BEAM4单元中文说明

Release 10.0 Documentation for ANSYS

BEAM4

3-D Elastic Beam

三维弹性梁

BEAM4 Element Description BEAM4单元描述

BEAM4 is a uniaxial element with tension, compression, torsion, and bending

capabilities. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. Stress

stiffening and large deflection capabilities are included. A consistent tangent stiffness matrix option is available for use in large deflection (finite rotation) analyses. See BEAM4 in the ANSYS, Inc. Theory Reference for more details about this element. A tapered unsymmetrical elastic beam is described in BEAM44 and a 3-D plastic beam in BEAM24.

Beam4是一种可用于承受拉、压、弯、扭的单轴受力单元。这种单元在每个节点上有六个自由度：x、y、z三个方向的线位移和绕x、y、z三个轴的角位移。可用于计算应力刚化及大变形的问题。通过一个相容切线刚度矩阵的选项用来考虑大变形（有限旋转）的分析。关于本单元更详细的介绍请参阅《ansys理论手册》,关于渐变的非对称弹性梁的问题应按beam44单元考虑，三维塑性梁应按beam24单元考虑。

Figure 4.1 BEAM4 Geometry

BEAM4 Input Data BEAM4 输入数据

The geometry, node locations, and coordinate systems for this element are shown in Figure 4.1: \. The element is defined by two or three nodes, the cross-sectional area, two area moments of inertia (IZZ and IYY), two thicknesses (TKY and TKZ), an angle of orientation (θ) about the element x-axis, the torsional moment of inertia (IXX), and the material properties. If IXX is not specified or is equal to 0.0, it is assumed equal to the polar moment of inertia (IYY + IZZ). IXX should be positive and is usually less than the polar moment of inertia. The element torsional stiffness decreases with decreasing values of IXX. An added mass per unit length may be input with the ADDMAS value.

关于本单元的几何模型，节点坐标及坐标系详见上图。本单元的定义通常是以下这些输入参数确定的：二或三个节点变量，横截面积变量，两个轴惯性矩（IZZ和IYY）变量，两个厚度变量（TKZ，TKY），绕单元座标系下X轴的转角变量（θ），绕X轴（单元座标系下）扭转惯性矩（IXX）及材料属性。如果IXX没有给定或输入值为0，那系统默认为其等于极惯性矩（IZZ＋IYY）。IXX应当主动给定且一般其小于极惯性矩。单元的扭转刚度随着IXX的减小而减小。参数ADDMAS要输入的值是每单位长度的附加质量。

The element x-axis is oriented from node I toward node J. For the two-node option, the default (θ = 0°) orientation of the element y-axis is automatically calculated to be parallel to the global X-Y plane. Several orientations are shown in Figure 4.1: \. For the case where the element is parallel to the global Z axis (or within a 0.01 percent slope of it), the element y axis is oriented parallel to the global Y axis (as shown). For user control of the element orientation about the

element x-axis, use the θ angle (THETA) or the third node option. If both are defined, the third node option takes precedence. The third node (K), if used, defines a plane (with I and J) containing the element x and z axes (as shown). If this element is used in a large deflection analysis, it should be noted that the location of the third node (K), or the angle (THETA), is used only to initially orient the element. (For information about orientation nodes and beam meshing, see Meshing Your Solid Model in the ANSYS Modeling and Meshing Guide.)

单元的X轴的方向是指从I节点到J节点。如果只给了两个节点参数，那单元Y轴的方向自动确定为平行于系统坐标系下的X－Y平面。有关示例见上图。当单元坐标的X轴平行于整体坐标系下的Z轴（包括0.01%的偏差在内），单元Y轴的方向是平行于总体坐标系下的Y轴。用户可以通过给定θ角或定义第三个节点的方法来控制单元的方向。如果前面的两个参数同时给定时，则以给定第三点的控制为准。第三点一经给出就意味着定义了一个由I，J，K三点定义的平面且该平面包含了单元坐标的X与Z轴。当本单元用于大变形分析时，那么给定的第三节点（K）或旋转角（θ）仅用来确定单元的初始状态。（有关方向节点及单元划分的详细信息参见《Meshing Your Solid Model》及《ANSYS Modeling and Meshing Guide》。）

The initial strain in the element (ISTRN) is given by Δ/L, where Δ is the difference between the element length, L, (as defined by the I and J node locations) and the zero strain length. The shear deflection constants (SHEARZ and SHEARY) are used only if shear deflection is to be included. A zero value of SHEAR_ may be used to neglect shear deflection in a particular direction. See Shear Deflection for details.

关于单元的初始应变（ISTRN）通过Δ/L给定，这里的Δ不是单元长度L（由节点I和J的坐标所决定）与零应变时的长度。剪切变形常数（SHARZ和SHEARY）只有当考虑剪切变形时才设定，该值为零时即表示忽略了剪切变形。Shear Deflection中介绍了细则。

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses [NLGEOM,ON]. You can often obtain more rapid convergence in a geometrically nonlinear analysis, such as a nonlinear buckling or postbuckling analysis, by activating this option. However, you should not use this option if you are using the element to simulate a rigid link or a group of coupled nodes. The resulting abrupt changes in stiffness within the structure make the consistent tangent stiffness matrix unsuitable for such applications.

