# Advanced Numerical Analysis of Transport Packaging
Building on this basic work, the technique was refined in two key areas: (1) testing hybrid corrugated board compositions with different fluting and liner materials and (2) enhanced numerical modelling. By examining the effects of these materials on dynamic load resistance, more sustainable and cost-effective packaging options were created without sacrificing strength. This strategy is consistent with the increased emphasis on sustainability in the packaging sector [31; 32], addressing the demand for decreased material consumption and lower prices while retaining superb performance [33; 34]. Augmented numerical modelling is another important area of advancement presented in the paper. Incorporating machine learning methods into the modelling process improved the accuracy of failure site predictions and optimised box geometries in real time. These algorithms were trained utilising large datasets derived from both laboratory tests and simulations, which increased the prediction capacity of the models [15; 16; 34; 35]. This integration enabled the quick customisation of package designs to individual requirements, resulting in maximum performance under dynamic load situations. In addition to these technological improvements, the proposed model employs dynamic, modal, and contact analyses to simulate the packaging deformation and subsequent strength reduction over multiple impact cycles, reflecting real-world conditions more accurately [36; 37; 38; 39]. Traditional dynamic analysis with FEM for VRV testing in the time domain is highly computationally expensive. To address this, we proposed the Power Spectral Density (PSD)-based method [40] to solve a substitute dynamic problem in the frequency domain, providing a solution to the original time-domain problem. The approach for evaluating the dynamic strength of corrugated packaging has been greatly improved by the proposedresearch directions. The performance and longevity of packaging solutions have been enhanced through the use of sophisticated numerical modelling and material optimisation. While enhanced vibration analysis has allowed for a more thorough understanding of package behaviour under real-world situations, the integration of machine learning algorithms has allowed for real-time optimisation and more precise failure predictions. This paper describes a complete method for improving the dynamic strength analysis of corrugated board packaging, with the ultimate goal of creating more effective, sustainable, and dependable packaging solutions for the transportation industry. This research leads to the evolution of packaging technology by utilising material innovation and advanced modelling approaches, and by placing an emphasis on sustainability, ensuring the safe and efficient transportation of goods while minimising environmental impacts. The comprehensive methodology results in a more accurate assessment of packing durability and dependability throughout transportation. Furthermore, in the future, Life Cycle Assessment (LCA) will be included into the package design process. LCA estimates the environmental effect of packaging materials and designs across their full life cycle, from manufacturing to disposal [41; 42]. LCA, combined with dynamic strength analysis, leads to the creation of packaging options that are both strong and ecologically friendly. This guarantees that packaging not only protects goods adequately, but also reduces environmental impacts, in line with global sustainability objectives. However, by incorporating life cycle analysis, packaging solutions are guaranteed to be eco-friendly and satisfy the packaging industry increasing demand for sustainable practises. Apart from the Introduction, the paper is organised as follows: Section 2 introduces the materials and methods, with a workflow of the study (Section 2.1), mechanical tests of the cardboards descriptions (Section 2.2), and an estimation of the packaging resistance to transport loads (Section 2.3). The results of the research are presented in Section 3, and discussed in Section 4.