动力松弛法在应变软化类结构有限元静力分析中的应用

结构静力分析中常因材料应变软化使得相应定解问题失去适定性,从而导致有限元分析不收敛。为解决此问题,在已有的相关研究基础上,采用动力松弛法(DRM)求解结构非线性有限元静力分析的增量步,将其应用于损伤型本构所描述的结构软化问题。本文方法依据两个原理,其一是苏联《数学百科全书》论述的原理——定义于时间域的任何定解问题适定可解,其二是DRM所用的原理——质量系统静力解为相应动力解的稳态部分。且DRM无需进行隐式静力分析时的总体刚度矩阵组装和求逆计算。本文用加荷载增量求解静力平衡路径硬化段,用加位移增量求解极值点和软化段。数值试验表明,本文方法能完成应变软化类结构的静力平衡路径求解。     

索-梁混合有限元模式及其在索桥分析中的应用

索桥是大变形柔性组合结构,其受力分析属于几何非线性问题,求解较复杂。本文应用有限元方法,结合索桥结构特征,提出三节点二次曲线元与直梁单元相结合的混合有限元模式。由Reissner广义变分原理导出有限元运动方程。用Newton-Raphson方法求解有限元平衡方程,用FORTRAN-77语言编制了相应的计算程序。并以跨距为200米的索道桥为实例进行几种载荷作用下的静力分析计算。计算结果与实测值对比显示出很好的一致性。表明混合有限元模式是有效的。     

各向同性硬化材料弹塑性本构关系的渐近积分及其计算精度

1.引言由于材料塑性性质依赖于变形的历史,弹塑性有限无分析一般都采用增量方法。其基本点是从已知的现时(时间t,对于静力分析、t可理解为加载水平)状态出发,利用虚功原理建立到达邻近(时间t+△t))状态的变形增量的运动方程。这样逐步求解,从而得到结构在整个时间历程的变形和应力状态。为得到足够精确的结果,一般情况下,在非线性分析的每个增量步中,还要进行平衡迭代。但是无论是采用哪种迭代(例如Newton-Raphson迭代,常刚度迭代等),每个增量步或每次迭代以后都要进行状态决定,即根据求得的位移增量决定新的变形状态的应力、应变等,作为下一增量步或下次迭代求解的出发点。因此状态决定在增量有限元分析中不仅在计算量上占很大比例,而且对解的精度有直接的影响。在状态决定的计算中,从位移增量计算应变增量仅涉及几何关系,而由应变增量计算应力增量则涉及材料的本构关系。关于后者,弹塑性增量理论中建立的是应力和应变的微分关系:     

空间杆系结构实用几何非线性分析

从简单实用的角度论述了空间杆系结构的几何非线性分析方法。文中分析了非线性有限元方法的求解过程,特别强调决定几何非线性收敛结果的关键问题,即由节点位移增量计算单元的内力增量。通过引入转随转坐标系,论述了平面和空间梁单元小应变时单元内力增量的计算问题。针对杆系结构的大应变问题,从有限应变理论出发进行分析,提出了对该问题的有效处理方法,并且用实例进行了验证。计算结果表明,该实用几何非线性分析方法是可靠和有效的。     

一种高效率弹塑性有限元分析新方法：增量杂交／混合修正弦线模量法

本文在文献[1]给出的放松应力增量平衡约束的修正余能广义变分原理基础上,提出一种高效率的弹塑性有限元分析的新方法——增量杂交/混合修正弦线模量法。该法保持了文[1]方法的全部优点,而在迭代过程中,依据材料的单向拉伸应力—应变关系,不断改变过渡区和塑性区单元柔度矩阵和塑性矩阵中的弹性模量;并在体积压缩模量不变假设下,相应地改变过渡区单元矩阵中的泊松系数。从而大大降低了迭代收敛次数和单刚计算量,提高了多类变量弹塑性有限元分析的计算效率和收敛精度。     

有限到无限:基于离散静力平衡推导悬链线方程和梁位移方程

悬链线问题是一类非常经典的力学问题,推导出悬链线方程的方法从静力平衡到变分原理,非常之多。本文基于离散的静力平衡模型,采用从有限到无限的求解方法,建立并求解了悬链线方程。在此基础上,本文进一步建立了含有扭簧作用的离散静力平衡模型,推导并求解梁位移方程。最后在不同参数下求解梁位移方程得到其渐变解,并分析了多种平衡状态的存在情况。     

有限到无限:基于离散静力平衡推导悬链线方程和梁位移方程

悬链线问题是一类非常经典的力学问题,推导出悬链线方程的方法从静力平衡到变分原理,非常之多。本文基于离散的静力平衡模型,采用从有限到无限的求解方法,建立并求解了悬链线方程。在此基础上,本文进一步建立了含有扭簧作用的离散静力平衡模型,推导并求解梁位移方程。最后在不同参数下求解梁位移方程得到其渐变解,并分析了多种平衡状态的存在情况。     

建筑结构显式拟静力推覆分析方法研究

基于结构的精细化非线性有限元模型和显式拟静力求解方法,提出了结构拟静力推覆分析方法(EQPA);为控制结构惯性效应,给出了加载模式和基于能量的评价方法。在自主研发的CPU+GPU并行有限元软件中开发实现EQPA,可有效克服大规模复杂结构隐式Push-Over分析中计算量大和收敛性差的问题。使用EQPA对某超高层剪力墙结构的抗震性能进行分析,并与三组人工地震动的简化动力增量分析(sIDA)对比。结果表明,EQPA的结构惯性效应得到有效抑制;EQPA耗时仅为sIDA耗时的4.97%;两种分析方法的结果有一定差异,但两者的结构能力谱曲线、层间变形规律、薄弱楼层和构件损伤规律较为接近。     

