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1.
基于向量式有限元基本原理,给出了八节点六面体等参实体单元的基本公式,通过投影方式将空间曲面六面体转换为投影六面体,采用参考面的逆向运动求解节点纯变形,通过单元形函的虚功方程计算节点内力;针对坐标模式和内力积分模式等关键问题提出了有效的处理方案。编制了六面体实体单元的数值计算程序,并进行工程结构算例分析。结果表明,所编制程序可有效模拟实体结构的静力、动力及大变形大位移行为分析,验证了本文理论和程序的正确性和实用性。  相似文献   

2.
由于在处理体积自锁方面的优势,近似不可压问题的大变形求解多采用六面体单元/网格,但对于复杂工程问题,由于网格剖分上的限制,往往更需要一种可以很好解决体积自锁的四面体单元。Bonet和Burton的平均节点压力4节点四面体单元是为数不多能够较好处理体积自锁问题的四面体单元之一,但是该单元目前主要用于显式计算。利用单元平均压力对位移增量的精确方向导数,得到了严格的一致切线阵,保证了Newton-Raphson迭代的二阶收敛,从而使得该单元可以用于隐式计算。该单元的压力平均计算会耦合相邻单元的节点自由度,从而增加切线刚度阵的非零带宽,但不增加自由度总数。分别采用线性六面体选择缩减积分单元、标准线性四面体单元和本文的单元计算了3个近似不可压的典型算例。算例表明,本文推导的单元可以有效克服体积自锁,达到与常用六面体单元相近的效果,使得四面体网格可以方便地用于不可压问题的大变形隐式求解。  相似文献   

3.
空间杆系结构实用几何非线性分析   总被引:6,自引:0,他引:6  
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。  相似文献   

4.
以往对桁架结构的大变形非线性分析,都是应用最小势能原理建立关于节点位移的非线性联立平衡方程,求解的工作量大,尤其对多自由度的大型复杂桁架更为突出.为了克服这个困难,本文采用两步交替迭代线性逐步逼近法,使平衡状态与变形状态协调统一,建立并求出变形后的平衡方程及其解.第一步,由已知杆件内力建立计算节点位移的连续方程并求解;第二步,由已知节点位移建立计算杆件内力的平衡方程并求解.通过多次迭代求得平衡状态与变形状态协调统一的非线性大变形分析的精确解.若干例题计算证明,本法是有效、精确的.尤其是对几何大变形桁架结构的优化设计,可将结构分析的迭代过程与优化过程相结合,省去了多次结构重分析的迭代过程,只在一次结构分析的迭代过程中即可完成优化设计,大大节省了时间.本法对扁桁架尤其有用.  相似文献   

5.
为了简便有效地解决板壳结构的大变形问题,本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成,不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法,对应变场另行假设,能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式,构造了大变形情况下的拟应变场表达式,给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明,本文针对相对自由度壳单元提出的方法及推导的公式,能够解决冲击动力问题中的大变形问题。  相似文献   

6.
覃海艺  马宁 《应用力学学报》2015,(1):139-144,179
基于h-p型有限元精度计算法,以薄壁弯曲结构为研究对象,系统地介绍了实体单元常见的分类方法及优缺点;通过理论公式推导了薄壁弯曲结构发生弹性和弹塑性变形时的位移和应力理论解;采用有限元法计算数值解,研究了影响有限元计算精度的因素和规律,并用算例证实了研究结果的合理性。研究结果表明:当单元类型、积分方式、阶次、长高比相同时,只有1层实体单元情况下得到的计算误差总是大于多层单元;只要严格控制单元长高比为1左右,单元层数不小于4层,采用一阶全积分六面体单元就可以控制位移及应力误差在5%以内;当采用一阶减缩积分六面体单元,只需2层单元就可以控制弹性位移误差在1%左右,但此时应力误差达30%以上,对于塑性变形,单元层数达6层时其位移误差仍达8%以上;对于二阶六面体及二阶四面体单元,只需2层单元,且不需严格控制单元长高比为1左右就可以使位移及应力计算误差在5%以内。  相似文献   

7.
钢框架结构在强震作用下将进入非线性状态,结构的刚度和强度等力学性能随之降低,从而影响到结构以后的抗震性能.本文利用断裂力学的基本原理,通过对栓焊节点存在焊缝裂纹的钢框架刚性连接节点的分析,推导了裂纹的有效长度和有效深度,获得了有损伤刚性连接节点的M-θ关系;并推导了节点有损伤的梁单元刚度矩阵.在数值计算的基础上分析了节点刚度变化对框架结构内力的影响,结果表明节点损伤对结构内力分析影响显著,对有损伤钢框架结构进行承载力评估时必须考虑节点损伤的影响.  相似文献   

8.
带旋转自由度C^0类任意四边形板(壳)单元   总被引:5,自引:0,他引:5  
朱菊芬  郑罡 《计算力学学报》2000,17(3):287-292300
基于Reissner-Mindilin板弯曲理论和Von-Karman大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Allman膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点C^0类板单元。大量算例表明:该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。  相似文献   

