一种新的大位移井钻柱几何非线性分析方法

提出了基于实测的井深及相应的井斜角和方位角来获得确保井内钻柱参考构形长度不变的井眼轴线插值方法．当以空间大位移井的井眼轴线为钻柱的参考构形时,钻柱内的初始内力可以由井眼轴线的曲率和挠率确定．利用基于在空间自然坐标系下的包含所有单元刚体位移和常应变模式的位移函数,严格地按虚功原理推出了具有初始曲率和挠率的钻柱单元内由初始内力所引起的等效节点力计算公式,为大位移井钻柱的几何非线性处理提供了理论依据．澄清了钻柱有限元分析中的若干基本概念．为随后进行的以井眼轴线为参考构形的小变形分析,计算钻柱的自重和基于自然坐标系下的线性刚度矩阵及一致载荷列阵提供了保证．     

旋转壳在子午面内整体弯曲的几何非线性摄动有限元法及在波纹管计算中的应用(Ⅰ)

为切实有效地计算波纹管,建立了旋转壳在子午面内整体弯曲几何非线性问题的摄动有限元法。以结构环向应变的均方根为摄动小参数,将有限元节点位移列式和节点力列式直接展开。通过摄动小参数将非线性有限元的载荷分级和迭代过程有机地统一起来,即载荷的分级是有约束的,每一级载荷增量和所对应的位移增量之间的关系是已知的,每一级的计算一步到位。为叙述方便并具实用性,将旋转壳用截锥壳单元进行离散。位移分量和载荷分量沿环向按Fourier级数展开,沿子午线用多项式插值,端面弯矩和横向力化成载荷分量离散到节点上。采用Sanders中小转角非线性几何方程和各向同性广义Hooke定律。对多层材料叠合而成的旋转壳按各层薄膜应变、弯曲应变、扭转应变相等的原则进行处理,该方法能方便有效地计算单层和多层波纹管整体纯弯曲、横向弯曲的几何非线性问题。并为有限元处理非线性问题提供了一条新途径。     

旋转壳在子午面内整体弯曲的几何非线性摄动有限元肖及在波纹管计算中的应用（Ⅰ）

为切实有效地计算波纹管，建立了旋转壳在子午面内整体弯曲几何非线性问题的摄动有限元法。以结构环向应变的均方根为摄动小参数，将有限元节点位移列式和节点力列式直接展开。通过摄动小参数将非线性有限元的载荷分级和迭代过程有机地统一起来，即载荷的分级是有约束的，每一级载荷增量和所对应的位移增量之间的关系是已知的，每一级的计算一步到位。为叙述方便并具实用性，将旋转壳用截锥壳单元进行离散。位移分量和载荷分量沿环向按Fourier级数展开，沿子午线用多项式插值，端面弯矩和横向力化成载荷分量离散到节点上。采用Sanders中小转角非线性几何方程和各向同性广义Hooke定律，对多层材料叠合而成的旋转壳按各层薄膜应变、弯曲应变、扭转应变相等的原则进行处理，该方法能方便有效地计算单层和多层波纹管整体纯弯曲、横向弯曲的几何非线性问题。并为有限元处理非线性问题提供了一条新途径。     

无锁定的退化的等参壳元

构造了一个无锁定的8节点退化的等参壳元。在自然坐标系中,对横向剪应变项插值修正使单元满足必要的模式(平移、转动和纯弯曲)以消除"剪切锁定";在局部坐标系中,对薄膜应变插值修正以消除"薄膜锁定"。这样构造的8节点单元的刚度矩阵具有正确的秩,同时具有恰当的零特征值和相应的刚体位移模式。这种单元对大跨-厚比情形既无"剪切锁定"又无"薄膜锁定",无虚假的零能模式和机构出现,可用于厚壳和薄壳。     

