2022年2022年框架单元翻译-- .pdf

15.4.1 Frame elements Product: ABAQUS/Standard References?“ Beam modeling: overview,” Section 15.3.1?“ Frame section behavior,” Section 15.4.2?“ Frame element library,” Section 15.4.3?*FRAME SECTIONOverview Frame elements: ?are 2-node, initially straight, slender beam elements intended for use in the elastic or elastic-plastic analysis of frame-like structures; ?are available in two or three dimensions; ?have elastic response that follows Euler-Bernoulli beam theory with fourth-order interpolation for the transverse displacements; ?have plastic response that is concentrated at the element ends (plastic hinges) and is modeled with a lumped plasticity model that includes nonlinear kinematic hardening; ?are implemented for small or large displacements (large rotations with small strains); ?output forces and moments at the element ends and midpoint; ?output elastic axial strain and curvatures at the element ends and midpoint and plastic displacements and rotations at the element ends only; 15.4.1 框架单元 Product: ABAQUS/Standard References?梁模型概述 15.3.1?框架截面性质 15.4.2?框架单元列表 15.4.3?框架截面Overview 框架单元: ?2 节点 , 初始是直的 , 用于框架结构的弹性和弹塑性分析的细长的梁单元 ?可以用于平面分析和空间分析 ?根据欧拉伯努力梁理论具有弹性响应， 并在横截面上具有四次插值。 ?在单元的端部具有塑性响应，并且集中塑性模型考虑非线形动力硬化。 ?实现小或大位移 （大旋转小应变） ?可以输出单元端部和中点的力和弯矩 ?输出弹性轴向应变、单元端部和中点处的曲率及单元端部的塑性位移和转角。 1名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页，共 9 页 - - - - - - - - - ?admit, optionally, a uniaxial “buckling strut ” response where the axial response of the element is governed by a damaged elasticity model in compression and an isotropic hardening plasticity model in tension and where all transverse forces and moments are zero; ?can switch to buckling strut response during the analysis (for pipe sections only); and ?can be used in static, implicit dynamic, and eigenfrequency extraction analyses only. Typical applications Frame elements are designed to be used for small-strain elastic or elastic-plastic analysis of frame-like structures composed of slender, initially straight beams. Typically, a single frame element will represent the entire structural member connecting two joints. A frame elements elastic response is governed by Euler-Bernoulli beam theory with fourth-order interpolations for the transverse displacement field; hence, the elements kinematics include the exact (Euler-Bernoulli) solution to concentrated end forces and moments and constant distributed loads. The elements can be used to solve a wide variety of civil engineering design applications, such as truss structures, bridges, internal frame structures of buildings, off-shore platforms, and jackets, etc. A frame elements plastic response is modeled with a lumped plasticity model at the element ends that simulates the formation of plastic hinges. The lumped plasticity model includes nonlinear kinematic hardening. The elements can, thus, be used for collapse load prediction based on the formation of plastic hinges.Slender, frame-like members loaded in compression often buckle in such a way that only axial force is supported by the member; all other forces and moments are negligibly small. Frame elements offer optional ?承认在单元的轴向响应被一个受压的破坏的弹性模型和等方行塑性硬化模型，和横截面力与弯矩均为零的情况下，产生单轴向的 “压杆屈曲” 响应 ?仅仅对于圆管截面的情况下，可以在分析过程中转化为压杆屈曲反映。 ?只可被用于静力分析，隐式动力分析和频率提取分析 典型应用框架单元被用于由细长的，直梁组成的框架结构的小弹性应变或者弹塑性分析。典型地，一个单独的框架单元将代表连接两个节点的整个结构杆件。框架单元的弹性响应由欧拉伯努力梁理论及在横截面处的位移场的四次插值控制。因此单元的动力学有集中于端部的力和力矩及均布荷载的精确界。框架单元可以用于解决很多土木工程领域的设计问题，比如桁架结构，桥，内部框架结构的建筑物，塔等。框架单元的塑性响应是模仿单元端部的集中塑性，即模拟形成塑性铰。塑性集中的模型包括非线形动力硬化。 这样，框架单元就可以基于塑性铰形成来预计结构的破坏荷载。细长的类似框架的杆件经常只由于受轴向压力而屈曲。其他的力和弯矩可以被认为很小。