结构非线性分析ABAQUS.docx

1、结构非线性分析ABAQUS工程结构非线性作业学院： 土 木 工 程 学 院 专业： 结 构 工 程 * * * 学号： S* 教师： 方志（教授） 作业31 偏压柱的跨中最大挠度的解析解32用有限元软件ABAQUS建立题中所给的弯压柱的力学模型，并计算跨中最大挠4 2.1 给出一个实例4 2.2 确定材料的本构模型4 2.3 建立有限元模型5 2.4 模拟结果分析对比123 ABAQUS有限元软件分析的理论背景（来自ABAQUS帮助文件）144 对结构几何非线性和稳定的关系进行讨论24结构非线性作业一（1）求出荷载柱中点侧移的解析解。（2）以具体的实例给出几何非线性效应得数值解（可用有限元程序

2、计算），并与解析解结果对比。（3）给出有限元程序理论背景的详细描述。（4）对结构几何非线性和稳定的关系进行讨论。1 偏压柱的跨中最大挠度的解析解图1 计算简图1.1跨中弯矩为： （1）1.2由材料力学中梁挠曲线的近似微分方程可以得到： 将（1）式代入其中得解微分方程得： 其中1.3 求跨中侧移：当时 2 用有限元软件ABAQUS建立题中所给的弯压柱的力学模型，并计算跨中最大挠度2.1 给出一个实例： 假设题中所给弯压柱所受荷载P=10KN, 偏心距e=0.1m，柱高为L=2m，采用屈服强度为345MP的钢材，弹性模量E=206000MP, 柱的截面尺寸如所示：图1 计算简图2.2 确定材料的本

3、构模型采用韩林海（2007）中的二次塑性流模型来模拟钢材， 其应力-应变关系曲线,分为弹性段(Oa)、弹塑性段(ab)、塑性段 (bc)、强化段(cd)和二次塑流(de)等五个阶段，如图1所示。图1中的点划线为钢材实际的应力-应变关系曲线，实线所示为简化的应力-应变关系曲线，模型的数学表达式如式(3-1)。其中：； fp、fy和 fu分别为钢材的比例极限、屈服极限和抗拉强度极限。 (3-1) 由该本构模型计算出材料的应力应变关系表1 计算的钢管的力学参数与应力应变曲线应变分段点0.0017296120.0013836890.0020755340.020755340.218143系数A1.488

4、77E+14B6.18E+11C-2850400002.3 建立有限元模型2.3.1 创建部件在ABAQUS里打开而为建模截面，创建一根二维的柱模型，长度为2000mm。如下图所示：图1 创建二维柱部件2.3.2 创建材料参数创建钢材料属性 采用韩林海（2007）二次 塑流模型Ec=206000;泊松比0.3；塑性应力应变参 数见表格；同时要对材料的的塑性性能进行编辑，将事先计算好的应力塑性应变数据导入到steel的塑性编辑表格里面去就可以了。在输入材料的应力塑性应变数据组的时候要保证所输入的塑性应变是递增的，并且初始塑性应变必须为零。将塑性数据输入到软件中去。表2 钢材塑性应变应力应力塑性应

5、变应力塑性应变27603450.0152300.8403450.0171320.160.00013450.019333.960.0001386.40.056342.240.0002427.80.09313450.0003469.20.13013450.0022510.60.16723450.00415520.20423450.00595520.22493450.00785520.24563450.00975520.26633450.01155520.2873450.01345520.3077图2 创建钢材材料属性2.3.3 创建并指派截面指派截面定义柱的截面为一个宽50mm，高100mm的矩形

6、截面如下：图3 创建柱界面并赋予构件上2.3.4 组装配件将各个部件建立起来并赋予了材料属性与截面属性之后，开始将各个部件组装在一起。Instance part选择需组装的部件。图4 装配构件2.3.5 设置分析步与相互作用在本模型中需要研究的是跨中挠度。所以在设置分析步中的历程输出中要创建相应的输出。为了便于计算机计算模型，需要创建一个分析步。需要输出的数据为跨中挠度。图5（a） 设置分析步图5（b） 设置分析步参数2.3.6 创建荷载，约束并划分网格构件受到一个偏心的轴力的作用，在这里假设柱受到一个轴力P=10KN，和一对弯矩M=2KNM作用。图6 创建荷载划分网格图7 划分网格2.3.7

7、 新建工作并提交运行进入到工作界面，新建工作，新建完工作之后要进行数据检查，检查完数据无误之后再点击提交开始运行。运行完之后就可以在可视化对话框中观察计算结果。2.3.8 模拟结果分析 运用Abqaus6.5有限元软件建模计算之后可以得出钢管混凝土叠合柱的各个部件在既定荷载下的受力情况。图 8（a）加载前的柱图图 8（b） 加载后的变形图图13 加载后的受力云图输出跨中挠度时间曲线3.5结果分析ABAQUS模拟计算出来跨中最大挠度为：0.52561mm利用前面建立的理论公式计算跨中挠度： 所以： 对比有限元软件结果0.52561mm与理论公式结果0.51865mm，差异度只有1.3%4 ABA

8、QUS有限元软件分析的理论背景（来自ABAQUS帮助文件）4.1Nonlinear solution methods in Abaqus/StandardProduct: Abaqus/StandardThe finite element models generated in Abaqus are usually nonlinear and can involve from a few to thousands of variables. In terms of these variables the equilibrium equations obtained by discretizin