Timoshenko梁单元超收敛结点应力的EEP法计算

将新近提出的单元能量投影(Element Energy Projection,简称EEP)法应用于Timoshenko梁单元的超收敛结点应力计算．根据单元投影定理具体推导了一般单元的计算公式,并对两个有代表性的单元给出了数值算例．分析和算例表明,EEP法对于解答是向量函数(即常微分方程组)的问题具有同样优良的表现,不仅能给出与结点位移精度同阶、同量级的超收敛结点应力,而且在位移出现了剪切闭锁的情况下仍能有效地克服应力的剪切闭锁．该研究为EEP法广泛应用于一般的一维常微分方程组问题的有限元解答的超收敛计算打下了良好的基础．     

一般杆系结构的非线性数值分析

本文在total-Lagrange坐标系下,对Kirchhoff梁给出了考虑几何非线性的两种梁单元刚度的显式表达式.一种是一般的非线性梁元,它既考虑了应变增量和位移增量间的二次项,又计及了刚体位移的影响,另一种是简化的非线性梁元,它只在线性梁的平衡方程中直接加入了轴力对弯曲的影响.非线性方程采用混合法求解,文中通过一些算例的数值计算,对两种单元作了比较详细的分析和评估.     

壳体的非线性应变分量

壳体的非线性应变分量是非线性壳体力学的基础,在壳体的稳定以及各种大变形问题中须要用到它们.由于壳体几何复杂,在现有文献中,还未见到较全面地表示此种非线性应变分量的一般公式,现在导出六个用正交曲线坐标表示的包括线性与非线性部分的壳体应变分量的公式,其中三个为拉伸应变分量,另三个为剪切应变分量.     

基于剪切效应纤维梁单元的结构非线性有限元数值模拟

基于Euler-Bernoulli梁理论的经典纤维模型忽略了剪切变形给截面带来的影响,为了得到更加精确的梁单元模型,该文基于考虑剪切效应的纤维梁单元,根据Timoshenko梁理论,推导了该纤维梁单元的刚度矩阵,并结合弹塑性增量理论,同时考虑了几何非线性和材料非线性的双重影响,建立了压弯剪复杂应力状态下结构非线性有限元...     

一种h型自适应有限单元

ｈ型自适应有限单元在网格局部细划时．会产生非常规节点，从而破坏了一般意义上的单元连续性假定．本文利用参照节点对非常规单元进行坐标和位移插值．为保证单元之间坐标和位移的连续性，本文提出了一组修正的形函数，常用的形函数是它的一个特例．本方法应用于有限元程序时，除形函数外无须做任何改动．算例表明水文的方法具有方法简单、精度高、自由度少、计算量小等优点．     

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.     

Derivation of the consistent flexibility matrix for geometrically nonlinear Timoshenko frame finite element

A consistent flexibility matrix is presented for a large displacement equilibrium-based Timoshenko beam–column element. This development is an improvement and extension to Neuenhofer–Filippou [1] (1998. ASCE J. Struct. Eng. 124, 704–711) for geometrically nonlinear Euler–Bernoulli force-based beam element. In order to find weak form compatibility and strong form equilibrium equations of the beam, the Hellinger–Reissner potential is expressed. During the formulation process, an extended displacement interpolation technique named curvature/shearing based displacement interpolation (CSBDI) is proposed for the strain–displacement relationship. Finally, the extended CSBDI technique is validated for geometric nonlinear examples and accuracy of the method is investigated concluding improved convergence rates with respect to the general finite element formulation. Also it is seen that the use of force based formulation removes shear locking effects. The results demonstrate considerable accuracy even in presence of high axial loading in comparison with the displacement based approach.     

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.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 2. Geometrically Nonlinear Statement

Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells subjected to large displacements and arbitrarily large rotations. As the sought-for functions, six displacements and eleven strains of the shell faces are chosen, which allows us to use nonlinear deformation relationships exactly representing arbitrarily large displacements of the shell as a rigid body. The stiffness matrix of a shell element has a proper rank and is calculated based on exact analytical integration. The bilinear element developed does not allow false rigid displacements and is not subjected to the membrane, shear, or Poisson locking phenomenon. The results of solving the well-known test problem on a nonsymmetrically fixed circular arch subjected to a concentrated load and the problem on a locally loaded toroidal multilayer rubber-cord shell are presented.     

