Inflatable film cushions exhibit a highly nonlinear load-bearing behavior that can only be realistically captured through appropriate numerical methods. RFEM 6 offers specialized tools for form-finding, pressure modeling, and analysis of large deformations. This enables precise simulation and safe design of pneumatic membrane structures.
1. Basics
An inflatable body typically consists of an air-filled film sack with internal and external stiffening elements. The shape of the pressurized film sack depends on several factors:
- the applied pressure or the air volume introduced into the film cushion,
- the membrane stress distribution in the film skin, and
- the local placement and execution of the stiffening elements.
2. Procedure
RFEM 6 offers a significant advantage over RFEM 5 with its functionality. In RFEM 6, multiple forms can be simultaneously simulated in a model using initial states. This allows for a more straightforward comparison of behavior when adjusting pressure or membrane stress distribution.
The general process is as follows:
- Open RFEM 6 and activate the Form-finding Add-On
- Define the material properties for the enclosing film material and the enclosed air medium
- Model the film cushion geometry, including the stiffening elements, from membrane elements with a rough approximation of the desired target geometry
- Define a gas volume within the film sack with a description of the atmosphere
- Set the shape-giving form-finding loads for the form-finding process on the film body
- Specify the shape-giving internal film cushion pressure for the form-finding process via a gas pressure load
- Apply a realistic support for the film cushion body
- Start the calculation of the load case to evaluate the desired target geometry
- Create additional load cases, such as snow and wind
- Combine initial states with your load combinations
3. Example
I refer to a comparison with Example 3.8 from the book [1]. The following film cushion is considered:
| Span | B | 4 m |
| Length | L | 12 m |
| Material | Ex = Ey | 300 kN/m |
| Self-weight | gk | neglected |
| Internal pressure permanent load case | pi,k | 0.3 kN/m² |
| Internal pressure snow | pi,k | 0.6 kN/m² |
| Snow | sk | 0.52 kN/m² |
| Wind suction | ws,k | 0.78 kN/m² |
| Force | nx = ny | 1.56 kN/m (cushion center) |
| Sag | f0 | 0.4 m (cushion center) |
The initial shape is determined by specifying the force and internal pressure as follows:
3.1 Load combination 1: Internal pressure and snow, open volume
Below is the tabular comparison with the values in the literature [1].
| Results | analytical | numerical | RFEM 6 |
| Height ftop | 0.374 m | 0.355 m | 0.345 m |
| Force ny,top | 0.55 kN/m | 0.57 kN/m | 0.53 kN/m |
| Height fbottom | 0.434 m | 0.432 m | 0.425 m |
| Force ny,bottom | 2.99 kN/m | 2.91 kN/m | 2.91 kN/m |
The difference between the numerical solutions and the analytical solution is already mentioned in the literature. The numerical solution in the literature refers to a simplified cable net for determining the values. The RFEM 6 solution uses the 3D calculation model with surfaces and volumes.
3.2 Load combination 2: Internal pressure and snow, closed volume
Below is the tabular comparison with the values in the literature [1].
| Results | analytical | numerical | RFEM 6 |
| Internal pressure p0 | 0.3 kN/m² | 0.3 kN/m² | 0.3 kN/m² |
| Volume V0 | 2.147 m³ | 2.146 m³ | 20.10 m³ |
| Internal pressure p1 | 0.577 kN/m² | 0.579 kN/m² | 0.585 kN/m² |
| Volume V1 | 2.142 m³ | 2.135 m³ | 20.04 m³ |
| Height ftop | 0.367 m | 0.346 m | 0.352 m |
| Force ny,top | 0.32 kN/m | 0.44 kN/m | 0.40 kN/m |
| Height fbottom | 0.430 m | 0.429 m | 0.424 m |
| Force ny,bottom | 2.84 kN/m | 2.81 kN/m | 2.81 kN/m |
3.3 Load combination 3: Internal pressure and wind suction, open volume
Below is the tabular comparison with the values in the literature [1].
| Results | analytical | numerical | RFEM 6 |
| Height ftop | 0.475 m | 0.473 m | 0.469 m |
| Force ny,top | 4.80 kN/m | 4.75 kN/m | 4.80 kN/m |
| Height fbottom | 0.40 m | 0.399 m | 0.390 m |
| Force ny,bottom | 1.56 kN/m | 1.56 kN/m | 1.56 kN/m |
3.4 Load combination 4: Internal pressure and wind suction, closed volume
Below is the tabular comparison with the values in the literature [1].
| Results | analytical | numerical | RFEM 6 |
| Internal pressure p0 | 0.3 kN/m² | 0.3 kN/m² | 0.3 kN/m² |
| Volume V0 | 2.147 m³ | 2.146 m³ | 20.10 m³ |
| Internal pressure p1 | 0.02 kN/m² (negative) | 0.0 kN/m² | 0.02 kN/m² |
| Volume V1 | 2.154 m³ | 2.147 m³ | 20.16 m³ |
| Height ftop | 0.447 m | 0.448 m | 0.443 m |
| Force ny,top | 3.55 kN/m | 3.61 kN/m | 3.68 kN/m |
Evaluation
The values from our calculations coincide visibly with only minor deviations with the analytical and numerical values from the literature. The difference in volume is likely due to a small error in the document, where the comma was misplaced.
4. Conclusion
The conducted modelings and simulations show that RFEM 6, with its powerful material models, nonlinear calculation options, and flexible boundary conditions, is excellently suited for the analysis of inflatable structures. Especially with film cushions, both the load-bearing behavior under internal pressure and the interaction between pre-tensioning, material nonlinearities, and geometric stiffness can be realistically mapped. Thus, it is confirmed that RFEM 6 represents a reliable and practice-oriented tool for engineers who wish to plan, evaluate, and optimize complex pneumatic structures.
5. Outlook
The presented methodology for the calculation of film cushions can be prospectively transferred to other pneumatically stabilized structures. Especially air-supported structures exhibit similar physical basic principles: a thin-walled, flexible shell stabilized by internal pressure and subject to highly nonlinear interactions between membrane tensions, geometric changes, and external loads.
By further developing the numerical models - such as extended material laws, coupled fluid-structure interactions, and more precise representation of load changes - even complex air-supported structure designs can be reliably simulated and dimensioned. This includes consideration of dynamic wind loads as well as the analysis of pressure control concepts, leakage scenarios, and erection states.
This opens up a broad range of applications where the insights gained from the film cushion calculation can directly contribute to the optimization, safety, and efficiency of pneumatic lightweight structures.