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# Validation Case: Cantilever Plate Subjected to a Follower Pressure

This validation case belongs to solid mechanics. It uses a cantilever plate geometry to validate the follower pressure boundary condition.

SimScale results are compared to simulation results, presented in [SSNV145]$$^1$$. The reference uses Code_Aster to perform the analysis.

## Geometry

The geometry for this project consists of a cantilever plate, as seen in Figure 1:

The dimensions of the geometry are given in Table 1:

## Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Nonlinear static

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

Table 2 contains details of the resulting meshes:

Figure 2 shows the standard mesh, used for case A:

Similarly, Figure 3 shows the second-order hexahedral mesh, that was imported to SimScale.

Note

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.

The following article provides further information on second-order meshes for finite element analysis.

## Simulation Setup

Material:

• Material behavior: Linear elastic
• $$(E)$$ Young’s modulus = 1.2e+7 $$Pa$$
• $$(\nu)$$ Poisson’s ratio = 0.3
• $$(\rho)$$ Density = 1000 $$kg/m³$$

Boundary Conditions:

The boundary conditions will be defined based on Figure 1:

• Constraints
• Fixed support on face ABCD
• Follower Pressure $$P$$, applied on face CDHG. The following formulation is used:
$$P = t \tag{1}$$
Where $$t$$ is the pseudo-time for the nonlinear analysis. This validation case will run until $$t$$ = 26.

## Result Comparison

SimScale results will be compared against two reference simulations. The first one used Code_Aster, while the remaining one used the SAMCEF software.

The results for both reference simulations are found in . The displacements in the X and Z-directions are evaluated at point P (as seen in Figure 1).

In Figure 4, we compare the results for the displacements in the X-direction against Code_Aster. The reference results were extracted using WebPlotDigitizer.

A similar comparison was made for the displacements in the Z-direction:

Additionally, still using point P as a reference, the displacements obtained with SimScale are compared to the results from the SAMCEF software$$^1$$. Table 1 contains the displacements in the X-direction:

A comparison for the displacements in the Z-direction is also presented:

The results obtained with SimScale for both directions show a great agreement with the reference simulations.

Figure 6 shows the contours for displacements in the X-direction, for case A. The follower pressure boundary condition is updated after each pseudo time step, based on the current deformed state of the geometry. As a result, the plate gets rolled up: