How to verify that a thin-walled stainless steel vessel can withstand a pressure test before the prototype is manufactured? This is exactly the question that Schäffer-Sudex, in cooperation with TD-IS, addressed. The goal was to use Autodesk Inventor Nastran to simulate the vessel's behavior during a pressure test, capture the loss of structural stability, and compare the calculation results with real strain gauge measurements.

The result is a practical demonstration that advanced nonlinear simulations can significantly help already in the design phase. It is not just about color maps of stresses or deformations. In this case, we verified the simulation results on a real vessel during a pressure test.

When linear analysis is not enough

Autodesk Inventor is one of the most widely used 3D CAD systems in engineering practice. It also includes a basic computational module "Strength Analysis", which allows you to perform linear static and modal analyses. These are very useful in the early stages of design, for example, for quickly verifying the stiffness, stress or natural frequencies of a structure.

However, this basic approach is often not enough for pressure vessels. A typical vessel has very thin walls in the order of millimeters, while its overall dimensions can be in the order of meters. When loaded with internal pressure, significant deformations of the walls occur, geometry changes, and internal forces are redistributed. Membrane stresses and geometric stiffening play a significant role in the behavior of the structure.

In such cases, it is necessary to use more advanced computational tools that can handle large deformations, nonlinear material behavior, and possible loss of stability. One such tool is Autodesk Inventor Nastran.

Pressure testing as a design challenge

Schäffer-Sudex manufactures stainless steel vessels that must pass a number of verification tests before being put into operation. One of these is a pressure test. In this test, the vessel, shown in Figure 1, is filled with water and then gradually loaded up to the prescribed test pressure.

The type of container being tested undergoes significant permanent deformation during the test. The structure must safely withstand the pressure and must not fail. It is therefore important for the developer to know not only whether the stress exceeds a certain limit, but also how the container will deform, whether it will lose stability, and what the resulting deformed shape will be.

The aim of the simulation was to capture these phenomena already in the design phase. Therefore, TD-IS supported the introduction of Inventor Nastran calculations into the development process through training, consultations and support for the designers.

Two computational approaches in Inventor Nastran

We used two computational approaches to simulate the pressure test. The first was a nonlinear static analysis with large deformations turned on. The second was an explicit dynamic analysis. For pressures of 0,5, 1 and 2 bar, the results of both simulation approaches are shown in Figure 2.

The vessel material was described as a nonlinear stainless steel. This allowed the plastic behavior of the material to be included and it was possible to evaluate whether the structure approached the chosen ultimate plastic deformation during loading.

The explicit dynamic solver was used in this case as a robust tool for passing through the instability region. Although the pressure test itself is of quasi-static nature, explicit calculation may be suitable for problems in which the structure suddenly jumps to a new deformed configuration. The loading was therefore conducted in such a way that the result corresponds to the slow nature of the actual pressure test.

Verification on a real container

In order to verify the simulation results, in cooperation with the Regional Institute of Technology at the University of West Bohemia in Pilsen, we prepared experimental measurements on a real vessel. Strain gauges on the vessel recorded the relative deformation during gradual pressurization. The vessel equipped with strain gauges is shown in Figure 1.

The vessel was filled with water before the test for thermal stability. However, this already caused initial deformations due to hydrostatic pressure, which were not included in the computational model. This fact later proved to be important in interpreting the differences between the simulation and the experiment.

During the test, the vessel was gradually loaded up to a value of approximately 1,8 bar. The measured deformations were then compared with the results of both computational models.

Figure 3 shows an overview of the measured locations and the results of both simulation approaches.

Loss of stability around 0,5 bar

The simulation results showed that at approximately 0,5 bar, a snap-through loss of stability occurs. This is a jump of the structure to a new deformed configuration. In this particular case, this phenomenon was associated with permanent plastic deformation of the vessel.

Nonlinear static analysis was able to identify this critical pressure approximately. However, in the stability jump area, convergence problems were evident with a finer computational mesh. For this calculation, we therefore used a coarser mesh, which allowed us to capture the basic behavior of the structure, but did not allow us to follow the entire subsequent deformation process in detail.

Explicit dynamic analysis, on the other hand, allowed us to stably calculate the deformation process even on a finer mesh and continue up to a test pressure of 2 bar. Thanks to this, we were able to better describe the resulting deformed shape of the container after the stability jump.

Comparison with strain gauge measurement

In the places equipped with strain gauge roses, the measured relative strains were compared with the results of both simulations. Strains in the horizontal and vertical directions were evaluated.

In the nonlinear static analysis, good agreement with the experiment was evident mainly in the centers of the walls, i.e. in positions 1R and 2R. In other measured locations, the agreement gradually disappeared after the pressure exceeded approximately 0,5 bar. The probable cause is precisely the stability jump and the subsequent change in the geometry of the vessel, which could not be stably monitored in the used nonlinear static analysis settings.

The explicit dynamic analysis showed very good agreement not only at the center of the sides, but also at position 5R, i.e. at the point between the two measured walls. The calculation also achieved relatively good agreement for the horizontal component of the deformation in the area of ​​the bottom edges.

The largest difference between the simulation and the experiment occurred in the vertical component of the strain at position 3R. This difference can probably be explained by the fact that the vessel was already filled with water before the strain gauges were installed. Hydrostatic pressure could have caused initial rounding, especially in the lower part of the vessel. Since this condition was not included as an initial deformation in the computational model, it could have affected the subsequent comparison of the results.

Result: simulation helps predict the behavior of the container before testing

The simulations in Inventor Nastran yielded several important results. Both computational approaches allowed us to identify the pressure at which the snap-through stability loss occurs. In addition, the explicit dynamic analysis was able to better capture the further course of the vessel deformation and the resulting deformed shape.

Comparison with strain gauge measurements confirmed that explicit dynamics is a suitable tool for this type of problem. It was able to reliably describe the behavior of the structure even after loss of stability, i.e. in the area where nonlinear static calculation encountered convergence limits.

The vessel did not break during the pressure test. None of the computational models showed that the ultimate plastic deformation of the stainless steel had been reached. The results thus confirmed that the vessel successfully passed the pressure test.

The benefits for the development process are obvious: advanced simulations allow for risk assessment before prototype production, better understanding of structural behavior, and targeted design adjustments. Combined with experimental measurements, they provide a reliable basis for decision-making in the design of thin-walled pressure vessels.

Author: Ing. Pavel Mareš, Ph.D., sales and technical manager, TD-IS, sro

Professional cooperation: Schäffer-Sudex, Regional Institute of Technology at the University of West Bohemia in Pilsen