9.
一种大变形曲壳单元   总被引:7,自引:0,他引:7  
本文用壳中面节点的位移矢量和节点处壳中面单位法线矢量的矢端位移矢量构造了一种大变形曲壳单元,它是大变形曲壳单元的一般形式,能包括已有的大变形曲壳单元,且公式最简单,计算中采用的载荷增量或位移增量可以很大。  相似文献   

10.
本文采用十节点曲边四面体转换为六面体网格,并采用非线性约束优化算法取Laplacian光滑处理算法有效地提高六面体单元的质量,实现了对任意实体的六面体网格自动划分。  相似文献   

11.
将无额外自由度的广义有限元法由线弹性分析扩展到弹塑性大变形分析.局部强化函数的构建依赖于已有节点,不引入额外自由度,避免了线性相关性问题.在更新拉格朗日框架下,通过控制方程弱形式的线性化推导得到了节点内力的率形式,并分为材料和几何两部分.考虑超弹性和亚弹-塑性两种材料模型,采用Newton-Raphson迭代求解,给出了相关的一致切线刚度阵.三个典型算例的数值结果表明,本文发展的非线性无额外自由度广义有限元方法不仅能够准确求解超弹性和弹塑性大变形问题,同时相比于传统的线性有限元方法具有更高的精度.本文工作进一步拓宽了无额外自由度广义有限元方法的应用领域.  相似文献   

12.
13.
An Internal Damping Model for the Absolute Nodal Coordinate Formulation   总被引:1,自引:0,他引:1  
Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation, damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically. Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green–Lagrange strain–displacement relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated.  相似文献   

14.
基面力概念在几何非线性余能有限元中的应用   总被引:2,自引:0,他引:2  
彭一江  刘应华 《力学学报》2008,40(4):496-501
以基面力为基本未知量描述一个弹性系统的应力状态并表征单元的余能,将大变形的余能分解为变形余能部分和转动余能部分,采用Lagrange乘子法放松单元的平衡方程,利用已有的弹性大变形余能原理建立了一种几何非线性显式有限元模型,编制了相应的几何非线性余能原理有限元程序. 数值算例表明:该方法具有较好的收敛性和计算精度,可进行大载荷步的大位移、大转动计算.   相似文献   

15.
We propose a new approach for developing continuum models for the mechanical behavior of woven fabrics in planar deformation. We generate a physically motivated continuum model that can both simulate existing fabrics and predict the behavior of novel fabrics based on the properties of the yarns and the weave. The approach relies on the selection of a geometric model for the fabric weave, coupled with constitutive models for the yarn behaviors. The fabric structural configuration is related to the macroscopic deformation through an energy minimization method, and is used to calculate the internal forces carried by the yarn families. The macroscopic stresses are determined from the internal forces using equilibrium arguments. Using this approach, we develop a model for plain weave ballistic fabrics, such as Kevlar®, based on a pin-joined beam geometry. We implement this model into the finite element code ABAQUS and simulate fabrics under different modes of deformation. We present comparisons between model predictions and experimental findings for quasi-static modes of in-plane loading.  相似文献   

16.
基于余能原理的有限变形问题有限元列式   总被引:1,自引:0,他引:1  
利用基面力概念,推导了一种基于余能原理的有限变形问题显式有限元列式,可应用于结构的大位移、大转动问题。以基面力为状态变量来表达单元的余能,将有限变形情况下的单元余能分解为变形余能部分和转动余能部分,利用Lagrange乘子法推导出余能原理有限元的控制方程,编制了相应的非线性有限元程序。通过算例分析,说明该列式和程序的可靠性和精确性。  相似文献   

17.
18.
In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.  相似文献   

19.
In the general theory of continuum mechanics, the state of rotation and deformation of material points can be uniquely defined from the displacement field by using the nine independent components of the displacement gradients. For this reason, the use of the absolute rotation parameters as nodal coordinates, without relating them to the displacement gradients, leads to coordinate redundancy that leads to numerical and fundamental problems in many existing large rotation finite element formulations. Because of this fundamental problem, special measures that require modifications of the numerical integration methods were proposed in the literature in order to satisfy the principle of work and energy. As demonstrated in this paper, no such measures need to be taken when the finite element absolute nodal coordinate formulation is used since the principle of work and energy are automatically satisfied. This formulation does not suffer from the problem of coordinate redundancy and ensures the continuity of stresses and strains at the nodal points. In this study, the use of the implicit integration methods with the consistent Lagrangian elasto-plastic tangent moduli is examined when the absolute nodal coordinate formulation is used. The performance of different numerical integration methods in the dynamic analysis of large elasto-plastic deformation problems is investigated. It is shown that all these methods, in the case of convergence, yield a solution that satisfies the principle of work and energy without the need of taking any special measures. Semi-implicit integration methods, however, can lead to numerical difficulties in the case of very stiff problems due to the linearization made in these methods in order to avoid the iterative Newton--Raphson procedure. It is also demonstrated that the use of the consistent Lagrangian-plastic tangent moduli derived in this investigation using the absolute nodal coordinate formulation leads to better convergence of the iterative Newton--Raphson procedure used in the implicit integration methods.  相似文献   

20.
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