Degree of Element (DOF) of Element in Finite Element Method (FEM)

 1-D element

• Rod     -    2 DOF/ node (U_x, θ_x) 
• Bar      -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Beam   -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Pipe     -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Axisymmetric shell   -    3 DOF / node (U_x, U_z, θ_y ) 

2-D element

• Plane Stress     -    2 DOF / node (U_x, U_y ) 
• Plane Strain     -    2 DOF / node (U_x, U_y ) 
• Plate                 -    3 DOF / node ( U_z , θ_x, θ_y ) 
• Membrane        -    3 DOF / node (U_x, U_y, θ_z ) 
• Thin Shell        -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Axisymmetric Solid    -    2 DOF / node (U_x, U_y ) 

3-D element

• Tetra                    -    3 DOF / node (U_x, U_y, U_z  ) 
• Penta or Wedge   -    3 DOF / node (U_x, U_y, U_z  ) 
• Hexa or brick       -    3 DOF / node (U_x, U_y, U_z  ) 
• Pyramid               -    3 DOF / node (U_x, U_y, U_z  ) 

What is Finite Element Analysis/Method

 The Finite Element Method is self-explanatory, as the definition of the FEM is hidden in these three words.

• Finite: As we know, every continuous component has millions of Degree of Freedom as it is made up of millions of particles. We generally call the degree of freedom (DOF) of a continuous object is infinite. It is not possible to solve the problem of an infinite degree of freedom(DOF). So, for the sake of simplicity, we reduce the degree of freedom(DOF) from infinite to finite with the help of the discretization process, which is called the meshing (Node and Element). 

• Element: In the Finite Element Method, all the calculation activities are done on a limited number of points, which are called Nodes. Node is a specific point, which does not consume any space, it is an infinitesimal. The entity, which joins these nodes point, is called Element. There are many types of element shapes, i.e. Line, triangular, Quadrilateral, Box, Hexahedran, Penta, Tetrahedron. The result variable (i.e. stress etc.) is calculated on these nodes. Then the result variable is interpolated based on these elements based on an interpolated function that depends on the shape of the element.

•  Method: As there are 3 Methods to solve any engineering problem: Theoretical, Numerical, and Practical. The Finite Element method uses the Numerical method of Problem Solving. 

Line body analysis in ANSYS

Problem 2: 3D analysis of a plate with hole in center

A square plate with a hole at the center is under a tension load p in x direction as shown in the figure below. the dimension of the plate is 10in X 10in, thickness is 0.1in, and radius of hole is 1 in. Assume material structural Steel and p = 100 psi. FInd the maxium stress in plate.

Result:- 

1. Deflection(total )

2. Deflection( x- direction)

3. Deflection( y- direction)

4. Stress(von-Mises)

5. Strain(von-Mises )

6. Stress concentration factor

justify your answer with correct explanation, applying your subject knowledge.

Analysis using workbench

Result

Problem 1: Analysis using ANSYS APDL Script : 3D Analysis of beam with Concentrated Load on Corner

Below there is script of Ansys APDL of 3D analysis of Beam with Concentrated Load on Corner

Firstly copy this script to "Notepad". Go to File Menu, Select "Read Input From". Select file from list.  

/PREP7
ET,1,SOLID186
MP,EX,1,200000000000
MP,PRXY,1,0.3
BLOCK,0,2,0,0.25,0,0.08
ESIZE,0.1
VMESH,1,1
DA,5,UX,0
DA,5,UY,0
DA,5,UZ,0
FK,7,FZ,-1000
/SOLU
SOLVE
/POST1
PLNSOL,U,SUM,1

Frictionless Support

An object have six degree of freedom in space. There are three translational and three rotational Degree of Freedom.

1.       Translation in X (Ux)

2.       Translation in Y (Uy)

3.       Translation in Z (Uz)

4.       Rotation about X (RotX)

5.       Rotation about Y (RotY)

6.       Rotation about Z (RotZ)

We apply support to restrict these DOF. In ANSYS, Frictionless Support provide Support in normal direction to the selected face or edge. The body can not move or rotate or deform in normal direction. But free to move or rotate or rotate in tangential direction.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Modal

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Supported- 3D only
• Edge: Supported – 2D only
• Vertex: Not Supported
• Node: Not Supported

Fixed Support

An object have six degree of freedom in space. There are three translational and three rotational Degree of Freedom.