框架单2名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 9 页 - - - - - - - - - buckling strut response whereby the element only carries axial force, which is calculated based on a damaged elasticity model in compression and an isotropic hardening plasticity model in tension. This model provides a simple phenomenological approximation to the highly nonlinear geometric and material response that takes place during buckling and postbuckling deformation of slender members loaded in compression.For pipe sections only, frame elements allow switching to optional uniaxial buckling strut response during the analysis. The criterion for switching is the “ISO” equation together with the “strength ” equation (see “ Buckling strut response for frame elements,” Section 3.9.3 of the ABAQUS Theory Manual). When the ISO and strength equations are satisfied, the elastic or elastic-plastic frame element undergoes a one-time-only switch in behavior to buckling strut response. Element cross-sectional axis systemThe orientation of the frame elements cross-section is defined in ABAQUS/Standard in terms of a local, right-handed (, , ) axis system, where is the tangent to the axis of the element, positive in the direction from the first to the second node of the element, and and are basis vectors that define the local 1- and 2-directions of the cross-section. is referred to as the first axis direction, and is referred to as the normal to the element. Since these elements are initially straight and assume small strains, the cross-section directions are constant along each element and possibly discontinuous between elements. Defining the n1-direction at the nodes For frame elements in a plane the -direction is always (0.0, 0.0, 1.0); that is, normal to the plane in which the motion occurs. Therefore, planar frame elements can 元可在杆件只受轴力的情况下提供屈曲压杆响应，这是基于在受压时的弹性模式和拉时的等方塑性硬化模式破坏。这一模式可以提供一个接近于高度几何与材料非线形响应的现象。这些都发生在受压细长杆件的屈曲和屈曲后变形时。 仅当截面为圆管状时，框架单元允许在分析过程中转化为单轴向受压屈曲响应。变化的标准是ISO 方程与强度方程（ 参看“框架单元的受压屈曲响应”，第 3.9.3章 ABAQUS理论手册 ）当 ISO 和强度方程被满足时，弹性和弹塑性框架单元将经历仅为一次的受压屈曲响应的转变。 单元横截面的轴向系统 框架单元的横截面的方向可以由ABAQUS/ STANDARD 里的局部的，右手系（, , ）来决定，这里t 是单元的轴切线方向，以从第一节点到第二节点的方向为正。 N1 和 N2是决定横截面的局部的1-和 2-方向。 N1是第一轴向， N2 是单元的法向。由于这些单元初始都是直的，并且假设小应变，横截面的方向是沿着每个单元是恒定的， 在单元间是可以不连续的。用节点来决定 N1方向 对于平面的框架单元n1的方向总是（0，0，-1），即垂直于平面。因此，平面框架单元只能沿3名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页，共 9 页 - - - - - - - - - bend only about the first axis direction. For frame elements in space the approximate direction of must be defined directly as part of the element section definition or by specifying an additional node off the elements axis. This additional node is included in the elements connectivity list (see “ Element definition,” Section 2.2.1). ?If an additional node is specified, the approximate direction of is defined by the vector extending from the first node of the element to the additional node. ?If both input methods are used, the direction calculated by using the additional node will take precedence. ?If the approximate direction is not defined by either of the above methods, the default value is (0.0, 0.0, 1.0). The -direction is then the normal to the elements axis that lies in the plane defined by the elements axis and this approximate -direction. The -direction is defined as . Large-displacement assumptions The frame elements formulation includes the effect of large rigid body motions (displacements and rotations) when geometrically nonlinear analysis is selected (see “ General and linear perturbation procedures,” Section 6.1.2). Strains in these elements are assumed to remain small. Material response (section properties) of frame elements 一轴弯曲。 对于空间的框架单元， n1 的方向应该作为单元截面定义的一部分而直接定义，或者由单元轴线外的一附加节点来定义。而这个附加节点必须属于单元连通的名单。(see “ Element definition,” Section 2.2.1). ?如果附加节点被选定，那么 n1 的大致方向就被确定下来（通过单元的第一节点到附加节点的向量） ?