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1、3-D Curved BeamProblem SpecificationThe problem cons idered here is the curved beam of uniform trapezoidal cross-section in example 6.15 of Cook et al. The beam is bent in its own plane by moments M. The problem is not axisymmetric because displacements have circumferential as well as radial and axi
2、al components. So we use 3D solid elements rather than axisymmetric elements. The geometry can nevertheless be described in cylindrical coordinates. We would like to obtain the stresses for the trapezoidal cross-section AA shown above. Stresses in the curved beam do not vary with , so we can reduce
3、the model and analyze only a typical slice between two closely spaced radial planes as shown below. The angle between AB and CD is taken to be 5 deg. as suggested by Cook el al.The bending moment M must be applied indirectly in the reduced model since we dont know a priori the circumferential stress
4、 distribution it produces on the cross-section. Instead, well prescribe displacements such that radial plane sections remain plane and a pure moment load acts on the model i.e. no net force acts on it. The moment M can be computed from the stress distribution on the cross-section obtained from FEA.
5、Stresses scale linearly with the applied moment. So the stresses associated with a prescribed moment Mp can be obtained by multiplying the computed stresses by the ratio Mp/M. The z-constant plane containing A, B, C and D is a symmetry plane. So only half the cross-section needs to be modeled.Bounda
6、ry ConditionsThe nodal d.o.f. in the radial (u), circumferential (v), and axial (w) directions are constrained as follows:Face 1Face 2u=0 at node Av=0 at all nodesv=0.0001(rc-r)at all nodesw=0 along ABw=0 along CDAll remaining d.o.f. are unrestrained. Setting u=0 at A prevents rigid body motion in t
7、he r-direction. Setting v=0 on face 1 nodes prevents circumferential motion of face 1. Setting w=0 on ABCD imposes symmetry about the middle r- plane. The above BC on face 2 nodes causes face 2 to remain plane as it rotates about a z-parallel axis at r=rc. The factor 0.0001 is arbitrarily chosen. At
8、 the outset, the appropriate value of rc is not known. The right value of rc will give a pure bending load so that the radial reaction RA at node A is zero. Two preliminary FE analysis with guess values of rc=60mm and rc=70mm were done. The respective RA values turn out to be 2001N and 357N. By line
9、ar extrapolation, RA=0 when rc=72.2mm. So well use rc=72.2mm in our analysis. Step 1: Start-up and preliminary set-upCreate a folder Create a folder called cbeam at a convenient location. Well use this folder to store files created during the session.Start ANSYSStart Programs ANSYS Release 7.0 ANSYS
10、 Interactive Enter the location of the folder cbeam that you just created as your Working directory by browsing to it. Enter cbeam as your Initial jobname. So all files generated during this ANSYS session will have cbeam as the prefix. Click on Run.Step 2: Specify element type and constants Specify
11、Element TypeMain Menu Preprocessor Element Type Add/Edit/Delete Add. Pick Structural Solid in the left field and Brick 8-node 45 in the right field. Click OK.Close the Element Types dialog box and also the Element Type menu.Specify Element ConstantsMain Menu Preprocessor Real Constants Add/Edit/Dele
12、te Add. This brings up the Element Type for Real Constants menu with a list of the element types defined in the previous step. We have only one element type and it is automatically selected. Click OK.You should get a note saying Please check and change keyopt setting for element SOLID45 before proce