KEYOPT（2）用来控制在大变形分析时是否激活（用命令，[NLGEOM,ON]）相容切线刚度矩阵（也就是，由主切线刚度矩阵加上相容应力矩阵所组成的矩阵）。打开这项设置则在几何非线性分析时将获得快速收敛，例如在非线性屈曲分析时就可打开该项。但在分析刚性连结或耦合结点时不能激活该项。在刚度急剧变化的结构分析中也不应打开该项。

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamic analyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in the positive element x direction). The element must be symmetric with this option (e.g., IYY = IZZ and SHEARY = SHEARZ).

KEYOPT（7）用来控制是否进行不对称回转阻尼矩阵的计算（常用于转子动态分析），所须转动频率在实常数SPIN中输入（单位为：弧度/时间，正方向为单元X轴正向），且单元本身必须是对称的（如，IYY＝IZZ，SHEARY＝SHEARZ）。

Element loads are described in Node and Element Loads. Pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure 4.1: \. Positive normal pressures act into the element. Lateral pressures are input as a force per unit length. End \KEYOPT(10) allows tapered lateral pressures to be offset from the nodes.

Temperatures may be input as element body loads at the eight \

shown in Figure 4.1: \. The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. If only T1 and T4 are input, T2 defaults to T1 and T3 defaults to T4. In both cases, T5 through T8 default to T1 through T4. For any other input pattern, unspecified temperatures default to TUNIF.

“Node and Element Loads”一节对单元荷载有专门介绍。可以在本单元的表面施加面荷载，如图Figure 4.1中带圈数字所示，其中箭头指向为面荷载作用正向。横向均布压力的单位为力每单位长度，端点作用的压力应以集中力的形式输入。KEYOPT（10）用来控制线性变化的横向压力相对单元节点的偏移量。可在单元几何图形的八个角上设定温度值，其被当作体荷载处理。第一个角上的温度T1的默认值为TUNIF，如其它角的温度未给定时其默认值等于第一个角的温度，如给定了T1和T2则T3的默认值为T2，T4的默认值为T1；T5到T8的值默认与T1到T4的值相对应。

KEYOPT(9) is used to request output at intermediate locations. It is based on

equilibrium (free body of a portion of the element) considerations and is not valid if:

KEYOPT（9）用来控制两节点中间部分相关值的输出情况，值是按平衡条件得出的。但在下列情况下这些值不能得到：

? ? ? ? ? ?

stress stiffening is turned on [SSTIF,ON] 考虑应力刚化时［SSTIF，ON］；

more than one component of angular velocity is applied [OMEGA] 一个以上的部件作用有角速度时［OMEGA]；

any angular velocities or accelerations are applied with the CGOMGA, DOMEGA, or DCGOMG commands.

通过命令CGOMGA, DOMEGA, or DCG/MG作用了角速度或加速度时。

BEAM4 Input Summary BEAM4 输入参数汇总

Nodes 节点

I, J, K (K orientation node is optional) （K为方向节点，是可选的） Degrees of Freedom 自由度

UX, UY, UZ, ROTX, ROTY, ROTZ Real Constants 实常数

AREA, IZZ, IYY, TKZ, TKY, THETA

ISTRN, IXX, SHEARZ, SHEARY, SPIN, ADDMAS

See Table 4.1: \ for a description of the real constants.

这些实常数的含义见Table 4.1: \。

Material Properties 材料属性

EX, ALPX (or CTEX or THSX), DENS, GXY, DAMP Surface Loads 表面荷载

Pressures -- 压力

face 1 (I-J) (-Z normal direction) face 2 (I-J) (-Y normal direction) face 3 (I-J) (+X tangential direction) face 4 (I) (+X axial direction) face 5 (J) (-X axial direction)

(use negative value for opposite loading)

（如输入的压力为负值表示与几何模型图中方向反向作用)

Body Loads 体荷载

Temperatures -- 温度

T1, T2, T3, T4, T5, T6, T7, T8 Special Features 特性

Stress stiffening 应力刚化

Large deflection 大变形 Birth and death 单元生死 KEYOPT(2)

Stress stiffening option:应力刚化选项

0 -- （结构分析中只能为0，见最后产品说明）

Use only the main tangent stiffness matrix when NLGEOM is ON. (Stress stiffening effects used in linear buckling or other linear prestressed analyses must be activated separately with PSTRES,ON.)

在“大变形选项”被考虑（即NELGEOM设为ON）时仅用于主切线刚度矩阵部分（应力刚化关效应用于线性屈曲分析或用PSTRES激活（即设为ON）后的线性预应力分析中）。

1 --

Use the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffness matrix plus the consistent stress stiffness matrix) when NLGEOM is ON. (SSTIF,ON will be ignored for this element when KEYOPT(2) = 1 is activated.) Note that if SOLCONTROL is ON and NLGEOM is ON, KEYOPT(2) is automatically set to 1; i.e., the consistent tangent will be used.

在“大变形选项”被考虑（即NELGEOM设为ON）时用于相容切线刚度矩阵（即主切线刚度矩阵与相容应力刚度矩阵的和），且此时用于设定非线性问题中考虑应力刚

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