充气薄膜管的弯皱行为分析

基于Stein-Hedgepeth褶皱理论,并通过引入"收缩系数"表征了膜结构褶皱形变特性,联合褶皱时的应力平衡条件完成了充气膜结构褶皱分析。将方法拓展应用于充气薄膜管情况,分析了充气管结构的弯皱变形特性,得到了临界皱曲弯矩和失效弯矩,并分析了弯矩随管半径和气压的变化规律。通过弯皱试验与分析结果进行比较,验证了分析结果的准确性。     

块体单元法的理论和计算模型

本文提出一种数值分析的离散模型。它以块体单元的刚体位移为基本未知量,根据块体在外力和缝面应力作用下的平衡条件、变形协调条件和缝面材料的本构关系,采用变分原理导出块体单元法的支配方程。由于相邻块体的位移不同,这是一种位移不协调的单元,文章应用广义变分原理证明了它的收敛性。根据缝面材料不同的本构关系,可以对结构进行弹性、弹塑性或流变分析。这种方法可以解决非连续介质问题,特别适用于解决具有众多节理、裂隙岩体的变形、应力和稳定分析。研究和算例表明,它具有效率较高,精度较好的优点。     

压电热弹性材料四边简支层合板的精确解

根据压电热弹性材料的控制方程和热传导关系,重构压电热弹性材料的本构关系,通过新本构关系并结合压电热弹性材料热平衡方程,得出压电热弹性材料机-电-热耦合问题的齐次状态方程。应用精细积分法,状态方程可独立求解。此方法在分析压电热弹性体耦合问题时,避免了求解关于热传导方程和热平衡方程的二阶微分方程,大大减少了数值计算的工作量。     

The theory of Cosserat points applied to the analyses of wrinkled and slack membranes

Numerical simulations of wrinkling and slacking of geometrically nonlinear membrane structures are considered using planar Cosserat points. The finite element method (FEM) solves the problem by weakly projecting the governing PDEs and thus requires numerical integration. This is contrasted with Cosserat point elements wherein governing equations are solved in an averaged sense at a point. The point is equipped with a few directors and can describe the deformation kinematics of a finite region containing itself. Numerical modeling through the Cosserat point provides freedom from numerical integration and locking. Presently a plane stress quadrilateral Cosserat point element is used to study the wrinkling and slacking of isotropic membranes. The approach by Roddeman et al. (ASME J Appl Mech 54:884–892, 1987) is exploited to detect wrinkled/slack elements in the membrane structure. Here stretching parameters are employed to modify the deformation tensor to represent a fictive non-wrinkled surface. A variation of the algorithm to detect spatial variations of the stretching parameters within a point element is also described. Several numerical examples on static deformations of wrinkled/slack membranes are presented. Limited comparisons with a reported experiment and with results via the FEM as well as a mesh-free approach are provided to assess the performance of the approach.     

A nonlinear complementarity approach for elastoplastic problems by BEM without internal cells

A nonlinear complementarity approach is presented to solve elastoplastic problems by the boundary element method, in which the equations are formulated by stress equations and complementarity function obtained from the plasticity constitutive law. The domain integrals involved are transformed into boundary integrals by radial integration method, using compactly supported radial basis functions. Two numerical examples demonstrate the algorithm’s applicability and effectiveness.     

受弯充气锥台的褶皱特性分析

充气锥台是空间充气膜结构的主要承载力构件单元之一,膜面褶皱是导致其承载力降低的关键因素。该文基于薄膜理论分析了受弯充气锥台的褶皱特性。借助褶皱的应力判定准则对褶皱特征参数进行了预报,得到了初始起皱位置和起皱力随充气锥台两端半径比的变化规律,并得到了数值分析结果的验证。该文的结果为空间充气薄膜结构的承载能力预报提供重要依...     

An approach to finite static axially symmetric deformation of a hyperelastic membrane

Summary A simple approach to the problem of finite quasi-static axially symmetric deformation of an isotropic incompressible hyperelastic membrane is presented. Lagrangian type equilibrium equations, expressed in terms of the Biot stresses, are used along with constitutive relations expressing the principal components of Biot stress in terms of the principal stretches. Numerical results, obtained from the application of a finite element method to the governing equilibrium equations and constitutive relations, are presented for two problems, and for two different strain energy functions. It is shown how the proposed equilibrium equations can be obtained from a variational principle, and the variational principle is also used to obtain approximate solutions.     