13、eding. This means that there are no real constants to be specified for this element, as you might recall from the plate tutorial.Close the Real Constants menu.Save your work: Toolbar SAVE_DB Step 3: Specify material properties Main Menu Preprocessor Material Props Material Models In the Define Mater
14、ial Model Behavior menu, double-click on Structural, Linear, Elastic, and Isotropic.Enter 200e9 for Youngs modulus EX, 0.3 for Poissons Ratio PRXY. Click OK. Close the Define Material Model Behavior menu.Save your work: Toolbar SAVE_DB Step 4: Specify geometryWell first create keypoints correspondin
15、g to the eight vertices of the model and then generate a volume from the keypoints. The keypoints will be created in the cylindrical coordinate system. Four of the keypoints are the vertices A,B,C and D shown in the figure of the geometry. The other four keypoints have the same r and as A,B,C and D
16、but are displaced in the z-direction with respect to them.Create Scalar ParametersFor convenience, well create scalar parameters for the geometric dimensions in SI unitsUtility Menu Parameters Scalar ParametersEnter the following parameters, clicking Accept after each. Check the figure of the geomet
17、ry to see what dimension each parameter corresponds to.R1=44e-3R2=R1+88e-3Z1=65e-3Z2=14e-3Click Close.Switch to Cylindrical Coordinate SystemUtility Menu WorkPlane Change Active CS to Global Cylindrical Check that ANSYS reports the active coordinate system in the Output window :The reference number
18、that ANSYS uses for the cylindrical coordinate system is 1 (the Cartesian system is 0).Save your work: Toolbar SAVE_DB Create KeypointsMain Menu Preprocessor Modeling Create Keypoints In Active CS When the active coordinate system is set to cylindrical, X, Y, and Z in the menus refer to the cylindri
19、cal coordinates r, (in degrees) and z, respectively. Remember to make this mental substitution as you enter the keypoint coordinates. Also, you can use the tab key to move the cursor to the next entry field. Dont forget to change the keypoint number as you enter the coordinates of the keypoints.Ente
20、r the keypoint locations (think about where each one lies as you enter its coordinates): Keypoint 1: X=R1, Y=90, Z=0, Click Apply. Keypoint 2: X=R1, Y=95, Z=0, Click Apply.Keypoint 3: X=R1, Y=95, Z=Z1, Click Apply.Keypoint 4: X=R1, Y=90, Z=Z1, Click Apply.Keypoint 5: X=R2, Y=90, Z=0, Click Apply.Key
21、point 6: X=R2, Y=95, Z=0, Click Apply.Keypoint 7: X=R2, Y=95, Z=Z2, Click Apply.Keypoint 8: X=R2, Y=90, Z=Z2, Click OK.Save your work: Toolbar SAVE_DB Switch to the isometric view: Utility Menu PlotCtrls Pan, Zoom, Rotate Iso (Click Picture for Larger Image)Note the orientation of the x-y-z triad at
22、 the bottom in the isometric view. The Pan-Zoom-Rotate menu, as the name indicates, can be used to change the viewing direction, zoom in and out and rotate the model. Close this menu.ANSYS reports csys=1 at the top of the Graphics window, csys referring to the coordinate system. This is a quick way
23、to check the current active coordinate system.Create VolumeWell next generate a volume from the 8 keypoints. The order of the keypoints should be around the bottom first and then the top. Switch to the Cartesian coordinate system for generating the volume:Utility Menu WorkPlane Change Active CS to G
24、lobal Cartesian ANSYS reports csys=0 at the top of the Graphics window.The lines (i.e. edges) connecting the keypoints that ANSYS generates during the volume creation are straight in the active coordinate system. Since we want these edges to be straight, the active coordinate system needs to be Cart