如果两种 inp 方法都被使用，那么使用附加节点的方法确定的方向会被优先考虑。 ?如果大致方向没有被上述任何方法确定，那么默认的方向就是（0，0，-1）.方向垂直于单元的轴向，而单元的轴向属于被单元轴向和n1所确定的平面。 N2方向被定义为. 大位移假设 当几何非线形分析被选择时，框架单元的公式包含大的刚体移动（位移和转角）的影响(see “ General and linear perturbation procedures,” Section 6.1.2). 这些单元的应变会被假设一直保持很小。 框架单元的材料响应（截面4名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 9 页 - - - - - - - - - For frame elements the geometric and material properties are specified together as part of the frame section definition. No separate material definition is required. You can choose one of the section shapes that is valid for frame elements from the beam cross-section library (see “ Beam cross-section library,” Section 15.3.9 ). The valid section shapes depend upon whether elastic or elastic-plastic material response is specified or whether buckling strut response is included. See “ Frame section behavior,” Section 15.4.2 , for a complete discussion of specifying the geometric and material section properties.Input File Usage: *FRAME SECTION, SECTION=section_typeMechanical response and mass formulation The mechanical response of a frame element includes elastic and plastic behavior. Optionally, uniaxial buckling strut response is available. Elastic response The elastic response of a frame element is governed by Euler-Bernoulli beam theory. The displacement interpolations for the deflections transverse to the frame elements axis (the local 1- and 2-directions in three dimensions; the local 2-direction in two dimensions) are fourth-order polynomials, allowing quadratic variation of the curvature along the elements axis. Thus, each single frame element exactly models the static, elastic solution to force and moment loading at its ends and constant distributed loading along its axis (such as 性质） 对于框架单元来说，几何和材料的性质将一起作为框架截面的部分被定义。不需要单独定义材料。你可以从梁的横截面列表中选择一种可以被框架单元使用的截面。(see “ Beam cross-section library,” Section 15.3.9). 可用的截面形状取决于材料的弹性和弹塑性响应是否被指定，或者压杆屈曲响应是否被包含。 See “ Frame section behavior,” Section 15.4.2, 这里包含完整的关于框架单元截面的几何和材料的定义。 力学响应和质量公式 框架单元的力学响应包括弹性和塑性性质。可选择地，单轴向的屈曲响应也可以被考虑。 弹性响应 框架单元的弹性响应由欧拉-伯努力梁的理论来确定。框架单元的横向位移插值 （三维的局部 1-和 2-方向或二维的 2-方向）是四次多项式，允许沿单元轴向的曲率有二次的变化。这样，每个框架单元都可以得到静定的，弹性的关于作用在端部的力和位移的5名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 9 页 - - - - - - - - - gravity loading). The displacement interpolation along an elements axis is a second-order polynomial, allowing linear variation of the axial strain. In three dimensions the twist rotation interpolation along an elements axis is linear, allowing constant twist strain. The elastic stiffness matrix is integrated numericallyand used to calculate 15 nodal forces and moments in three dimensions: an axial force, two shear forces, two bending moments, and a twist moment at each end node, and an axial force and two shear forces at the midpoint node. In two dimensions 8 nodal forces and moments exist: an axial force, a shear force, and a moment at each end, and an axial force and a shear force at the midpoint. The forces and moments are illustrated in Figure 15.4.1 1 . Figure 15.4.1 1 Forces and moments on a frame element in space. Elastic-plastic response The plastic response of the element is treated with a “lumped” plasticity model such that plastic deformations can develop only at the elements ends through plastic rotations (hinges) and plastic axial displacement. The growth of the plastic zone through the elements cross-section from initial yield to a fully yielded plastic hinge is modeled with nonlinear kinematic hardening. It is assumed that the 解，及恒定的均布在它轴向上的力（比如重力）。沿单元轴向的位移插值是二次多项式，允许轴向的线形应变。在三维模型中，沿单元轴向的扭转插值允许为恒定的扭转应变。弹性刚度矩阵在三维的情况下可以计算15个力和位移：每个端点的一个轴力，两个剪力， 两个弯矩，一个扭矩，及中点处的轴力和两个弯矩。在二维的计算中，8 个节点力和弯矩存在：两端的一个轴力，一个剪力，一个弯矩，和中点处的轴力和一个剪力。