1.       Translation in X (Ux)

2.       Translation in Y (Uy)

3.       Translation in Z (Uz)

4.       Rotation about X (RotX)

5.       Rotation about Y (RotY)

6.       Rotation about Z (RotZ)

We apply support to restrict these DOF. In ANSYS, for Fixed support, we restrict all the DOF at a point, edge or face.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Explicit Dynamics
• Modal

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Supported, in Explicit Analysis
• Face: Supported
• Edge: Supported
• Vertex: Supported
• Node: Not Supported

Load in ANSYS Structural

Load in ANSYS Structural

There is list of load available in ANSYS structural analysis

1. Force

2. Pressure

3. Moment

4. Hydrostatic Pressure

5. Pipe Pressure

6. Remote Force

7. Bearing Load

8. Line Pressure

Line Pressure

Line pressure is equal to uniformly distributed load (UDL). It have unit load per unit length. Generally we use unit KN/m.

In ANSYS, for 3D simulation, a line pressure load applied a distributed force on one edge only.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Explicit Dynamics

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Not Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Not Supported
• Edge: Supported
• Vertex: Not Supported
• Node: Not Supported

Bearing Load

When a shaft rest on a component, then it exert the load on that component. That load is called bearing load. On the basis of that load, supporting part are known as bearing. Bearing load have two component

• Radial load
• Axial load

Radial load act perpendicular to the axis of rotation, while axial (thrust) load acts parallel to the axis of rotation.

In ANSYS, the bearing load boundary condition analyze radial force only. It will be applied on the interior face of a cylinder in the radial direction. If you will apply a portion of the load to be in axial direction, the solver stops the solution and issues an appropriate error message.

When you apply bearing load on different circle, then the load will be distributed equally as proportion of area.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Not Supported
• Wire body/ line body / Beam: Not Supported

Topology

• Body: Not Supported
• Face: Supported
• Edge: Supported – 2D simulation only
• Vertex: Not Supported
• Node: Not Supported

Remote Force

Remote force is a type of force, which act a force as well as produce some effect of moment. It produce effect on a point of a face or edge without creating point on that.

In ANSYS, the remote force boundary condition is equivalent to a regular force load on a face or a force load on an edge, plus some moment. The advantage of using a remote force is that you can directly specify the location in space from which the force originates. A remote force is classified as a remote boundary condition.

A remote force boundary condition can be applied to a face, edge or vertex of a 3D model or to an edge or vertex of a 2D model.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Rigid Dynamics

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Not, 3D only
• Edge: Supported
• Vertex: Supported
• Node: Supported

Pipe Pressure

Pipe is generally used for transfer the fluid from one point to another. These fluid exert some pressure on pipe. This is called generally internal pressure. In some region, where we have to deal with snow region or water zone like ocean. In this region, there is generated external pressure, which try to compress the pipe.

In ANSYS, this boundary condition is applied only to pipe in the form of line bodies. This is very useful for pipe design and pipe stress analysis.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Explicit Dynamics
• Harmonic Response

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation:  Not Supported

Geometry Type

• Solid: Not Supported
• Surface/Shell: Not Supported
• Wire body/ line body / Beam: Supported, line bodies only

Topology

• Body: Not Supported
• Face: Not Supported
• Edge: Supported
• Vertex: Not Supported
• Node: Not Supported

Hydrostatic Pressure

Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due the force of gravity. Hydrostatic pressure increases proportional to depth measured from the surface because of the increasing weight of fluid exerting downward force from above.

                                                                  P = rho x g x h

                                                      Where p = pressure

                                                                 Rho  = density of fluid

                                                                 G = gravity acceleration

                                                                  h = height of fluid above the object

In ANSYS, hydrostatic pressure load simulates pressure that occurs due to fluid weight.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Explicit Dynamics

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Supported -3D
• Edge: Supported-2D
• Vertex: Not Supported
• Node: Not Supported

Moment

The moment of a force is a measure of its tendency to cause a body to rotate about a specific point or axis. For developing moment, the force must act upon the body in such a manner that the body would begin to twist. The magnitude of the moment of a force acting about a point or axis is directly proportional to the distance of the force from the point or axis.

M = F . d

The unit of moment is newton –meter (N-m). A moment also have sense; a clockwise rotation about the center of moment will be considered as positive moment, while a counter-clockwise rotation about the center of moment will be considered negative.

