严格求解夹层圆柱壳在轴压下的轴对称失稳问题

本文在文献[1]的基础上,用严格的方法求解两端简支的夹层圆柱壳在均匀轴压下的轴对称失稳问题.内、外表层很薄弹性模量又大,按薄壳理论处理;夹心较厚弹性模量又相当小,横向剪切变形的影响必须考虑,在研究夹层壳的整体失稳尤其是局部失稳时,横向的拉伸和压缩变形也不可忽略,用数学弹性力学的方法处理.本文导得了可求解轴对称整体失稳和局部失稳临界载荷的超越方程,用数值计算的方法可算得临界载荷的最小值.对于整体失稳的情况,给出算例,与夹层壳理论的解作了比较.     

具有非轴对称几何缺陷的双曲旋转壳应力分析

本文探讨了分析具有非轴对称几何缺陷的双曲旋转壳的一种近似方法,在这种方法中,缺陷的影响是由虚构的载荷模拟的.并提出了在非轴对称载荷作用下,使用该方法分析具有鼓包形缺陷壳体时的一种有效的算法.这种方法既分开了各种曲率误差对于内力和力矩的影响,又体现了它们之间的相互作用,避免了在非轴对称载荷下所需的重复运算,并能在一个仅有轴对称分析能力的程序上实现.本文用该方法分析了受自重载荷和风载荷作用的,具有鼓包形缺陷的双曲冷却塔,并同时用一个特殊的有限元程序直分析了缺陷塔.通过数字结果的比较,检查了等效载荷法的精度及适用性.     

考虑横向剪切变形和旋转惯性的层合正交异性球壳的动态响应

本文建立了计及横向剪切变形和旋转惯性的复合材料轴对称层合圆柱正交异性球壳的运动方程．在此基础上，用有限差分法计算了球壳在轴对称动力载荷下的动态响应，并讨论了材料参数、结构参数和横向剪切变形的影响．     

摄动有限元法解一般轴对称壳几何非线性问题

本文在处理几何非线性问题时,利用在变分方程中引入振动过程,得到各级变分摄动方程,并通过有限元法求解.由于有限元法能成功地处理各种复杂边界条件、几何形状的力学问题,摄动法又可将非线性问题转化为线性问题求解.若结合这两种方法的优点,将能够解决大量复杂的非线性力学问题.并能够消除单独使用有限元法或摄动法求解复杂非线性问题所出现的困难. 本文应用摄动有限元法求解了一般轴对称壳的几何非线性问题.     

扁薄球壳非对称大变形问题

本文用修正选代法研究了扁球壳非对称大变形问题，求得了在线性液体载荷作用下的扁球壳变形的二次近似解析解并绘出了摄动点的挠度与载荷的特征曲线族．应用本文方法还可对其他板壳的非轴对称大变形问题进行讨论．本文通过算例对平板及不同初挠度的扁球壳大挠度变形进行了讨论．     

扁薄锥壳非对称大变形问题

本文用双参数摄动法研究了扁锥壳非对称大变形问题，求得了在线性载荷作用下的扁锥壳变形的三次近似解析解并绘出了摄动点的挠度与载荷的特征曲线·应用本文方法还可对其它板壳的非轴对称大变形问题进行讨论·本文通过算例对平板及不同初挠度的扁锥壳大挠度变形进行了讨论·     

旋转壳的抗扭刚度

本文列出了旋转壳在包括扭转在内的轴对称变形下的一般平衡方程,并证明了旋转对称壳内的剪应力独立于壳内其它薄膜和弯曲应力.本文求解了只考虑薄膜应力的扭转问题,也求解了考虑弯曲扭应力在内的扭转问题,并指出了在薄壳中,抗扭刚度的主要部份来源于薄膜应力.     

