将风力发电塔视为带有附加质量的变截面悬臂梁,进行横向振动的自振特性分析.采用直接模态摄动法建立风力发电塔自振特性的近似求解方法,与采用梁单元模型和壳单元模型的有限元法的计算结果相比较.数值计算结果表明直接模态摄动法具有较好的精度,形成了半解析解形式.     

非线性弹性有限条分析

本文探讨适用于板壳结构物理非线性分析的半解析有限元法,可用以求解各种材料,任意形状与边界以及变厚度的平板与柱壳问题,将在很大程度上节省计算工作量。文中还讨论了非线性特性的结构效应。     

基于有限元分析的特征值反问题求解的逆摄动方法

本文研究特征值反问题的求解方法,根据广义特征值反问题理论和有限元法的特点,以转子系统平面梁单元有限元模型结构分析的特征值反问题求解为例,给出一种新的逆摄动方法,给出了本逆摄动法较完整的理论基础,给出了其逆摄动参数的显式计算公式及相应的取值方法,本逆摄动法也可推广到其他单元类型的有限元模型特征值反问题的求解。     

大位移弹塑性样条有限条分析

本文将弹性样条有限条分析推广到大位移弹塑性分析过程．开发了大位移样条有限条分析的Ｃ语言程序包．可用于任意边界条件及变厚度平板及柱壳结构的分析．与有限元法相比可节约大量计算机内存和机时，并可望推广到塑性加工领域中．     

夹层圆柱壳振动的谱有限元分析

从哈密顿变分原理获得夹层圆柱壳的运动微分方程和边界条件,将谱有限元法用于夹层圆柱壳结构,推导出不同周向模态下夹层圆柱壳单元的动力刚度矩阵和隐式动力形状函数,分析长径比、径厚比、芯表厚度比、芯表模量比对固有频率和模态损耗因子的影响.研究表明:小径厚比、大长径比及大芯表厚度比有利于抑制夹层圆柱壳振动.     

正常与钙化变厚度生物心瓣应力分布的数值模拟

采用八结点超参数板壳元，对猪主动脉瓣在闭合承载状态下的应力分布进行了非线性有限元数值模拟．分析了变厚度瓣膜和等厚度瓣膜应力分布的差别，发现厚度对应力分布具有较大影响．进一步分析了正常及具有几个散布钙化点的瓣膜的应力分布，发现钙化区域应力显著增大．本文结果与临床病变瓣膜的观察结果较为符合     

结构动力分析的随机变分原理及随机有限元法

将结构动力系统的参数及激励的随机性直接引入结构的动力泛函变分表达式中，基于瞬时最小势能原理，应用小参数摄动法，建立了随机结构动力分析的随机变分列式及相应的确机有限元法。算例表明，应用此法分析随机结构动力响应，具有程序实施简便，计算效率高的优点。     

变厚度柱壳水池的极限分析与优化设计

变厚度柱壳水池的极限分析等厚度柱壳水池的极限分析,已被用不同的方法研究过.其实象贮水池一类柱壳,由于载荷的特点,从经济观点来考虑,采用等厚度截面并不适宜.因此,本文研究线性变厚度柱壳水池的承载能力问题,并从优化设计的角度来考虑柱壳截面尺寸的合理选择.     

椭圆抛物面扁壳某些应力集中问题

本文采用摄动法讨论了椭圆抛物面扁壳在集中载荷附近和圆孔附近的应力集中问题,所取的参数为ε=(k_x-k_y)/(k_x+k_y)(这里k_x和k_y是壳面的主曲率).按摄动法求解时,其初始解就是曲率为(k_x+k_y)/2的球壳的解,而各次修正解也归结为球壳方程问题的解.文中采用Hankel变换方法求得了各次修正解,并给出了集中力问题最初几次修正解的数字结果.数字计算表明,摄动法的收敛性相当良好.     

