1.2.4 Elastic-plastic K-frame structure
Product: ABAQUS/Standard杭州早餐>难过的句子
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This example illustrates the u of the frame element FRAME2D. Frame elements (“Frame elements,” Section 15.4.1 of the ABAQUS Analysis Ur's Manual) can be ud to model elastic, elastic-plastic, and buckling strut respons of individual members of frame-like structures. The elastic respon is defined by Euler-Bernoulli beam theory. The respon of elastic-plastic is modeled with nonlinear kinematic hardening plasticity concentrated at element's ends, simulating the development of plastic hinges. The buckling strut respon is a simplified and phenomenological reprentation of the highly nonlinear cross-ction collap and material yielding that takes place when slender members are loaded in compression.
Therefore, frame elements can be elastic, elastic-plastic, behave as struts (with or without buckling), or switch during the analysis to strut behavior followed by postbuckling behavior.
Both the elastic-plastic and buckling strut respons are simplifications of highly nonlinear respons. They are designed to approximate the complex respons with a single finite element reprenting a structural member between connections. For parts of the model where higher solution resolution is re
quired, such as stress prediction, the model should be refined with beam elements.
The geometry in this example is a typical K-frame construction ud in applications 1.2.4 弹—塑性K型框架结构
Product: ABAQUS/Standard
这个例题阐述了如何使用平面框架单元。框架单元(“Frame elements,” Section 15.4.1 of the ABAQUS Analysis Ur's Manual)可以用于模拟框架结
构的弹性，弹塑性，和个别杆件的压杆屈曲响应。弹性响应由欧拉-伯努力梁理论定义。弹塑性响应由集中于单元端部的非线性运动硬化塑性来模拟塑性铰的发展。压杆屈曲响应是当细长杆件受压时，高度非线性横截面破坏和材料屈服的简化的现象化的表达。
因此，框架单元可以是弹性的，弹塑性的，具备压杆性质的（屈曲和非屈曲），或者可以在分析过程中随着屈曲后性质而转化为压杆性质。
弹塑性响应和压杆屈曲相应都是高度非线性的简化响应。它们用一个有限单元来代表节点间的杆件，以大概估算出这些复杂的响应。对于模型中需要高阶解的部分，比如预应力，模型需要由梁单元来（细化）！
这个例题的几何特征是K型框
such as offshore structures (e Figure 1.2.4–1).
土石方爆破
A push-over analysis is performed to determine the maximum horizontal load that the structure can support before collap results from the development of plastic hinges or buckling failure. During a push-over test, many structural members are loaded in compression. Slender members loaded in compression often fail due to geometric buckling, cross-ction collap, and/or material yielding. The buckling strut respon, which models such compressive behavior, is added in parate simulations to investigate the effect of the compressive failure of critical members in the structure. A dead load is applied to the top of the structure reprenting the weight supported by the K-frame. Push-over analys are either load or displacement control tests.
Geometry and model
The structure consists of 19 members between structural connections. Each finite element models a member of the frame. Hence, 19 frame elements are ud: 17 elements with PIPE cross-ctions of varying properties and 2 elements (the top platform) with I cross-ctions. The plastic respon of the elements is calculated from the yield stress of the material, using the plastic default values provid
ed by ABAQUS. (The default values for the plastic respon are bad on experiments with slender steel members. For details on the default values, e “Frame ction behavior,” Section 15.4.2 of the ABAQUS Analysis Ur's Manual.) The default plastic respon includes mild hardening for axial forces and strong hardening for bending moments. The default hardening respons for a typical element in the model are shown in Figure 1.2.4–2 and Figure 1.2.4–3. 架结构，经常被应用于近海结构中。(参看 图 1.2.4–1)
对结构进行Push-over分析，来得出结构在塑性铰的发展和屈曲失效之前所能承受的最大水平向的荷载。在pusho-over 过程中，很多结构杆件都受压。受压的细长杆件经常由于几何屈曲、横截面坍塌或材料屈服而失效。模拟了这种受压性质的压杆屈曲相应，被单独添加到模拟过程中以估算那些结构中临界杆件的受压屈服影响。
几何模型
结构包含19个杆件。每个有限单元都模拟了一根框架杆件。因此，共使用了19个单元：17个单元是圆管型横截面，2个单元（顶部平台）使用工字型横截面。单元的塑性响应由材料的屈服应力来计算，使用默认的ABAQUS提供的默认塑性值。（塑性响应的默认值是基于对细长钢杆件的试验的，关于默认值的细节，请参看“Frame ction behavior,” Section 15.4.2 of the ABAQUS Analysis Ur's Manua
优秀满分作文l.)默认塑性响应包括轴向力的柔和硬结和弯局的强烈硬结。模型里的一个典型单元默认硬结响应可参看图 1.2.4–2和 图
A dead load of 444.8 kN (100,000 lb) is applied to the top of the K-frame, reprenting the part of the structure above the K-frame. Subquently, the top platform is loaded or displaced horizontally. The load level or applied displacement is chon to be large enough so that the entire structure fails by the formation of plastic hinges and, conquently, los load carrying capacity.