9、g the virtual work equation can be written symbolically as where is the force component conjugate to the variable in the problem and is the value of the variable. The basic problem is to solve Equation 2.2.11 for the throughout the history of interest. Many of the problems to which Abaqus will be ap

10、plied are history-dependent, so the solution must be developed by a series of “small” increments. Two issues arise: how the discrete equilibrium statement Equation 2.2.11 is to be solved at each increment, and how the increment size is chosen.Abaqus/Standard generally uses Newtons method as a numeri

11、cal technique for solving the nonlinear equilibrium equations. The motivation for this choice is primarily the convergence rate obtained by using Newtons method compared to the convergence rates exhibited by alternate methods (usually modified Newton or quasi-Newton methods) for the types of nonline

12、ar problems most often studied with Abaqus. The basic formalism of Newtons method is as follows. Assume that, after an iteration i, an approximation , to the solution has been obtained. Let be the difference between this solution and the exact solution to the discrete equilibrium equation Equation 2

13、.2.11. This means that Expanding the left-hand side of this equation in a Taylor series about the approximate solution then gives If is a close approximation to the solution, the magnitude of each will be small, and so all but the first two terms above can be neglected giving a linear system of equa

14、tions: where is the Jacobian matrix and The next approximation to the solution is then and the iteration continues. Convergence of Newtons method is best measured by ensuring that all entries in and all entries in are sufficiently small. Both these criteria are checked by default in an Abaqus/Standa

15、rd solution. Abaqus/Standard also prints peak values in the force residuals, incremental displacements, and corrections to the incremental displacements at each iteration so that the user can check for these contingencies himself.Newtons method is usually avoided in large finite element codes, appar

16、ently for two reasons. First, the complete Jacobian matrix is sometimes difficult to formulate; and for some problems it can be impossible to obtain this matrix in closed form, so it must be calculated numericallyan expensive (and not always reliable) process. Secondly, the method is expensive per i

17、teration, because the Jacobian must be formed and solved at each iteration. The most commonly used alternative to Newton is the modified Newton method, in which the Jacobian in Equation 2.2.12 is recalculated only occasionally (or not at all, as in the initial strain method of simple contained plast

18、icity problems). This method is attractive for mildly nonlinear problems involving softening behavior (such as contained plasticity with monotonic straining) but is not suitable for severely nonlinear cases. (In some cases Abaqus/Standard uses an approximate Newton method if it is either not able to

19、 compute the exact Jacobian matrix or if an approximation would result in a quicker total solution time. For example, several of the models in Abaqus/Standard result in a nonsymmetric Jacobian matrix, but the user is allowed to choose a symmetric approximation to the Jacobian on the grounds that the

20、 resulting modified Newton method converges quite well and that the extra cost of solving the full nonsymmetric system does not justify the savings in iteration achieved by the quadratic convergence of the full Newton method. In other cases the user is allowed to drop interfield coupling terms in co

21、upled procedures for similar reasons.)Another alternative is the quasi-Newton method, in which Equation 2.2.12 is symbolically rewritten and the inverse Jacobian is obtained by an iteration process. There are a wide range of quasi-Newton methods. The more appropriate methods for structural applicati

22、ons appear to be reasonably well behaved in all but the most extremely nonlinear casesthe trade-off is that more iterations are required to converge, compared to Newton. While the savings in forming and solving the Jacobian might seem large, the savings might be offset by the additional arithmetic i

23、nvolved in the residual evaluations (that is, in calculating the ), and in the cascading vector transformations associated with the quasi-Newton iterations. Thus, for some practical cases quasi-Newton methods are more economic than full Newton, but in other cases they are more expensive. Abaqus/Stan

24、dard offers the “BFGS” quasi-Newton method: it is described in “Quasi-Newton solution technique,” Section 2.2.2.When any iterative algorithm is applied to a history-dependent problem, the intermediate, nonconverged solutions obtained during the iteration process are usually not on the actual solutio

25、n path; thus, the integration of history-dependent variables must be performed completely over the increment at each iteration and not obtained as the sum of integrations associated with each Newton iteration, . In Abaqus/Standard this is done by assuming that the basic nodal variables, , vary linea

26、rly over the increment, so that where represents “time” during the increment. Then, for any history-dependent variable, , we compute at each iteration. The issue of choosing suitable time steps is a difficult problem to resolve. First of all, the considerations are quite different in static, dynamic

27、, or diffusion cases. It is always necessary to model the response as a function of time to some acceptable level of accuracy. In the case of dynamic or diffusion problems time is a physical dimension for the problem and the time stepping scheme must provide suitable steps to allow accurate modeling

28、 in this dimension. Even if the problem is linear, this accuracy requirement imposes restrictions on the choice of time step. In contrast, most static problems have no imposed time scale, and the only criterion involved in time step choice is accuracy in modeling nonlinear effects. In dynamic and di

29、ffusion problems it is exceptional to encounter discontinuities in the time history, because inertia or viscous effects provide smoothing in the solution. (One of the exceptions is impact. The technique used in Abaqus/Standard for this is discussed in “Intermittent contact/impact,” Section 2.4.2.) H

30、owever, in static cases sharp discontinuities (such as bifurcations caused by buckling) are common. Softening systems, or unconstrained systems, require special consideration in static cases but are handled naturally in dynamic or diffusion cases. Thus, the considerations upon which time step choice is made are quite different for the three different problem classes.Abaqus provides both “automatic” time step choice and direct user control for all classes of problems. Direct user control can be useful in