管线随机有限元的抗震可靠性研究

基于动力分析的摄动有限元法及管线可靠度分析模型 ,建立管线的动态随机有限元方程 ,分析了管线质量随机性和几何特征随机性 ,得出了在Elcentro地震波的激励下 ,管线结构的动力响应及具有非穿透性裂纹的抗震可靠度 ;并与Monte Carlo有限元法进行计算比较 ,表明了方法的正确性和可行性     

PERTURBATION FINITE ELEMENT METHOD FOR SOLVING GEOMETRICALLY NONLINEAR PROBLEMS OF AXISYMMETRICAL SHELL

In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell, the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions, and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely. The paper derives all the formulas concerning an axisym-metric shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

随机杆系结构几何非线性分析的递推求解方法

建立了随机静力作用下考虑几何非线性的随机杆系结构的随机非线性平衡方程. 将和 位移耦合的随机割线弹性模量以及随机响应量表示为非正交多项式展开式，运用传统的摄动方法获 得了关于非正交多项式展式的待定系数的确定性的递推方程. 在求解了待定系数后，利用非 正交多项式展开式和正交多项式展开式的关系矩阵，可以很方便地得到未知响应量的二阶统计矩. 两杆结构和平面桁架拱的算例结果表明，当随机量涨落较大时，递推随机有限元方法比基于 二阶泰勒展开的摄动随机有限元方法更逼近蒙特卡洛模拟结果，显示了该方法对几何非线性 随机问题求解的有效性.     

含模糊参数结构有限元方程的一种新解法

实际工程问题中，常常会包含一些难以准确描述的系统参数。本文根据模糊集理论，将结构中的不确定参数转化为模糊参数，从而建立起含模糊参数的有限元平衡方程，应用一般模糊线性方程解的基本原理，对模糊有限元平衡方程解的概念及方法进行了讨论，并在此基础上提出了一种改进解的概念以及以摄动法为基础的求解方法。该方法假定当不确定参数相对于其清晰值的分解度不很大时，可以将其在清晰值附近作摄动展开。文中也简要讨论了改进解与现有的模糊有限元方程组各种解之间的关系。相对于现有的其它解法，本文建议的方法更易于与常规的有限元软件结合，用于处理工程实际问题。对算例结果的分析表明，本文方法可较好地符合实际要求。     

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL-Ⅱ: FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

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The solution of rectangular plates with large deflection by spline functions

In this paper, Von Karman ’s set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point (SFP) method and by the spline finite element (SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.     

Adaptive and anisotropic mesh strategy for thin shell problems. Case of inhibited parabolic shells

The aim of this paper is to show the reliability of an adaptive and anisotropic mesh procedure for thin shell problems. We consider singular perturbation problems only for parabolic shells whose behavior is described by the Koiter model. The corresponding system of equations, which depends on the relative thickness ε of the shell, is elliptic except at the limit for ε = 0 where it is parabolic. In a first part of this paper, we study theoretically the phenomena of internal layers appearing during the singular perturbation process, when the loading is somewhat singular. These layers have very different structures either they are along or across the asymptotic lines of the middle surface of the shell. In a second part, numerical computations are performed using a finite element software coupled with an adaptive anisotropic mesh generator. This technique enables to approach accurately the singularities and the layers predicted by the theory especially for very small values of the thickness. The efficiency of such a procedure in comparison with uniform meshes is put in a prominent position.     

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

In this paper a finite element formulation of a reduction method for dynamic buckling analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The implementation of a single-mode dynamic buckling analysis in a general purpose finite element code is described. The effectiveness of the approach is illustrated by application to the dynamic buckling of composite cylindrical shells under axial and radial step loads. Results of the reduction method are compared with results available in the literature. The results are also compared with full model finite element explicit dynamic analysis, and a reasonable agreement is obtained.     

随机结构有限元分析的递推求解方法

提出了一种新的谱随机有限元分析方法——递推求解方法。该方法将随机结构的随机响应表示成非正交多项式展式,建立了和摄动法类似的一系列确定的递推方程,并通过确定性有限元方法对这些递推方程进行静力问题求解。算例表明,当随机量出现较大涨落时,计算结果相对于传统摄动法有不小的改进。