非均匀圆柱壳非线性轴对称变形一般解

本文利用阶梯折算法[1],得到了非均匀圆柱壳非线性轴对称变形的一般解.文中导出了在任意轴对称载荷下求解非均匀圆柱壳非线性弯曲的位移和内力的一般公式,并给出一致收敛于精确解的证明.问题最后归结为求解二元一次代数方程组,文末给出算例.算例表明,无论内力和位移都可得到满意的结果,并收敛于精确解.     

厚球壳与实心球轴对称问题的一般解

本文试图从更一般的三维问题基本方程出发研究任意厚球壳与实心球的轴对称问题.对于受任意轴对称载荷的厚球壳和实心球体,文中运用加权残值法给出了以Legendre级数表示的一般解.     

开孔浅球壳的非线性动力响应及其动力稳定

本文建立了具轴对称变形、考虑横向剪切影响的浅球壳的非线性运动方程:对周边弹性支承开孔浅球壳的非线性静、动力响应及动力稳定问题进行了探讨.在解题方法上,对位移函数在空间上采用正交配点法离散.在时间上采用平均加速度法(Newmark-β法)离散.变求解一组非线性微分方程为求解一组线性代数方程.文中给出了不同情况下的若干数值结果,且与有关文献的结果作了比较.     

基于FEMLIP的全风化边坡失稳破坏全过程的数值模拟研究

边坡坡角和强度是影响边坡稳定性的重要因素,而边坡失稳往往伴随着大变形的发生,其变形从数十米至数千米不等.目前,传统有限元法在处理大变形问题时常常因网格畸变而导致计算终止.因此,为了实现边坡失稳破坏全过程的模拟,并研究边坡坡角和强度对边坡稳定性的影响,基于Lagrange(拉格朗日)积分点有限元法（FEMLIP）,采用C语言编写了能够模拟边坡失稳滑塌全过程的Ellipsis程序,并通过一个典型案例对该方法的正确性和可行性进行了验证.采用该方法分析了边坡在不同坡角和强度条件下的稳定性和滑坡过程.研究结果表明,Lagrange积分点有限元法可以较准确地模拟边坡的潜在滑移面,并且可以模拟边坡失稳后的滑坡发展过程,为边坡滑坡大变形分析提供了一种新的数值计算方法.     

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach is presented. A rate-independent, non-associated, strain-softening Drucker–Prager plasticity model is formulated in the context of strong discontinuities and implemented along with an enhanced quadrilateral element within the framework of an assumed enhanced strain finite element method. For simple model problems such as uniform compression, the strong discontinuity approach has been shown to lead to mesh-independent finite element solutions when localized deformation is present. In this paper, a finite element analysis of localized deformation occurring in a more complex model problem of slope stability is conducted in a nearly mesh-independent manner. The effect of dilatancy on the orientation of slip lines is demonstrated for the slope stability problem.     

Static and dynamic analyses of isogeometric curvilinearly stiffened plates

The isogeometric analysis (IGA) is a new approach which builds a seamless connection between Computer Aided Design (CAD) and Computer Aided Engineering (CAE). This approach which uses the B-Splines or the Non-Uniform Rational B-Splines (NURBS) as a geometric representation of the object is a discretization technology for numerical analysis. The IGA has advantages of capturing exact geometry and making the flexibility of refinement, which results in higher calculation accuracy. To study the static and dynamic characteristics of curvilinearly stiffened plates, the NURBS based isogeometric analysis approach is developed in this paper. We use this approach to analyze the static deformation, the free vibration and the vibration behavior in the presence of in-plane loads of curvilinearly stiffened plates. Furthermore, the large deformation and the large amplitude vibration of the curvilinearly stiffened plates are also studied based on the von Karman's large deformation theory. One of the superiorities of the present method in the analysis of the stiffened plates is that the element number is much less than commercial finite element software, whereas another advantage is that the mesh refinement process is much more convenient compared with traditional finite element method (FEM). Some numerical examples are shown to validate the correctness and superiority of the present method by comparing with the results from commercial software and finite element analysis.     