In ANSYS, this boundary condition distributes a moment “about” (the vector of) an axis across one or more flat or curved faces, or about one or more edge or vertex.

Moment boundary condition classified as a remote boundary condition in ansys.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Supported -3D
• Edge: Supported
• Vertex: Supported
• Node: Supported

Pressure

Pressure is defined as force per unit area. The standard unit for pressure is Pascal, which is equal to 1 Newton per square meter.

Pressure = Force / Area  =  F/A

It is generally applied perpendicular to the applied surface.

In ANSYS, Pressure load applies a constant pressure or a varying pressure in a single direction (x, y or z) to one or more flat or curved surface.

A positive value of pressure act toward the face, compressing the body. A negative value of pressure act opposite to the face, form tension in body.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Explicit Dynamics

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported

Geometry Type

• Solid: Supported
• Surface/Shell: Supported

Topology

• Body: Not Supported
• Face: Supported – 3D
• Edge: Supported – 2D
• Vertex: Not Supported
• Node: Not Supported

If you select multiple face or edge, when defining the pressure, the same pressure value gets applied to all selected face or edge.

Force

A force is a push or pull upon an object resulting from the object’s interaction with another object.

F = m x a

Force is measured using Newton.

1 N = 1 kg x m/s²

Force is a vector quantity. It has both magnitude and direction. Because it have direction so we have to apply direction at time of applying load.

Analysis Type – This boundary condition are available in only following ANSYS Analysis type

• Static Structural
• Transient Structural
• Harmonic Response
• Explicit Dynamics

Properties of Boundary Condition

Dimensional Analysis

• 3D Simulation: Supported
• 2D Simulation: Supported, Force load are not supported for 2D axis-symmetric explicit dynamic analysis.

Geometry Type

• Solid: Supported
• Surface/Shell: Supported
• Wire body/ line body / Beam: Supported

Topology

• Body: Not Supported
• Face: Supported

            Force will convert into pressure based on total area of all selected face.  If selected faces are not connected to each other or are from different part then there will be no selection.

• Edge: Supported

             If you select multiple edge, the magnitude of the force is distributed equally over all selected edge. If you select multiple selection without connected to each other, then no selection will occure.

• Vertex: Supported

           If you will select multiple vertices when defining the force, the force magnitude will be distributed evenly across all selected vertices.

• Node: Supported

Deformation

Deformation is change in shape or size due to load or temperature variation. but in ANSYS, Deformation is displacement of a point from its initial position. Deformations are calculated relative to the part or assembly world coordinate system

Deformation have three different component as follows

1. Ux

2. Uy

3. Uz

theses are called Directional Deformation in ANSYS.

After combination of these, that are called Total Deformation

Problem 1: anaysis using APDL : 3D Analysis of beam with Concentrated Load on Corner

Firstly Go to ANSYS>ANSYS APDL Product Launcher. New window will open. Select ANSYS Multiphysiscs  under the License. Now click on Run Tab.

Now New window will open.

Now you Go to Main Menu > Preferences. New dialog box Preferences for GUI Filtering will open. Select structural in Dailog Box. Then click on OK tab.

Now Go to Main Menu > Preprocessor > Element Type > Add/Edit/Delete. Then new dialog box with name of Elements type will open. Now, click on Add…. Then a new dialog box will open Library of Element Types will open. Select solid in first dialog box and 20node 186 in second column. Then click on OK button. Then dialog box will be close. Then click on Close tab in Elements type dialog box.

Now go to Main Menu > Preprocessor > Material Models. New dailog box Define Material Model Behaviour will will open. Select Material Model number 1 From Material Model Defined Column. Then select Structural > Linear > Isotropic from Material Models Available column.

Then new dialog box Linear Isotropic Properties for Material Number 1 will open. Type 200000000000 in Ex and 0.3 in PRXY. Now click on OK Button to close dialog box. Now close Define Material Model Behaviour dialog box.

Now go to Main Menu>Preprocessor > Modeling > Create > Volumes > Block > By Dimensions. Now new dialog Box Create Dialog Box by Dimensions will open.

Insert 0, 2, 0, 0.25, 0, and 0.08 in X1, X2, Y1, Y2, Z1 and Z2 field respectively.

Click on OK to generate the required geometry.

Now go to Main Menu > Preprocessor > Meshing > Size control > Manual Size > Global > Size. New Dialog box Global Element sizes will open. Type 0.01 in Size Element edge length insert field (As per your system resources are available). Click on Ok to close the dialog box.

