Thin-walled structures are susceptible to damages and malfunctioning due to initial geometrical imperfections emanating from the manufacturing processes. If not handled properly, these geometric imperfections can significantly affect the buckling load and reduce the load-carrying capacities of the structures. Considering the continuous increase in the application of thin-walled plates in various lightweight construction, effective buckling analysis of thin-walled structures is highly desirable. These approaches should take into account the uncertain nature of the geometric imperfections. However, a major challenge in the analysis of the buckling behavior of thin-walled structures is the difficulty in quantifying the uncertain shape of geometric imperfections.
In practical applications, dimensions tolerances of the relevant manufacturing process have been used in the identification of the variations bound in plate thickness resulting from uncertain imperfections. In line with this, the interval-field technique has been developed to describe the uncertainties based on the interval factors. Unfortunately, this technique is only suitable for only one-dimensional structure analysis. This is why buckling analysis of thin-walled structures with bounded field uncertainties has attracted significant research attention.
Recently, Dr. Yangjun Luo, Junjie Zhan, and Pai Liu from the Dalian University of Technology proposed a new systematic buckling assessment method for thin-walled plates with initial geometrical imperfections. This approach is fundamentally based on a non-probabilistic description of bounded field uncertainties, as a convenient alternative for probabilistic random field presentation of the uncertainties. The research work is currently published in the journal, Thin-Walled Structures.
Briefly, the research team represented the bounded field uncertainty as a function of reduced uncorrelated uncertain coefficients using the non-probabilistic series expansion of geometrical imperfections. Next, the buckling problem of thin-walled plates was constructed and its feasibility in minimizing the critical buckling load under non-probabilistic field description of imperfections and volume constraints of plates was assessed. Finally, a standard gradient-based algorithm with adjoint-variable sensitivity analysis was used to solve the optimization problem.
Results showed the capability of the gradient-based algorithm to efficiently solve the proposed buckling assessment model with convex set constraints. As proof of the concept, the method was used to evaluate the critical buckling loads of two thin-walled structures to determine their worst-case imperfection patterns. The lowest buckling load factor was observed to increase as the distribution surface of thickness imperfections became smoother. Additionally, the relationship between the buckling load and the material volume fraction was illustrated. For instance, the correlation length exhibited a remarkable effect on the buckling load factor thus demonstrating its critical role in assessing the lowest buckling load of a thinned walled plate. On the other hand, the worst-case critical buckling mode with thickness imperfections varied with material fraction volume and the patterns were different from those of perfect structures.
In summary, a novel optimized strategy is introduced to evaluate the critical buckling load of thin-walled plates with uncertain initial imperfections. The numerical examples presented revealed the importance of taking into consideration the initial thickness imperfection during buckling analysis. Based on the results, Dr. Yangjun Luo in a statement to Advances in Engineering noted that the non-probabilistic field model is a promising approach for critical buckling analysis in thin-walled structures which will henceforth expand their applications.
Luo, Y., Zhan, J., & Liu, P. (2019). Buckling assessment of thin-walled plates with uncertain geometrical imperfections based on non-probabilistic field model. Thin-Walled Structures, 145, 106435.