The incremental perturbation method for large displacement analysis of elastic-plastic structures

A procedure of applying the perturbation method is presented for the incremental numerical analysis of materially and combined non-linear problems of discrete and discretized structral systems. Small but finite strain and stress increments are strictly distinguished from the strain rates and stress rates, respectively. It is shown that, by applying the perturbation procedure not only to the non-linear strain-displacement relations and equilibrium equations, but also to the constitutive equations in terms of rate quantities, all the governing equations can be satisfied to any desired accuracy at every instantaneous configuration in between the starting and terminal points of an incremental step. The proposed method provides also means of finding, to a desired accuracy, every point on an equilibrium path of a discrete system at which a new element will start yielding or unloading and possible critical points on the path. The significance of the proposed method is expected to be appreciated particularly in numerical investigations of critical behaviours and post-buckling behaviours.     

考虑膜材各向异性的膜结构褶皱分析

推导了应用于向量式有限元三角形膜单元的各向异性膜材本构矩阵;进一步推导了各向异性膜材褶皱状态下的修正本构矩阵,并提出更为合理的主偏夹角计算方法。在此基础上编制了考虑膜材各向异性的膜结构荷载分析与褶皱分析程序,并进行了算例验证。算例分析表明,所编制的向量式有限元程序可以很好地完成各向异性膜结构的荷载分析与褶皱分析,验证了理论推导的正确性和分析程序的可靠性。分析结果还表明膜材的各向异性与褶皱效应会对膜结构的受力性能产生显著影响。     

Numerical algorithm for triphasic model of charged and hydrated soft tissues

 This paper devises an efficient numerical algorithm for solving a two-dimensional triphasic model of charged and hydrated soft tissue by using the radial basis functions. The proposed numerical method is applied directly as a simple meshless collocation algorithm to approximate the solution of the governing system of continuity, momentum, and constitutive equations for the triphasic model. Since there is no requirement on meshing, the method can easily be applied to solve problems under complicated geometry. For verification, numerical simulations of stress, strain, and fluid flow patterns for a plane strain and an axisymmetric mechano-electrochemical coupling model with real synovial joint are given respectively. Classical domain decomposition technique is also combined successfully with the proposed method for solving large scale problems with numerical verification given in solving the axisymmetric case. Received 20 November 2001 / Accepted 28 November 2001     

Finite element analysis of membrane wrinkling

New results are presented for the finite element analysis of wrinkling in curved elastic membranes under‐going large deformation. Concise continuum level governing equations are derived in which singularities are eliminated. A simple and efficient algorithm with robust convergence properties is established to find the real strain and stress of the wrinkled membrane for Hookean materials. The continuum theory is implemented into a finite element code. Explicit formulas for the internal forces and the tangent stiffness matrix are derived. Numerical examples are presented that demonstrate the effectiveness of the new theory for predicting wrinkling in membranes undergoing large deformation. Copyright © 2001 John Wiley & Sons, Ltd.     

A WEAK–WEAK FORMULATION FOR LARGE DISPLACEMENTS BEAM STATICS: A FINITE VOLUMES APPROXIMATION

This paper addresses the problem of the numerical solution of beam statics undergoing large displacements. A kinematic analysis outlines the beam geometrical model through the definition of its Lagrangian co-ordinate and strain parameters. A definition of the stress parameters, a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain. The equations governing the beam equilibrium are introduced and their weak form is derived. These equations are then proved to be equivalent to the primal and mixed form of Principle of Virtual Work. The numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form. The weak–weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain. Some numerical examples prove the capability of present formulation in handling actual problems.     

铝合金薄板冲压成形过程中的侧壁起皱及有限元模拟

针对铝合金薄板的侧壁起皱问题,本文通过有限元软件分析工艺参数对成形质量的影响,提出了一种基于数值模拟与智能算法相结合的优化方法。首先,利用最优拉丁超立方抽样进行实验设计,并依据数值模拟获取实验值;其次,基于BP神经网络拟合工艺参数与成形质量之间的关系,预测结果的平均相对误差为2.69%,建立了准确的预测模型;最后,用遗传算法极值寻优获取了一组最优的工艺参数组合,起皱幅值的预测值和仿真值相对误差仅为4.03%,实验结果与仿真分析结果相近,验证了该优化方法的合理性和有效性。研究表明:以料厚、摩擦系数和压边力作为优化变量,以最大起皱幅值最小化为优化目标,建立几何模型,并利用有限元软件Autoform进行仿真分析;依据起皱轮廓线径向位移的实验和数值模拟对比,验证了有限元模型的正确性,表明利用神经网络和遗传算法极值寻优可以有效解决铝合金侧壁起皱缺陷。     

On the contact mechanics of a rolling cylinder on a graded coating. Part 1: Analytical formulation

In this paper, the fully coupled rolling contact problem of a graded coating/substrate system under the action of a rigid cylinder is investigated. Using the singular integral equation approach, the governing equations of the rolling contact problem are constructed for all possible stick/slip regimes. Applying the Gauss–Chebyshev numerical integration method, the governing equations are converted to systems of algebraic equations. A new numerical algorithm is proposed to solve these systems of equations. Both the coupled and the uncoupled solutions to the problem are found through an implemented iterative procedure. In Part I of this paper, the analytical formulation of the rolling contact problem and the discretization of the governing equations are introduced for all assumed stick/slip regimes. A detailed discussion of the proposed numerical algorithm, the iteration procedure and the numerical results, obtained using the analytical formulation, are given in Part II.     

