基于平均法的旋转薄壁圆柱壳非线性行波振动研究

应用Donnell's简化壳理论,在考虑阻尼和几何非线性的情况下,基于平均法对旋转的薄壁悬臂圆柱壳在法向激振力作用下的非线性行波振动进行了研究.在分析过程中,首先,引入考虑阻尼及几何非线性的薄壁圆柱壳非线性波动方程,进行降阶处理后,得到模态坐标下的振动方程;其次,对模态方程进行平均化处理,确定转换矩阵,进行变量的幅值相角化,从而得到自治的标准化方程组;最后,由系统谐波共振周期解对应平均方程稳态解的原理,得到幅频特性方程.根据上述所得结果,进行了系统参数振动及稳定性研究,并进一步将结果与谐波平衡法及数值解作了比较.     

三维编织复合材料圆柱壳在外压作用下的屈曲分析

提出一种三维四向编织复合材料圆柱壳的细观力学模型,宏观上基于Reddy高阶剪切变形理论和广义Kármán型方程,采用奇异摄动法求解在固支边界条件下三维四向编织复合材料圆柱壳在外压作用下的屈曲和后屈曲.分析中同时考虑非线性前屈曲、大挠度和初始几何缺陷的影响.讨论了纤维体积含量、壳体几何参数等因素对圆柱壳屈曲行为的影响.     

带初始几何缺陷FGM固支圆柱壳的非线性动力学分析

本文主要研究了带初始几何缺陷的功能梯度固支圆柱壳在不同体积分数下的非线性动力学行为。假定该功能梯度圆柱壳材料的组分是沿厚度的方向呈梯度几何变化的。运用经典板壳理论、von-Karman几何非线性应变位移关系以及Hamilton原理,推导出两端固支FGM圆柱壳的偏微分非线性运动控制方程。本文考虑了圆柱壳的对称模态,利用Galerkin法对上述非线性动力学方程进行截断,得到常微分形式的非线性动力学方程。主要运用Runge-Kutta法进行数值仿真,并且画出了其最大lyapunov指数图,主要研究了面内载荷对振动响应的影响,并对比了不同体积分数对系统非线性动力学的影响。     

激光辐照下圆柱壳结构的稳定性分析

针对航天工程中常用的承受轴压作用的薄壁圆柱壳,分别采用解析方法与特征值屈曲有限元方法分析了圆柱壳结构在均匀轴压作用下的稳定性能,得到了屈曲承载力.并进行了对比,验证了有限元模型的合理性.采用线性屈曲特征值有限元方法分析了强激光辐照作用下圆柱壳的稳定性能,分析表明激光辐照导致壳体局部温度上升并由此带来材料参数的改变,是因为激光辐照在壳体中引起了热应力与热应变,使轴压圆柱壳的屈曲承载力明显降低.论文还着重对加筋圆柱壳结构的稳定性进行了研究,数值分析结果表明,加筋能有效提高圆柱壳结构的抗压承载力,激光辐照作用下,加筋对轴压作用下圆柱壳的屈曲承载力的提高作用更为明显.     

横向荷载作用下插入式大直径圆柱壳结构的优化数学模型

基于非线性弹簧元数值分析模型,建立了横向荷载作用下原状软粘土中插入式大圆柱壳结构的最优化设计数学模型,从中可以求得多工况荷载组合作用下,结构最佳受力的圆柱壳最佳尺度匹配.采用Monte Carlo 方向探索随机行走法作为最优化方法,对通用有限元软件ANSYS进行了优化技术的再开发,基于FORTRAN与ANSYS软件平台联合构建适合薄壁圆柱壳结构自身特殊问题分析的优化过程.算例表明此优化技术是可行有效的,结构经优化设计后相对于原设计,受力条件更优,材料用量有所节省.     

四节点二十四自由度平板壳单元几何刚度矩阵显式解析式的推演算法研究

几何刚度矩阵的推演是结构几何非线性有限元分析的重点和难点之一。推导几何刚度矩阵显式解析表达式成为简化非线性有限元列式,提高分析效率的关键。本文在协同转动法框架下,基于刚体运动法则对四节点二十四自由度的平板壳单元几何刚度矩阵显式解析式进行了推导和讨论;分析了悬臂梁大转动、不同壁厚条件下简支圆柱形屋顶空间大变位两个经典算例。研究结果表明：（1）几何刚度矩阵的显式计算公式不仅为板壳结构几何非线性列式提供了方便而且具有良好的精度;（2）推导的几何刚度矩阵适用于各类型四边形二十四自由度平板壳单元模型;（3）与数值积分相比,采用解析形式的几何刚度矩阵可以显著提高非线性响应计算效率。     

含裂纹薄壁圆柱壳弹塑性失稳极限荷载的解析解

为了得到含环向裂纹压弯薄壁圆柱壳失稳的极限荷载,基于Je?ek解析法,先利用裂纹面的平衡方程、变形几何关系和物理方程,得到在压弯荷载作用下圆柱壳轴力与裂纹面挠度的关系式;再利用极值条件,推导出在轴压和弯矩共同作用下含裂纹薄壁圆柱壳失稳时极限荷载的解析表达式。利用数值计算分析裂纹长度、长细比以及端部施加弯矩对圆柱壳极限荷载、弹性区高度和圆柱壳裂纹截面处挠度的影响,通过有限元数值结果验证极限荷载解析解的准确性。计算结果表明:与无裂纹完善构件相比,弯矩对含裂纹圆柱壳的极限荷载Pu的影响最为显著,其降低幅值可达3.78%～23.18%;弯矩的增加也会导致构件弹性区高度逐渐减小,裂纹面处的挠度呈非线性增长。本文研究弥补了目前该类问题缺乏理论解析解的不足。     

