{"id":32504,"date":"2020-08-24T19:02:34","date_gmt":"2020-08-24T19:02:34","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=32504"},"modified":"2023-09-04T21:00:20","modified_gmt":"2023-09-04T21:00:20","slug":"follower-pressure","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/follower-pressure\/","title":{"rendered":"Validation Case: Cantilever Plate Subjected to a Follower Pressure"},"content":{"rendered":"\n\n\n\n

This validation case belongs to solid mechanics. It uses a cantilever plate geometry to validate the follower pressure boundary condition.<\/p>\n\n\n\n

SimScale results are compared to simulation results, presented in [SSNV145]\\(^1\\). The reference uses Code_Aster to perform the analysis.<\/p>\n\n\n\n

\n \n View Project <\/a>\n<\/div>\n\n\n\n\n

Geometry<\/h2>\n\n\n\n

The geometry for this project consists of a cantilever plate, as seen in Figure 1:<\/p>\n\n\n

\n
\"cantilever<\/a>
Figure 1: Cantilever plate geometry. The results will be assessed at point P.<\/figcaption><\/figure>\n<\/div>\n\n\n

The dimensions of the geometry are given in Table 1:<\/p>\n\n\n\n

Coordinates<\/strong><\/td>A<\/strong><\/td>B<\/strong><\/td>C<\/strong><\/td>D<\/strong><\/td>E<\/strong><\/td>F<\/strong><\/td>G<\/strong><\/td>H<\/strong><\/td>P<\/strong><\/td><\/tr>
x \\([m]\\)<\/td>0<\/td>0<\/td>0<\/td>0<\/td>10<\/td>10<\/td>10<\/td>10<\/td>10<\/td><\/tr>
y \\([m]\\)<\/td>0.5<\/td>-0.5<\/td>-0.5<\/td>0.5<\/td>0.5<\/td>-0.5<\/td>-0.5<\/td>0.5<\/td>0<\/td><\/tr>
z \\([m]\\)<\/td>-0.05<\/td>-0.05<\/td>0.05<\/td>0.05<\/td>-0.05<\/td>-0.05<\/td>0.05<\/td>0.05<\/td>0<\/td><\/tr><\/tbody><\/table>
Table 1: Coordinates of points within the cantilever plate geometry<\/figcaption><\/figure>\n\n\n\n

Analysis Type and Mesh<\/h2>\n\n\n\n

Tool Type<\/strong>: Code_Aster<\/a><\/p>\n\n\n\n

Analysis Type<\/strong>: Nonlinear static<\/a><\/p>\n\n\n\n

Mesh and Element Types<\/strong>: Two meshes are used in this case. The first one is a second-order mesh created in SimScale with the standard algorithm<\/a>. Case B uses a second-order hexahedral mesh. It was created locally and imported to SimScale.<\/p>\n\n\n\n

Table 2 contains details of the resulting meshes:<\/p>\n\n\n\n

Case<\/strong><\/td>Mesh Type<\/strong><\/td>Nodes<\/strong><\/td>Element Type<\/strong><\/td><\/tr>
A<\/td>Second-order standard<\/td>9700<\/td>Standard<\/td><\/tr>
B<\/td>Second-order hexahedral<\/td>3502<\/td>Standard<\/td><\/tr><\/tbody><\/table>
Table 2: Characteristics of the meshes used for cases A and B<\/figcaption><\/figure>\n\n\n\n

Figure 2 shows the standard mesh, used for case A:<\/p>\n\n\n

\n
\"second<\/a>
Figure 2: Discretization obtained with a second-order standard mesh<\/figcaption><\/figure>\n<\/div>\n\n\n

Similarly, Figure 3 shows the second-order hexahedral mesh, that was imported to SimScale.<\/p>\n\n\n

\n
\"hexahedral<\/a>
Figure 3: Hexahedral mesh imported to SimScale. It contains a total of 3502 nodes.<\/figcaption><\/figure>\n<\/div>\n\n\n
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<\/i>Note<\/p>\n <\/div>\n

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Especially for nonlinear analysis, such as this one, we recommend second-order meshes. They provide more accurate results, due to the higher number of nodes.\r\n
\r\n
\r\nThe following article<\/a> provides further information on second-order meshes for finite element analysis.<\/p>\n <\/div>\n<\/div>\n\n\n\n

Simulation Setup<\/h2>\n\n\n\n

Material<\/strong>:<\/p>\n\n\n\n