CALCULATION OF HYPERELASTIC RESPONSE OF FINITELY DEFORMED ELASTIC-VISCOPLASTIC MATERIALS

The objective of this paper is to present a numerical algorithm for calculating hyperelastic constitutive equations characterizing the thermomechanical response of elastically isotropic elastic-viscoplastic materials. The algorithm is developed within the context of an alternative formulation of plasticity in which elastic distortional deformation is determined directly by integrating an evolution equation which includes the current velocity gradient and quantities that depend only on the present state of the material. Consequently, the formulation is independent of the particular choice of a measure of plastic deformation, the reference configuration, and the total deformation gradient from the reference configuration. These features allow the constitutive equations to be easily implemented into computer codes which currently use a hypoelastic formulation for calculating plasticity.     

Equilibrium analysis of finitely deformed elastic networks

A specialized membrane theory is used to analyze equilibrium configurations of finitely deformed elastic networks. The effects of wrinkling of the network are incorporated by using a certain relaxed strain energy function derived from minimum energy considerations. The stresses derived from this function are non-compressive at all values of the strain. In particular, a fibre strain associated with vanishing fibre stress may be viewed as resulting from fine-scale wrinkling of the fibre. In this way destabilizing compressive stresses are automatically excluded from the solution of an equilibrium boundary value problem.The properties of the relaxed strain energy are used to show that all equilibrium configurations are absolute minimizers of the total potential energy, for certain classes of boundary data. The equilibrium equations are discretized by a differencing method derived from Green's theorem, and artificial mass, damping and time are incorporated. Equilibrium configurations are then obtained in the long-time limit of a damped dynamical problem. Several examples of two- and three-dimensional deformations are presented, and comparisons with analytical solutions are made wherever possible.     

OPTIMIZATION METHODS FOR SOLVING NON-LINEAR EQUATIONS IN VISCOELASTIC FLOW PROBLEMS

Numerical simulation of complex flows of viscoelastic fluids requires the use of efficient algorithms for solving the non-linear governing equations. In this paper, optimization algorithms, associated to a non-linear least squares methods are considered. The governing equations are written in the context of stream-tube analysis. This method is particularly adapted to handle memory-integral constitutive equations and permits calculation of flows by considering elementary sub-domains in a mapped computational domain where the transformed streamlines are parallel and straight. The procedure used to solve the equations is the Trust Region optimization algorithm, which satisfies a global convergence property. Using an integral codeformational equation, various tests involving the influence of parameters of the algorithms are applied to different flow geometries and underline the robustness and efficiency of the Trust Region algorithm.     

热过屈曲梁振动的解析解

该文导出了面内热载荷作用下, 梁在其过屈曲构形附近微幅振动的解析解。首先基于经典梁理论, 推导了控制轴向和横向变形的基本方程。然后, 将2 个非线性方程化为一个关于横向挠度的四阶非线性积分-微分方程。假设梁的振幅以及由此引起的附加应变为无限小, 另设其响应为谐振, 则该非线性积分-微分方程将化为两组耦合的微分方程:一组控制非线性静态响应;另一组就是叠加于梁屈曲构形之上的线性振动方程。直接求解这些问题, 可以得到梁热过屈曲构形以及固有频率的解析解, 这些解是外加热载荷的函数。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。     

Wrinkling on irreversibly deforming foundations

Wrinkling is a mechanical instability occurring in multi-layer structures comprising a thin and stiff layer resting on a supporting underlying compliant layer. The present study is motivated by experimental observations of wrinkling leading to irreversible deformation and to the initiation of defects. An incremental Spectral Method is employed to solve the governing differential equations. This approach enables the analysis of wrinkling processes non-linear foundations and under cyclic loading. Numerical simulation results are compared to a set of analytical solutions describing wrinkling events on nonlinear foundations. Wrinkling is analyzed for cases of elastic, elastic damageable, and elastic plastic foundations. The behavior of homogeneous foundation properties is contrasted to situations where local defects are present.     

Wrinkling of nonlinear membranes

 Membranes are stiff under tension but switch over to wrinkling when compression occurs. Roddeman proposed a kinematic model to handle this phenomenon under finite deformation conditions. The wrinkling conditions of Roddeman are transformed into the reference configuration. This results in a more simple nonlinear formulation. For application in a finite element code a consistent linearization was carried out. Numerical examples for linear and nonlinear orthotropic constitutive equations are discussed. Received 21 December 2001 / Accepted 10 April 2002