Home / Examples / Stress Analysis [Galileo] / Example 72 Bending Analysis with Shell Elements

Example 72 Bending Analysis with Shell Elements

General

• Using shell elements, a model with a large aspect ratio can be analyzed with fewer meshes.
   

• Unless specified in the list below, the default conditions will be applied.
  

• Obtain this session's project file. (Right-click and choose 'Save link as')
  
  

• Results will vary depending on Femtet version and the PC environment.

 

Analysis Conditions

 

Item	Settings
Solver	Stress Analysis [Galileo]
Analysis Space	3D
Analysis Type	Static Analysis
Unit	mm
Analysis Options	Select [Constrain the freedom of shells]

 

Model

To model a thin beam with sheet elements, create a sheet body, of which body attribute name is Beam, with a size of 10x1 mm, and specify 0.1 mm as the thickness of sheet body.

 

 

Body Attributes and Materials Setting

Body Number/Type	Body Attribute Name	Material Name
0/Sheet	Beam	Material Property_001 *

* To compare the results with theoretical calculations, a special case is considered in which Young's modulus and Poisson's ratio of the material properties are set to 200 GPa and 0, respectively.

Boundary Condition

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
Fix/Edge	Mechanical	Displacement	Select all UX/UY/UZ components. UX=0, UY=0, UZ=0   Unselect all RX/RY/RZ components.
Fix_z/Edge	Mechanical	Displacement	Select the UZ component UZ=0   Unselect other boundaries
Tributary_Moment/Edge	Mechanical	Distributed Face Load	Select [Set the total load]. MX=0.001

Results

Below is the displacement diagram with contours of Z displacement.

 

 

 

Comparison with Theoretical Calculation

Compare the results with the theoretical calculation of the bending moment load problem below.

 

Below is shown the theoretical model replicating the analysis model.

 

 

The following table lists the values of the model variables for the theoretical solution.

The values are given to match the model dimensions, boundary conditions, body attributes, and material properties of the project file.

Item	Symbol	Value	Unit
Moment Load	M	0.001	N·m
Young's Modulus	E	2e+11	Pa
Poisson's Ratio	ν	0	-
Length of beam	L	0.01	m
Width of beam	b	0.001	m
Thickness of beam	h	0.0001	m

 

 

Below are formulas that give the second moment of a section in the bending load applied direction

and the bending displacement, z, at the position, y.

Noted that gravity is not taken into account.

 

 

 

 

The result of the comparison between the calculated result from the equations above and the analysis result of Example 72 is shown below.