微机网络并行环境下杆壳组合结构动力特性并行计算

回顾了有限元并行计算发展的历史,阐述了微机网络并行计算环境的意义,给出了基于微机网络并行环境的杆壳组合结构动力分析并行算法,该算法包括杆壳组合结构总刚度矩阵和总质量矩阵的并行计算以及求解广义特征值问题的并行子空间迭代法的并行计算,在多台微机上安装PVM．使用Linux操作系统．构成分布式微机网络并行计算环境,将上述算法用于某型号飞机机翼及某型号挂架动力特性的并行计算,在该并行环境下的教值试验表明所给算法是非常有效的。     

壳结构的无网格局部Petrov-Galerkin方法

无网格近似函数具有高度光滑性,能够很好的逼近曲壳表面及其位移场。无网格局部Petrov-Galerkin方法不论插值还是离散都不需要单元,是一种真正的无网格方法。本文基于无网格局部Petrov-Galerkin方法的基本原理,采用移动最小二乘插值,利用控制微分方程弱形式,建立了Mindlin壳结构的无网格局部Petrov-Galerkin分析方法,用屋顶壳、受夹圆柱壳、几何非线性圆柱壳作为计算实例分析了求解精度、收敛性和稳定性,并与精确解和有限元计算结果进行了对比,表明该方法计算精度高及收敛性好。     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

基于有限单元柔度法的材料与几何双重非线性空间梁柱单元

从有限单元柔度法的基本思想出发,基于完全拉格朗日格式(TL格式),建立了能考虑材料与几何双重非线性的一般化空间梁柱单元,适用于满足Euler-Bernoulli梁柱二阶分析理论假定的空间杆系结构非线性分析。另外,在梁柱单元截面分析中引入纤维模型,使其适用于解决钢筋混凝土这类复合材料结构的非线性分析问题。对钢筋混凝土双向偏心受压柱试验结果的模拟分析表明,本文所提方法是正确、可靠的,能有效地分析钢筋混凝土框架柱的材料与几何双重非线性问题。     

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.     

A polygonal finite element formulation for modeling nearly incompressible materials

The objective of the present paper is to develop a finite element formulation for modeling nearly incompressible materials at large strains using polygonal elements. The present finite element formulation is a simplified version of the three-field mixed formulation and, in particular, it reduces the functional of the internal potential energy by expressing the field of the average volume-change in terms of the displacement field, where the latter is discretized using the Wachspress shape functions. The reduced mixed formulation eliminates the volumetric locking in nearly incompressible materials and enhances the computational efficiency as the static condensation is circumvented. A detailed implementation of the finite element formulation is presented in this study. Also, different example problems, including eigenvalue analysis, nonlinear patch test and other benchmark problems are presented for demonstrating the accuracy and the reliability of the developed formulation for polygonal elements.

     

Kinematic limit analysis of frictional materials using nonlinear programming

In this paper, a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming, limit analysis and the conventional displacement-based finite element method. The analysis is based on a general yield function which can take the form of the Mohr–Coulomb or Drucker–Prager criterion. By using an associated flow rule, a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization. The plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained. The nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation. The calculation is based entirely on kinematically admissible velocities without calculation of the stress field. The finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint. The objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load. An effective, direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem. The effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples.     

A finite element formulation for analysis of functionally graded plates and shells

Summary A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constitutent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a scalar variable and a constant matrix through the thickness. The nonlinear heat-transfer equation is solved for thermal distribution through the thickness by the Rayleigh-Ritz method. According to the results, the formulation accounts for the nonlinear variation in the stress components through the thickness especially for regions with a variation in martial propperties near the free surfaces.     

Performance review of locking alleviation methods for continuum ANCF beam elements

Nonlinear Dynamics - The absolute nodal coordinate formulation (ANCF) is a nonlinear finite element approach proposed for the large deformation dynamics analysis of beam- and plate/shell-type...     

Visco-hyperelastic model with internal state variable coupled with discontinuous damage concept under total Lagrangian formulation

The silica-filled rubber material presented in this paper exhibits nonlinear elasticity, nonlinear rate dependence and stress-softening effect under cyclic loading. In order to model the material behavior in a finite element code, the internal state variable concept is considered for finite deformation viscoelasticity. Moreover, the so-called Mullins' effect is taken into account by using a discontinuous damage concept. A total Lagrangian formulation with incompressibility constraint is adopted in the finite element code. The constitutive equations with their optimized set of parameters are validated by comparing the simulated results with experimental data. This result is very useful for the fatigue lifetime analysis of the investigated silica-filled rubber material.     

饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

Semiclosed-form solution for static nonlinear analysis of extensible cables

The analysis of a cable deforming under statically applied body forces leads to a series of differential equations that are inherently nonlinear due to coupling of geometry and loading. These equations have been solved by nonlinear finite element technique, finite difference formulation, or a two-step shooting method. However, a semiclosed-form solution is presented herein in which the governing differential equations are integrated to yield exact expressions for the unknown cable forces and the parameters defining the geometry of the loaded cable. The formulation presented herein is capable of taking care of the large sag and deformation in the cable without employing any numerical solution procedure.     

Incremental analysis for nonlinear rubber-like materials by hybrid stress finite element

In this paper, on the basis of the incremental Reissner variational principle, a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.