力和弯矩参见图片 15.4.1-4 Figure 15.4.1 1 空间框架单元的力和位移 弹塑性响应 单元的塑性响应被处理为集中的塑性形式，即塑性变形只能在单元的端部发展，只有塑性转动和塑性轴向位移。塑性区域由截面的起始屈服位置发展为整个屈服的塑性铰，这是由非线形动力硬化来模拟的。假设端部的塑性变形只受到端部节点上的力和弯矩的影响。 6名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 6 页，共 9 页 - - - - - - - - - plastic deformation at an end node is influenced by the moments and axial force at that node only. Hence, the yield function at each node, also called the plastic interaction surface, is assumed to be a function of that nodes axial force and three moment components only. No length is associated with the plastic hinge. In reality, the plastic hinge will have a finite size determined by the elements length and the specific loading that causes yielding; the hinge size will influence the hardening rate but not the ultimate load. Hence, if the rate of hardening and, thus, the plastic deformation for a given load are important, the lumped plasticity model should be calibrated with the elements length and the loading situation taken into account. For details on the elastic-plastic element formulation, see “ Frame elements with lumped plasticity,” Section 3.9.2 of the ABAQUS Theory Manual . Uniaxial linear elastic and buckling strut response with tensile yield You can obtain a frame elements response to uniaxial force only, based on linear elasticity, buckling strut response, and tensile yield. In that case all transverse forces and moments in the element are zero. For linear elastic response the element behaves like an axial spring with constant stiffness. For buckling strut response if the tensile axial force in the element does not exceed the yield force, the axial force in the element is constrained to remain inside a buckling envelope. See “ Frame section behavior,” Section 15.4.2 , for a description of this envelope. Inside the envelope the force is related to strain by a damaged elastic modulus. The cyclic, hysteretic response of this model is phenomenological and approximates the response of thin-walled, pipe-like members. When the element is loaded in tension beyond the yield force, the force response is governed by isotropic hardening 因此，每个节点处的屈服行为，又叫塑性交互面，被假设为节点轴力和三个弯矩造成的。塑性铰与长度无关。事实上，塑性铰应该有一个由单元长度和造成屈服的荷载确定。铰的大小会影响硬化率，而不是极限荷载。因此，如果硬化率，即基于给定荷载造成的塑性变形是重要的，那么集中的塑性行为就要将单元长度和荷载情况考虑进去。 对于单元弹塑性方程的细节，参看 “ Frame elements with lumped plasticity,” Section 3.9.2 of the ABAQUS Theory Manual. 拉伸屈服下的单轴向线弹性及屈曲响应 基于线弹性、压杆屈曲响应及受拉屈服，你只能得到单元对轴向力的反应。在这种情况下单元的所有的横向力和弯矩均为零。由于线弹性响应，单元就像一个有着恒定刚度的弹簧。 如果单元内的轴向拉力没有超过屈服力，那么由于压杆屈曲响应，单元的轴向力将低于屈曲包络线。参看“ Frame section behavior,” Section 15.4.2, 关于这个包络线的描述。在这个包络线里，力与通过弹性破坏系数衡量的应变有关。这个模式的循环的、三维响应在现象上是类似于薄壁圆管状的杆件。当单元的拉力超过了屈服荷载，力的响应取决于各向同性的塑性硬化。而压力响应则取决于屈曲包络线，这个包络线是由与塑性轴向应变等量的沿着7名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 7 页，共 9 页 - - - - - - - - - plasticity. In reverse loading the response is governed by the buckling envelope translated along the strain axis by an amount equal to the axial plastic strain. For details of the buckling strut formulation, see “ Buckling strut response for frame elements,” Section 3.9.3 of the ABAQUS Theory Manual . Mass formulation The frame element uses a lumped mass formulation for both dynamic analysis and gravity loading. The mass matrix for the translational degrees of freedom is derived from a quadratic interpolation of the axial and transverse displacement components. The rotary inertia for the element is isotropic and concentrated at the two ends. For buckling strut response a lumped mass scheme is used, where the elements mass is concentrated at the two ends; no rotary inertia is included. Using frame elements in contact problems When contact conditions play a role ina structures behavior, frame elements have to be used with