非完善板屈曲路径的有限元增量摄动法

本文以Thompson一般稳定性理论为基础,提出非完善结构(有初始几何缺陷)屈曲平衡路径分析的有限元增量摄动法,它克服了增量迭代法及摄动法各自的缺点,利用增量摄动法,还建立了非完善板屈曲平衡路径的数学分析模型,对非完善矩形板在各种边界条件下的屈曲路径实现了数值程序分析,得到了符合实验的结果。     

钢筋凝混土壳体的非线性分析

本文采用有限元数值方法,分析计算了大型钢筋混凝土壳的几何、物理非线性静力问题。对非线性方程组的求解,文中提出了一种将载荷增量和位移增量相结合的合理方法,保证了在临界点附近迭代法的收敛性。最后,文中通过对实际双曲冷却塔壳的分析,得到了一些对实际工程设计具有指导意义的有益结论。     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

Lower bound shakedown analysis by the symmetric Galerkin boundary element method

In this paper, the static shakedown theorem is reformulated making use of the symmetric Galerkin boundary element method (SGBEM) rather than of finite element method. Based on the classical Melan’s theorem, a numerical solution procedure is presented for shakedown analysis of structures made of elastic-perfectly plastic material. The self-equilibrium stress field is constructed by linear combination of several basis self-equilibrium stress fields with parameters to be determined. These basis self-equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains obtained through elastic–plastic incremental analysis. The lower bound of shakedown load is obtained via a non-linear mathematical programming problem solved by the Complex method. Numerical examples show that it is feasible and efficient to solve the problems of shakedown analysis by using the SGBEM.     

一种空间缆索结构静力分析的解析元法

将空间缆索结构简化为具有拉伸刚度的质点系,给出了缆索结构空间解析元法的基本方程和求解方法,单元间的作用力与坐标变化的关系可以用解析法得到,对所得到的反映结构特性的质点系方程组进行力的平衡迭代,求解方程组.采用自动的动态可变步长的迭代方法,能够提高计算效率,保证收敛.这种方法既考虑了几何非线性,又适用于材料非线性的计算,比有限元法优越之处还在于,它不用求解线性方程组,所以适用范围广,允许求解多自由度的几何可变体系,而有限元法在求解此类问题时经常不收敛.     

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.     

基于单源模糊数的模糊随机动态有限元方程的解法

本文提出一种模糊随机动态有限元方程的解法,指出利用单源模糊数和它的运算法则,可以把一个不含阻尼项的模糊随机动态有限元平衡方程转化为两类不同集合下的方程组,一种是模糊数方程,另一种是普通的动态有限元平衡方程。前者可用模糊数运算法则求解。通常这类方程的表达式非常简单,故很容易求解,后者可利用现有的求解随机动态随机有限元平衡方程的方法计算,这时求解该方程的计算量几乎等同于求解相应的普通随机动态有限元平衡方程的计算量。最后的算例表明,本文提出的方法与通常所用的γ截集法计算结果基本相同,而且所用的计算量远远小于用γ截集法所用的计算量。     

The equilibrium state of a structure subject to frictional contact

A structure in frictional contact subject to static loads has not, in general, a unique static equilibrium state. This is because the state, displacements and contact forces, depend on the load history of the structure.In cases where the exact load history is not known it would be of interest to find a state that is in some sense likely and define this as the equilibrium state. In this paper, it is assumed that the state with the smallest potential energy is the most likely one. The implication of this definition of likely state is analysed and shows that the resulting problem basically can be seen as a generalization of the frictionless contact problem to structures where no frictionless state is possible, i.e. structures where non-zero friction forces are necessary to satisfy force equilibrium.The results of several numerical experiments are given. The structures in the experiments are trusses and structures modelled by the finite element method. Both a sequential quadratic programming method and an enumeration method are used to solve the likely-state problem.     

A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (19872016, 50178016, 19832010) and the Foundation for University Key Teacher by the Ministry of Education of China     

Analysis of thermally induced multistable composites

This paper models the non-linear flexural response of laminates that have piecewise variation of lay-up in the planform, using finite element analysis. Attention is focused on the effects that thermal stresses have on the potential multiple shapes of a composite structure. Unsymmetric laminates may possess more than a single equilibrium configuration, and during the cool-down the solution thus bifurcates at a critical temperature. In static analyses, numerical solutions are often coaxed to converge into one or the other branch of the solution. A methodology to overcome this problem is presented. Such modelling is necessary to allow application of multistable composite within morphing aircraft structures as multistable composites could provide a viable solution for the realisation of shape-adaptable structures.     

Elasto-plastic vibrational analysis of tapered bars under uniform axial loading considering shear deformation and rotary inertia

The analysis of structures in the plastic regime is important in order to develop an adequate and competitive design in engineering. This paper presents a study of the small-amplitude free vibration of tapered bars under pre-stress in the post-elastic regime due to a uniform axial loading. The plastic behavior is taken into account using an energy approach. The method does not require an iterative procedure, unlike conventional methods used in plasticity. The Timoshenko beam theory and the dynamic version of the principle of virtual work are used to derive the eigenvalue problem. The solution is carried out using beam finite elements. The results are validated using 3D finite element software and results from the open literature. A variety of numerical results are given in order to analyze the influence of plastic behavior for various bar geometries and material parameters. The combined effect of the stiffening due to the axial loading and the plastic softening may produce an increase or decrease of the natural frequencies as the tensile load increases. The plastic softening effect is seen to be pronounced for short bars and for high taper ratios. In addition, axial normal modes are more affected than bending modes.