Now go to Main Menu > Preprocessor > Meshing >Mesh Tool. A new dialog box will come in right side,  named Mesh tool. Click on Mesh Button. Then new dialog box will open. Then you have to select the geometry. Then click on OK button.

Now meshing is started.

When meshing is done, click on Close button to close the Mesh tool dialog box.

Now go to Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > on Areas.

Then a new dialog box will open. Select face on which you have to apply fixed support. Then click on Ok button in dialog box.

Then a new dialog box will open. Select All DOF in DOFs to be constrained selection field. This will restrict all the degree of freedom at specified Surface. Then click on OK button in Dialog Box to apply the condition and close the dialog Box.

Now go to Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Force/Moment > On Keypoints. Then new dialog box will open. Now select the point where you want to apply load. Click on Ok button to apply & close the dialog box.

Then new dialog box Apply F/M on KPs will open. Select FY from Direction of force/mom selection field. Type -1000 in Force/moment value insert field. Now click on OK button.

Now go to Main Menu > Solution > Current LS. New dialog box will be open. Click on OK button to start analysis.

Now solution is done.

Now go to Main Menu > General PostProc > Plot Results > Contour Plot > Nodal Solu. New dialog box will open. Now go to Nodal Solution > DOF Solution > Displacement vector sum. Click on OK button to apply this.

Then the following Result will come.

Problem 1: anaysis using workbench : 3D Analysis of beam with Concentrated Load on Corner

For the analysis in Workbench, we have to divide the procedure in following step.

• Geometry
• Meshing
• Load and support
• Solve
• Result

In problem,

L = 2m, b = .25m, h = 0.8m, load = 1000N,

ANSYS Workbench

First go All Programs>ANSYS16.0>workbench, for open the workbench for analysis.

Then new window will open as shown below. This is welcome window of ANSYS workbench. In which there is Title bar, menu bar, Standard tool bar, toolbox, Project Schematic and properties of Project Schematic.

Go to Toolbox > Analysis System. Double click on “Static Structural” for structural analysis. Static structural analysis System will come on Project schematic.

Default material is Structural steel. So we do not have to select material. So, we will not go in Engineering Data tab.

Now we have to create the geometry. Double Click on Geometry tab for entering in Geometry workbench.Then there will be open a window & sub window. In Sub window u have to select unit meter. Then following window will open.

Now, Go to Tree outline box, select XYPlane. Now select look At Face/Plane/Sketch  .

Now select sketching tab, there will Tab – Draw, modify, dimensions, constraints, Settings. In Draw tab, select Rectangle tab. Now select origin in drawing space for specifying first point of rectangle. Then click on opposite corner to specify the second corner of rectangle.

Now Go to Dimensions tab select General. Now select horizontal line & place it below the line. Now select Vertical line of rectangle and place it aside of line. Now go to Detail View, type 2.5 and 0.25 for H1 and V2 respectively.

Now go to create menu, select Extrude Commend.

Now select sketch1 from tree outline then go to Detail View, click on apply ahead of Geometry tab & type 0.08 m in Depth Tab. Then click on Generate Tool.   

Now Close the window.

Analysis

Now Double click on Model tab. New window will open.

Go to Outline Tab,  select mesh from tree, and now go to detail box, then  expend sizing. Now type 0.01 in Element size. (It depend on your computer resources.)

Now right click on static structural in outline box. Select Force from expended list Select point cursor from selection toolbar. Select corner of beam created. Now go in Detail Box, type 1000 in Magnitude. Click on direction, when apply button is showing, Select the top face of Beam. Then apply the direction as per need. Then click on apply.

Again right click on Static structural, select Fixed Support , select another face of As shown in figure, on which you have to apply fixed support.

Now right click on Solution, select Deformation > Totaldeformation.  Then right click on total deformation select convergence.  Now click on Solve in Toolbar.

Then you result will be look like this.

Now Again right click on solution, select probe > Deformation Probe. Select point where you want to found the result. Now select total in Result Selection.

Problem 1: 3D Analysis of beam with Concentrated Load on Corner

Consider the beam Below. There is applied concentrated load on corner. Find out displacement at corner.

Result:- Deflection(total ):

              Deflection( z- direction):-

Solution Using Workbench

Solution Using APDL

Solution Using APDL Script

Solution Comparison