Three different models are investigated. A limit load is expected, since the goal of the analysis is to determine when the structure los overall stiffness. Large-and small-displacement analys are performed for all three models for comparison. Large-displacement analys using frame elements are valid for large overall rotations but small strains, since frame elements assume that the strains are small. In the first model all elements u elastic-plastic material respon. In the cond model buckling is checked for all elements with PIPE cross-ctions. The ISO equation is ud as a criteria for buckling, and the default Marshall strut envelope is followed for the postbuckling behavior.The buckling strut envelope is calculated from the yield stress of the material and the default Marshall Strut theory. (For details on the default buckling strut envelope, e “Frame ction behavior,” Section 15.4.2 of the ABAQUS Analysis Ur's Manual.) All frame members that u the BUCKLING
parameter on the *FRAME SECTION option check the ISO criteria for the switching-to-strut algorithm.In the third model the member that switches to strut behavior in the cond model (element 7) is replaced by a frame element with buckling strut respon from the beginning of the analysis. To proceed beyond the unstable pha of the respon, the Riks static solution procedure is ud in the elastic-plastic problems. To decrea the number of solution 1.2.4–3.
444.8 kN的恒荷载加在K型框架的顶点处，代表K型框架之上的结构（作用在其上的荷载）。然后对顶端的平台施加荷载或横向位移。所施加的荷载大小或位移要足够大，使之能够让整个结构由于塑性铰的形成而失效，同时丧失承载能力。
本例题采用了三种不同的模型。我们期望得到一个极限荷载，因为进行分析的目的是断定在什么样的情况下结构会丧失整体刚度。对三个模型进行大位移和小位移分析以进行对比。使用框架单元进行大位移分析适用于整体转动大而应变小的情况，因为框架单元假定应变是小的。在第一个模型中，所有的单元都采用弹塑性材料响应。在第二个模型中，检查所有具有圆管截面的单元的屈曲情况。ISO方程用来决定屈曲的界限，默认的马歇尔压杆包络线被用来决定后屈曲性质。压杆屈曲包络线是通过材料的屈服应力和默认的马歇尔压杆理论来计算的。（关于默认屈曲包络线的详情，请察看以下章节“Frame ction behavior,” Section 15.4.2 of the ABAQUS Analysis Ur's Manual.)在框架截面中所有使用“屈曲”参数的框架杆件均检查了ISO关于转化为压杆算
法的标准。第三个模型中，那些在第二模型中变为压杆性质的杆件均在分析初始时被替换为被赋予屈曲性质的框架单元。为了顺利地进行不稳定阶段的反应，弧长静力解决方法
iterations, the *CONTROLS option is ud in the elastic-plastic problem with large displacement, with the value of the ratio of the largest solution correction to the largest incremental solution t to 1.0, since displacement increments are very small after plasticity occurs.
圣诞传说Results and discussion
The structure is loaded or displaced to the point at which all load carrying capacity is lost.In the first model with elastic-plastic frame elements, the results for the linear and nonlinear geometries compare as expected. That is, the limit load for the large-displacement analysis is reached at a load of 1141 kN (256,000 lb) as compared to a higher load of 1290 kN (291,000 lb)in the small-displacement analysis. The plastic hinge pattern is the same in both cas.
