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:

Coordinates	A	B	C	D	E	F	G	H	P
x \([m]\)	0	0	0	0	10	10	10	10	10
y \([m]\)	0.5	-0.5	-0.5	0.5	0.5	-0.5	-0.5	0.5	0
z \([m]\)	-0.05	-0.05	0.05	0.05	-0.05	-0.05	0.05	0.05	0

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 created in SimScale with an extrusion refinement.

Table 2 contains details of the resulting meshes:

Case	Mesh Type	Nodes	Element Type
A	Second-order standard	9700	Standard
B	Second-order hexahedral	4362	Standard

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

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

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
• Surface loads
  • 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 [1]. 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:

Pseudo-time \([s]\)	SAMCEF – DX \([m]\)	Case A – DX \([m]\)	Error [%]	Case B – DX \([m]\)	Error [%]
11	-7.3664	-7.0953	-3.68	-7.0823	-4.01
13	-9.03743	-8.7143	-3.58	-8.6969	-3.92
22	-13.5098	-13.2380	-2.01	-13.2169	-2.22
26	-14.1513	-13.9797	-1.21	-13.9645	-1.34

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

Pseudo-time \([s]\)	SAMCEF – DZ \([m]\)	Case A – DZ \([m]\)	Error [%]	Case B – DZ \([m]\)	Error [%]
11	-8.44920	-8.3929	-0.67	-8.3907	-0.70
13	-8.42753	-8.4310	0.04	-8.4316	0.048
22	-5.78828	-6.0759	4.97	-6.0972	5.34
26	-4.43375	-4.7696	7.57	-4.7969	8.19

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:

Last updated: April 3rd, 2026