A spatial shear deformable beam finite element based on the absolute nodal coordinate formulation

In the present paper a three-dimensional beam finite element undergoing large deformations is proposed. Since the definition of the proposed finite element is based on the absolute nodal coordinate formulation (ANCF), no rotational coordinates occur in the formulation. In the current approach, the orientation of the cross section is parameterized by means of slope vectors. Since those are no unit vectors, the cross-section can deform, similar to existing thick beam and shell elements. The nodal displacements and the directional derivatives of the displacements are chosen as nodal coordinates, but in contrast to standard ANCF elements, the proposed formulation is based on the two transversal slope vectors per node only. Different approaches for the virtual work of elastic forces are presented: a continuum mechanics based formulation, as well as a structural mechanics based formulation, which is in accordance with classical nonlinear beam finite elements. Since different interpolation functions as in standard ANCF elements are used, a much better convergence rate (up to order four) can be obtained. Therefore, the present element has high potential for application in geometrically nonlinear problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficient mixed interpolated curved beam element for geometrically nonlinear analysis

In this study, a curved beam element is developed for geometrically nonlinear analysis of planar structures. The main contribution of this research is to use high-performance formulation to alleviate locking phenomena and consider finite rotation. This scheme is based on the mixed interpolation of the strain fields. In this study, special tying points are found and utilized. One of the interesting advantages of the proposed element is the ability to model tapered structures. Moreover, the First-order Shear Deformation Theory (FSDT) and the Green-Lagrange strain are included. Several complicated and applicable nonlinear problems are solved to depict the efficiency and high accuracy of the proposed element, especially by fewer numbers of elements.     

A Piezoelectric Finite Shell Element for the Geometrically Nonlinear Analysis of Sensors

A geometrically nonlinear finite element formulation to analyze piezoelectric shell structures is presented. The formulation is based on the mixed field variational functional of Hu–Washizu. Within this variational principle the independent fields are displacements, electric potential, strains, electric field, stresses and dielectric displacements. The mixed formulation allows an interpolation of the strains and the electric field through the shell thickness, which is an essential advantage when using a three dimensional material law. It is remarked that no simplification regarding the constitutive relation is assumed. The normal zero stress condition and the normal zero dielectric displacement condition are enforced by the independent resultant stress and resultant dielectric displacement fields. The shell structure is modeled by a reference surface with a four node element. Each node possesses six mechanical degrees of freedom, three displacements and three rotations, and one electrical degree of freedom, which is the difference of the electric potential through the shell thickness. The developed mixed hybrid shell element fulfills the in–plane, bending and shear patch tests, which have been adopted for coupled field problems. A numerical investigation of a smart antenna demonstrates the applicability of the piezoelectric shell element under the consideration of geometrical nonlinearity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

A geometrically nonlinear (3,2) reduced degree-of-freedom unified zigzag laminated beam element for large deformation analysis

A geometrically nonlinear (3,2) unified zigzag beam element is developed with a reduced number of degree-of-freedom for the large deformation analysis. The main merit of the beam element model is the Kirchhoff and Cauchy shear stress solution for large deformation and large strain analysis is more accurate. The geometrically nonlinearity is considered in the calculation of the zigzag coefficients. Thus, the results of shear Cauchy stress are matching well with solid element analysis in case of the beam with aspect ratio greater than 20 under large deformation. The zigzag coefficients are derived explicitly. The Green strain and the second Piola Kirchhoff stress are used. The second Piola Kirchhoff shear stress is continuous at the interface between adjacent layers priori. The bottom surface second Piola Kirchhoff shear stress condition is used to determine the zigzag coefficient and the top surface second Piola Kirchhoff shear stress condition is used to reduce one degree-of-freedom. The nonlinear finite element equations are derived. In the numerical tests, several benchmark problems with large deformation are solved to verify the accuracy. It is observed that the proposed beam has accurate solution for beam with aspect ratio greater than 20. The second Piola Kirchhoff and Cauchy shear stress accuracy is also good. A convergence study is also presented.