The cond model us the switching algorithm. It shows that element 7 first violates the ISO equation (buckles) at a prescribed displacement equal to 1.32 cm (0.52 in), before any elements form plastic hinges. The critical compressive force in this element is –318 kN (–71,400 lb). Next, plasticity develops at veral elements, and the structure reaches its limit capacity. The frame eleme
nts with the switching algorithm predict the structural behavior in the most accurate way, since the possibility of buckling is checked for all elements in the model, and highly compresd members switch automatically to postbuckling behavior (e the plastic and buckled frame elements in Figure 1.2.4–4). When the structure can no longer support horizontal loading, the patterns of plastic hinges for linear and nonlinear geometry are the same. The results differ more for loads clo to the limit load.被应用于弹塑性问题。为了减少解的数量的反复，*CONTROLS选项被用在大位移的弹塑性问题中，此选项设定了最大修正解与最大增量步解之间的比例值为1.0，因为当塑性发生时，位移增量是非常小的。
结果与讨论
结构被施加荷载或替换到那些已经丧失承载能力的点。在第一个具有弹塑性单元的模型中，线性和非线性的几何对比与预想相同。这也就是说，大位移分析的极限荷载已经达到1141 kN，而在同样的小位移分析中的极限荷载是1290 kN 。两种情况中塑性铰的形式都是一样的。
第二个模型使用了转换算法。这种算法显示第七单元是第一个违反ISO方程（即屈曲）的，在其他杆件塑性铰之前就达到了预计的1.32 cm。此单元的临界压力是–318 kN。其次，几个单元出现了塑性，并且结构达到了它的极限承载能力。采用转换算法的框架单元十分精确地预言了结构性质，因为模型
中所有的单元屈曲的可能性都被检查过了，而且高度受压的杆件自动转化并具有屈曲后性质(参看塑性和屈曲框架单
元图 1.2.4–4)。当结构不能再承受水平荷载时，对于线性和非线性几何来讲塑性铰的形式都是一样的。荷载越接近极限值，结果越不一样。
To investigate the effect of buckling, the first and the third (element 7 defined with buckling strut respon from the beginning) models are compared (kframe_loadcntrl_nlgeom.inp and kframe_dispcntrl_buckle_nlgeom.inp). Load versus horizontal deflection curves for the large-displacement analys are shown in Figure 1.2.4–5. Similar to the model with switching algorithm, first element 7 buckles. As the other members deform and absorb the load no longer carried by the buckled member, the structure regains stiffness and plasticity develops in other members. When ven members develop plastic hinges, the structure can no longer support additional horizontal loading. The limit load in the third model is only about 28% of the limit load in the model without buckling. The load-displacement curves for the switching algorithm and for the example with element 7 using buckling strut respon compare well and are not shown.
Input files
kframe_loadcntrl_nlgeom.inp
Elastic-plastic analysis with load control; large-displacement analysis.
屈原是哪里人
kframe_loadcntrl.inp
Elastic-plastic analysis with load control; small-displacement analysis.
kframe_dispcntrl_switch_nlgeom.inp
Elastic-plastic frame element with the switching algorithm and displacement control; large-displacement analysis.
kframe_dispcntrl_switch.inp
Elastic-plastic frame element with the 为了研究屈曲的影响，我们将第一模型和第三模型（第七单元被定义为从初始就具备压杆屈曲响应的性质）进行了对比（kframe_loadcntrl_nlgeom. inp和
kframe_dispcntrl_buckle_nl geom.inp)。大位移分析的荷载-水平位移曲线见图1.2.4–5。对于具备转换算法的模型也是一样的，第七单元屈曲。随着其余杆件的变形并吸收那些不再被屈曲杆件所承受的荷
载，结构重新获得刚度，并且塑性向其他杆件发展。当七个杆件出现塑性铰时，结构不能再承受附加的水平荷载。第三模型的荷载仅为不具备屈曲性质的模型的28%。转换算法的荷载-位移曲线，及对第七单元采用压杆屈曲相应的曲线吻合得非常好，这里不再显示。
Input 文件
kframe_loadcntrl_nlgeom.inp
具备位移控制的弹塑性分析；大位移分析。诵读红色经典
kframe_loadcntrl.inp
具备位移控制的弹塑性分析；小位移分析。
kframe_dispcntrl_switch_nlgeom .inp
采用转换算法和位移控制的弹塑性框架单元；大位移分析。
kframe_dispcntrl_switch.inp