25、esian rather than a curvilinear system like the Cylindrical. Main Menu Preprocessor Modeling Create Volumes Arbitrary Through KPs Pick the 8 keypoints in the order in which they are numbered. Click OK in the pick menu.Plot LinesLets take a look at the lines that ANSYS generated in the volume creatio
26、n process:Utility Menu Plot Lines Turn off the background (otherwise it looks like the line connecting keypoints 7 and 8 is missing):Utility Menu PlotCtrls Style Background Display Picture Background Save Your WorkToolbar SAVE_DB 三维弯曲梁分析实例问题详述本例中所考虑的问题是一种具有不规则四边形等截面的梯形弯曲梁，见库克ET A1中例6.15。例中梁在飞机中受弯曲力矩
27、M作用。所以此例中我们用三维实体而非对称实体元素来建立模型。进而可以通过圆柱形坐标系来描述该模型。在此我们想获得作用于不规则梯形截面AA上的力。由于作用于曲梁上的力不随角度变化，所以我们将模型和分析过程简化为一种介于两发射状平面间的特殊薄片形梁，如下图所示。平面AB与CD间的起始角为5度。见库克ET A1。弯力矩M必须间接作用于简化模型，因此我们不知道截面上产生的瞬间切应力分布情况。作为替代，我们指定该发射状平面剩余部分的位移和一作用于模型上的瞬间力即非均布力，共同作用于简化模型上。弯力矩M可以通过作用在截面上的应力而推算得到。力矩与应力成线性比例。由此可知该应力是与一特定的力矩Mp相关联的，
28、并可通过对比例式Mp/M的乘法运算得出。由A、B、C、D四点组成的固定平面Z为一轴对称平面。所以只需建立拥有一半截面积的模型即可。边界条件。该节点沿径向（u），切向（v），轴向（w）自由度情况如下：F1F2u=0 于节点Av=0 于所有节点v=0.0001(rc-r)于所有节点w=0 沿AB方向w=0 沿 CD方向其余自由度不受限制。节点A处给定u=0，以限制R方向上的刚性运动。平面1处各节点给定v=0，以限制平面1的周向运动 。给定W0以限制ABCD关于中间平面r-的对称性。前面所述BC在平面2上，由其限定平面绕着以Z轴平行的直线转动，角速度r=rc。其中乘数0.0001为任意给定的。起初我
29、们不知道rc的确切值。由于理论上rc会施加一个纯弯曲载荷，所以节点A处的响应值RA=0。两初始点FE的预期分析值rc=60mm和rc=70mm已知。由此得出对应的RA值分别为2001N和357N。按线性关系推断当rc=72.2mm时RA=0。所以在本例中我们取rc=72.2mm。步骤1：启动及前处理新建文件夹。在合适的地方建立一个名为cbeam的文件夹。该文件夹用以保存操作过程中生成的所有文件。启动ANSYS。执行：开始 所有程序 ANSYS Release 7.0 ANSYS Interactive打开刚才建立的文件夹cbeam，并将其设定为默认的工作目录。定义初始工作文件名为cbeam。这
30、样期间生成的所有文件都将以cbeam为前缀。单击完成。步骤2：定义单元类型和各项参数给定单元类型。执行：Main Menu Preprocessor Element Type Add/Edit/Delete Add.，在弹出的对话框中分别选择左边“Structural Solid”和右边为“Brick 8-node 45”选项，单击OK按钮。关闭“Element Types”对话框和Element Types菜单。给定参数类型。执行：Main Menu Preprocessor Real Constants Add/Edit/Delete Add.，在弹出的对话框中给出了一些已定义的参数类型，
31、在此我们选择系统默认方案，单击OK按钮。此时你会看到一个说明选项“Please check and change keyopt setting for element SOLID45 before proceeding.”意思是该元件没有给定固定参数，需返回上一级菜单。关闭the Real Constants菜单。执行Toolbar SAVE_DB进行存盘。步骤3：定义材料性质执行：Main Menu Preprocessor Material Props Material Models，在“Define Material Model Behavior”菜单里依次双击Structural, L
32、inear, Elastic, and Isotropic，在“Youngs modulus EX”中输入200e9，在“Poissons Ratio PRXY”中输入0.3，单击OK按钮。关闭Define Material Model菜单。执行Toolbar SAVE_DB进行存盘。步骤4：建立几何模型首先我们分别在模型的八个顶点处建立关键点，然后再由这些关键点生成该实体。这些关键点需建立在一个三维坐标系中。其中四个关键点ABCD组成既定几何形状。其余四点以相似形状沿Z轴平移一定距离。参数设置。为了方便起见我们以国际制单位建立该实体尺寸参数。执行：Utility Menu Parameter
33、s Scalar Parameters，在弹出的对话框中依次键入下列参数。每次输入结束后单击Accept，在确认各项参数均正确无误后单击Close按钮。R1=44e-3 R2=R1+88e-3Z1=65e-3 Z2=14e-3点击结束。转换三维系统坐标。执行：Utility Menu WorkPlane Change Active CS to Global Cylindrical，在如图示输出窗口检验ANSYS报告的一致性。在三维坐标系中ANSYS参考数值为1（在笛卡尔坐标系中为0）。执行：Toolbar SAVE_DB进行存盘。生成关键点。执行：Main Menu Preprocessor
34、Modeling Create Keypoints In Active CS，此时原坐标系被设置成一球形坐标系，相应的原菜单中的X、Y、Z则分别被r、Z所取代。在键入关键点坐标时记得坐标系间的替换。另外,你也可以用TAB键将光标指定到相应的位置。当你将关键点输入到坐标系时，不要忘记改变关键点的编号。输入关键点坐标（输入时考虑每个点的位置）：关键点 1: X=R1, Y=90, Z=0, 单击 Apply；关键点 2: X=R1, Y=95, Z=0, 单击 Apply；关键点 3: X=R1, Y=95, Z=Z1, 单击 Apply；关键点 4: X=R1, Y=90, Z=Z1, 单击 A
35、pply；关键点 5: X=R2, Y=90, Z=0, 单击 Apply；关键点 6: X=R2, Y=95, Z=0, 单击 Apply；关键点 7: X=R2, Y=95, Z=Z2, 单击 Apply；关键点 8: X=R2, Y=90, Z=Z2, 单击 OK。执行：Toolbar SAVE_DB进行存盘。将工作平面转换到极坐标下。执行：Utility Menu PlotCtrls Pan, Zoom, Rotate Iso，（将视图缩小到全局）视图底部有一个三元坐标原点x-y-z，标示出各轴的方向。如名称所示，使用Pan-Zoom-Rotate菜单能够放大或缩小以及任意旋转模型的视
36、图。关闭菜单。在视图的左上角显示“csys=1”，csys表示的是坐标系。这是快速检验目前系统协调性的方法之一。生成实体。接下来我们将通过以上8个关键点生成一个模型的实体。各点按先底面后顶面的顺序联结。在笛卡尔坐标系中生成实体。执行：Utility Menu WorkPlane Change Active CS to Global Cartesian，在视图的左上角显示“csys=0”。关键点由直线（边）相联，致使坐标系中生成光滑的三维实体表面。既然我们想获得光滑的边缘，那么相较于一个曲线的球坐标系更倾向于使用笛卡尔坐标系。执行：Main Menu Preprocessor Modeling Create Volumes Arbitrary Through KPs，按关键点的编号顺序拾取各点。单击拾取菜单上的OK按钮。让我们来看看ANSYS实体创作过程中产生的线，执行：Utility Menu Plot Lines。关闭背景（否则我们将无法看到7、8号点生成的直线）。执行：Utility Menu PlotCtrls Style Background Display Picture Background，保存文件。执行：Toolbar SAVE_DB进行存盘。12