Hey there, fellow engineers and math enthusiasts! I’m a graduate student in aerospace engineering, and I’m currently working on a research project that involves sensitivity analysis of the buckling load of cylindrical shells with random geometric imperfections. Specifically, I need to generate random but smooth surface imperfections on cylindrical shells for use in numerical simulations.
My advisor recommended looking into Gaussian random fields (GRFs) and the Karhunen–Loève (K–L) expansion as potential tools for modeling these imperfections. But, I have to admit, I’m struggling to understand the theory behind these methods, particularly how the correlation structure and smoothness are controlled.
That’s why I’m reaching out for help. If you have experience with generating smooth random fields, especially in 2D for curved geometries, I’d love to hear from you. Here are some specific questions I have:
* What are the main methods for generating smooth random fields in 2D for curved geometries?
* What basic probability/statistics and stochastic process concepts should I revisit to understand these methods properly?
* Are there any recommended resources (books, papers, tutorials) for learning GRFs and the Karhunen–Loève expansion with applications in structural mechanics?
If you can offer any guidance or resources, I’d be forever grateful. Thanks in advance for your help!