The Iwan model is composed of elastoplastic elements and is widely used to represent the stiffness degradation of bolted joints under mixed-mode loading (normal and tangential loading). The latest static methods of parameter identification established the relationship between the elastoplastic elements and the contact pressure under normal loading. Under mixed-mode loading, the parameters of the Iwan model are dynamic for the evolution of contact conditions. Therefore, static parameter identification methods are not suitable for the dynamic Iwan model. A new technique was proposed to identify the parameters of the elastoplastic elements in this paper. Firstly, several different finite element models were established. The influence of the contact method and the thread structure were analyzed, and a reliable and efficient bolted-joint modeling method was proposed. Secondly, the evolution of contact conditions was studied. The dynamic elliptical contact model and the ellipticity discrete method were proposed. Finally, the residual stiffness of the Iwan model was analyzed to establish the mapping between the residual stiffness and the bending of the screw. The results can provide a technique for identifying the parameters of the dynamic Iwan model.

The dynamic response of complex equipment under mixed-mode loading is significant for structural design. Bolted joints are the primary connection mode of subsystem assembly, and the degradation of bolted joints may reduce the safety and reliability of the equipment. The Iwan model is widely used to describe the degradation of bolted joints, which has been continuously revised and experimentally verified. The classic Iwan model is a static model that lacks predictive ability. The latest dynamic Iwan model can predict the softening process and reveal the physical mechanism of degradation. However, the function of dynamic pressure distribution needs to be determined for the model solution. We analyzed the contact boundary and pressure distribution under mixed-mode loading with the finite element method (FEM) and proposed the dynamic functions. Secondly, we put forward two correction methods to compensate for the loss of preload caused by simplification and to achieve consistency between the pressure distribution function and the contact boundary function. Finally, the influence of discrete order on the correction of pressure distribution was analyzed. The results show that the constraint method is more suitable for the modification of the pressure distribution. The research results can be applied to the solution of the dynamic Iwan model.

Radio altimetry is important for sensing the near-ground altitude of airborne platforms operating at several-kilometre altitudes. In urban environments, multipath propagation and coherent superposition from buildings and ground surfaces can alter echo delay, energy, and waveform, thereby affecting downstream ranging and altitude-estimation decisions. Conventional echo models often cannot retain the geometric propagation delays, material properties, polarization transformations, and coherent phase relationships of individual scattering components in kilometer-scale three-dimensional scenes, limiting their ability to reconstruct physically consistent time-domain echoes. To address this, this study combines radio-altimetry echo simulation with electromagnetic simulation of urban environments and develops a finite-distance spherical-wave physical-optics method for modeling time-domain echoes in large-scale urban scenes. The method maps the scattering responses of urban surface facets to the received time-domain echo. Representative cases verify the accuracy of calculations of scattering amplitude, range attenuation, and two-way propagation delay. The results show that a uniform material assignment predominantly affects echo amplitude and energy while exerting only a limited influence on the delay structure. In contrast, variations in urban geometry alter the spatial locations and orientations of effective scattering facets and the coherence relationships among their complex fields, resulting in distinct main-peak positions, energy-delay distributions, and early- and late-arriving multipath structures.

As the low-altitude economy develops rapidly, precise radar altimetry is crucial for ensuring the safety and reliability of drone flights. In the context of urban radio detection, the presence of numerous buildings and ground surfaces gives rise to electromagnetic wave multipath propagation. This objective factor gives rise to errors in radar altimetry. Existing channel models often lack the intricate details required to accurately quantify multipath error mechanisms in kilometer-scale complex electromagnetic environments. Therefore, there is an urgent need for a high-fidelity simulation framework. The present study has put forward a pioneering approach to radio altimetry simulation and accuracy assessment in intricate urban environments. The objective of this study is to investigate the impact of multipath propagation on radar altimetry precision. The present study has proposed a novel integration of radar altimetry simulation with kilometre-scale urban electromagnetic simulation models. The simulation of echo signals has been achieved through the utilization of the shooting and bouncing rays (SBR) method and inverse fast Fourier transform (IFFT). A comparative analysis has been conducted based on ranging results from radar systems for different urban models, thereby enabling a mechanism analysis of factors affecting radar altimetry. The study has demonstrated that increased building density and height, along with reduced elevation angles during altimetry, exacerbate ranging errors.