Finite Element Analysis
of a Square Plate

 

Exact results of a square plate

Generation of the structure model

Input of the material data

Input of the boundary conditions

Input of the loads

FEM-Analysis

Results evaluation

 

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Exact results of a square plate

1.) Simply supported square plate

The following results should be calculated for a simply supported plate at the boundaries:

the maximum deflection in Z-direction, the maximum moments Mxx and Myy, the polar moment Mxy all located
in the plate center and the sum of the reaction forces.

We consider the cases:

 

The following results come from the tables (1), which are not exact, but are good approximations:

 

2.) Exact Results of a square plate clamped on 3 edges and simply
supported on one edge

All quantities are the same as in the previous case, but the plate is clamped on 3 sides, the 4th side has rotation dof about the x- and y-axes. Instead of the moment Mxx the reaction moments Mxs and Mys at the fixed edges are requested.

 

The following tables have been used to get the approximate results:

 

(1)Berechnungstafeln für Platten und Wandscheiben, Richard Bares, Bauverlag GmbH, Wiesbaden 1969

 

 

Generation of the structure model

to call the CAD icon bar and to create a line model

  • Start point: X=0, Y=0, Z=0

    1. end point: X=5, Y=0, Z=0

    2. end point: X=5, Y=6, Z=0

    3. end point: X=0, Y=6, Z=0

    4. end point: X=0, Y=0, Z=0

  •  

     

    Input of the material data

    Complete the dialog box with the menu Editor and Material Datas in NETGEN as shown below:

     

    The material data are:

    Thickness H1, H2, H3, H4 = 0.1 m

    Young's modulus = 20000000 kN/m2

    Poisson ratio = 0.3/0.15/0.0

     

     

    Input of the boundary conditions

    1.) Simply supported square plate

    The square plate is simply supported, i.e. the degrees of freedom at the plated edges are suppressed in the Z-direction.

    Marking with a polygon

    The outer boundary is marked by a polygon consisting of 10 points as shown below:

     

     

    2.) Clamped square plate with one edge simply supported

    The square plate is clamped on 3 edges and simply supported on one edge. This means that the translation degree
    of freedom in z-direction is suppressed at all edges and the rotation degrees of freedom about the x- and y-axes are
    suppressed on 3 edges.

    Use the x icons and the y icon and the buttons Create and Marking with a polygon.

     

    Input of the loads

    The distributed load is generated as follows:

    1. Input via keyboard
    2. Dragging with curser a rectangle
    3. Surface Model

    Both structure files are now complete and are saved as Square_Plate_PLA8S_simply_supported.fem and
    Square_Plate_PLA8S_clamped.fem

     

     

    FEM-Analysis

    As a prerequisite of the analysis select the result quantities in the menu FEM-Analysis and and Statics. Otherwise
    only the default quantities are calculated, the displacements and averaged nodal stresses.

    The analysis is started from the menu FEM-Analysis and FEM-Analysis.

    The analysis can be performed in 2 steps.

     

     

    Results evaluation

    The displacement in Z-direction and the distribution of the components of the moment Mxx and Myy
    result with the icon .

    Comparison of the results with different element types and mesh densities:

    1.) Simply supported square plate

     

    2.) Clamped square plate with one edge simply supported