A numerical study of singular stress field of 3D cracks

We investigate the stress distribution and the variation of the mode I stress intensity factor along a straight three-dimensional (3D) crack by the finite element method. The results are checked against plane strain theory near the mid-crack and against the 3D theory of Zhu at the free surface. Although Zhu's formulation is not perfect and has some typographical errors. The surface stress distribution of his results are in line with the present study by the finite element method. The stress intensity factors at the free surface are found to be much lower than that at the mid-crack.     

Nonlinear vibration of moderately thick laminated beams using finite element method

A finite element model is developed to study the large-amplitude free vibrations of generally-layered laminated composite beams. The Poisson effect, which is often neglected, is included in the laminated beam constitutive equation. The large deformation is accounted for by using von Karman strains and the transverse shear deformation is incorporated using a higher order theory. The beam element has eight degrees of freedom with the inplane displacement, transverse displacement, bending slope and bending rotation as the variables at each node. The direct iteration method is used to solve the nonlinear equations which are evaluated at the point of reversal of motion. The influence of boundary conditions, beam geometries, Poisson effect, and ply orientations on the nonlinear frequencies and mode shapes are demonstrated.     

Numerical Prediction of Macroscopic Material Failure

The aim of this contribution is the numerical determination of macroscopic material properties based on constitutive relationships characterising the microscale. A macroscopic failure criterion is computed using a three dimensional finite element formulation. The proposed finite element model implements the Strong Discontinuity Approach (SDA) in order to include the localised, fully nonlinear kinematics associated with the failure on the microscale. This numerical application exploits further the Enhanced–Assumed–Strain (EAS) concept to decompose additively the deformation gradient into a conforming part corresponding to a smooth deformation mapping and an enhanced part reflecting the final failure kinematics of the microscale. This finite element formulation is then used for the modelling of the microscale and for the discretisation of a representative volume element (RVE). The macroscopic material behaviour results from numerical computations of the RVE. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

大挠度钻柱强度分析的平衡微分方程法

对小井眼、大曲率井中钻柱强度问题,以井轴为基准轴,在对井轴弯挠描述和钻柱微段三维受力变形分析的基础上,建立大位移钻柱平衡微分方程,采用Longe-Kutta法解之求内力,并依此求应力和建立强度条件.对H767侧钻水平井施工中钻柱应力计算分析,结果说明与有限元模型和弹性化软绳模型比较相吻合,该模型比有限元模型计算简捷方便;比弹性化软绳模型更完善可信;该井钻柱破坏事故愿因在于井眼曲率过大,兼有应力集中.     

基面力单元法在空间几何非线性问题中的应用

基于基面力的概念,并结合Euler角的位移描述方法,提出了适用于几何非线性计算的空间6结点余能基面力单元.使用MATLAB语言编程并对典型梁、板结构进行弹性大变形数值模拟.由计算结果可以看出,基于余能原理的基面力元法(BFEM)在计算构件的空间大变形时有较好的计算精度,对比传统有限元计算方法具有网格尺寸影响小和抗畸变能力强的特点,有良好的计算性能.     

Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain–displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.     

The non-linear deformation and stability of elliptical cylindrical shells under transverse bending

A finite-element formulation of the solution of problems of the stability of non-circular cylindrical shells taking into account their bending moments and the non-linearity of their precritical stress-strain state in proposed. Explicit expressions for the displacements of the elements of non-circular cylindrical shells as rigid bodies are derived by integration of the equations obtained by equating the components of the linear strains to zero. These expressions are used to construct shape functions of an effective quadrilateral finite element of the natural curvature. An effective algorithm is developed for investigating the non-linear deformation and stability of the shells. The stability of a cylindrical shell of elliptical cross-section under transverse bending is investigated. The influence of the ellipticity and non-linearity of the deformation on the shell's stability is determined. The results of the analysis are compared with experimental data.