Research on strength testing technology for aircraft cargo hold restraint nets

3.1. Modeling scheme

Shell elements were used to model the structural of the barrier nets, with a basic element size of 10 mm, ensuring that the proportion of triangular elements in the overall model is less than 5 %, and the element warping is less than 10. For key areas involving contact, local mesh refinement was performed, with a basic size of 5 mm. The finite element model is shown in Fig. 2, with the load constraint points consistent with the positions of the hooks applied to the barrier net. The model includes 12,628 nodes and 9,811 elements. The 2D element coordinate system is consistent with the overall coordinate system.

Fig. 2Finite element model

The restraint net is constructed from a hyperelastic material with properties listed in Table 1, including a Young’s modulus of 1.20 MPa. The flexible material skin exhibits a fracture strain of 180.5 % and a tensile strength of 2.06 MPa. The Ogden model was employed to characterize the hyperelastic nonlinear behavior of the net, simulating its deformation performance. Engineering empirical parameters were incorporated to enhance the nonlinear analysis. The strain energy function of the Ogden model is expressed as:

where: ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ are the principal stretch ratios (deformed length divided by original length) (${\lambda }_1{\lambda }_2{\lambda }_3=1)$; ${\mu }_i$ and ${\alpha }_i$ are material parameters determined through fitting with existing experimental data; $N$ is the number of model terms, with higher $N$ improving the model’s fidelity to complex deformations. For this study, $N=$ 3.

3.2. Analysis results

The simulated structural deformation of the restraint net aligns closely with physical test results, with displacement errors below 1 % (Fig. 3).

4.1. Loading surface simulation

The deformation of the restraint net is influenced by cargo shape, flexibility, and contact area. In practical applications, the complexity and variability of cargo shapes and deformation behaviors make it impractical to quantitatively analyze their effects on net deformation. Additionally, precisely controlling cargo shape and deformation during testing to match the net’s deformation is technically challenging. Therefore, the experiment focused solely on the contact surface shape of the cargo dummy, designing a loading surface that aligns with the net’s deformation characteristics. Based on the results from virtual experiments (Fig. 4), the loading surface was designed to cover the entire net area.

The projected area of the loading surface perpendicular to the load direction is 2700 mm ×1250 mm, which is too large for fabrication using steel due to excessive weight. Hardwood was chosen as the material because it does not deform under the net’s load and satisfies strength and stiffness requirements. The surface must be sanded smooth to prevent damage to the net straps.

Fig. 3Displacement results

Fig. 4Full-network loading surface

Due to the large size of the loading surface, it was divided into multiple wooden blocks (Fig. 6). Each block was precision-machined via CNC processing and then arranged according to the designed surface profile to form the complete loading surface fixture (cargo dummy). This design ensures that longitudinal load-bearing straps act as primary load-carrying elements, while other straps deform coordinately in response to the main load path.

Fig. 5Full-network cargo dummy fixture

4.2. Constraint point load monitoring

The restraint net, as a flexible structure, is prone to inconsistent deformation among its load-bearing straps under rigid boundary support and the action of a non-deforming cargo dummy fixture. This can lead to excessive loads on primary load-bearing straps, causing premature failure. Additionally, per design requirements, the interface loads at the aircraft fuselage connection points must not exceed 10.8 kN to ensure airframe safety during emergencies. To achieve optimal strength test results, it is critical to identify the optimal installation configuration that enables coordinated deformation of the net.

To quantify constraint point reaction forces and provide a quantitative analysis basis for net adjustment, triaxial force sensors (Fig. 6) were selected to measure the reaction forces at each constraint point. These sensors monitor loads in all three directions with an error margin of ≤ 0.5 %, ensuring precise load distribution analysis.

Fig. 6Triaxial force sensors at constraint points

To ensure the restraint net achieves an optimal installation configuration prior to testing, a suitable adjustment method was employed. This configuration ensures that primary load-bearing straps share loads uniformly and collectively transmit forces to the boundary supports, while minimizing experimental result variability when identical test specimens undergo the same test under the same installation conditions. This process provides a basis for validating the net’s installation and operational performance on aircraft.

5.1. Failure load comparison

The failure loads of 3 test specimens under the forward load scenario are listed in Table 2.

Analysis of Table 2 shows that the failure loads of the three test specimens were closely aligned, with a maximum coefficient of variation of 3.9 %. This confirms the applicability of the adopted test methodology and techniques for evaluating flexible structures like the restraint net.

5.2. Failure mode comparison

All three restraint nets exhibited identical failure modes: fracture of the mounting base at primary load-bearing strap connection points (the mounting base is fixed to the aircraft structure and is not part of the net structure). This caused the straps to detach from the connection points, indicating that the straps themselves met the design strength requirements. The normal failure mode of the restraint net is shown in Fig. 7.

Fig. 7Normal failure mode of the restraint net

5.3. Constraint loads comparison

The interface loads at primary load-bearing strap connection points during failure are presented in Table 3.

Analysis of Table 3 reveals that the interface loads at all primary connection points remained below 10.8 kN during failure, fulfilling the design requirement to protect the air frame structure. The minimal load variation across the three trials demonstrates high test repeatability, validating the universality of the test method.

5.4. Comparison of physical and virtual experiments

In the virtual experiment, a multibody dynamics model of the restraint net was developed using finite element analysis. By applying boundary loads consistent with real cargo scenarios, the simulation predicted a maximum dynamic displacement of 229.5 mm (Table 4). In physical testing, high-precision displacement sensors recorded an actual maximum displacement of 230.1 mm.

The relative error between the two results was only 0.26 %, significantly exceeding the aviation industry’s allowable error threshold for flexible structure validation (≤ 3 %). This confirms that the virtual experiment model accurately predicts the net’s mechanical behavior under extreme conditions, meeting the required model credibility standards.

This validation not only provides a reliable simulation basis for the net’s digital design but also demonstrates the effectiveness of integrating virtual and physical testing methodologies. The precise agreement between simulation and physical results highlights breakthroughs in key technical areas, including boundary condition modeling, material constitutive model selection, and contact algorithm optimization. The outcomes align with design specifications and test requirements.