Session: 12-09-01: Instabilities in Solids and Structures

Paper Number: 142600

142600 - Unlocking Insights in the Post-Buckling Behavior of Mechanical Systems: Efficient Sensitivity Analysis via Hypad-Fem 

Leveraging the nature of elastic instability has allowed researchers to design unique structures that can perform different tasks, e.g., matching target shapes, terrestrial and aquatic locomotion, transition between one stable mechanical configuration to another, and exhibit tunable mechanical properties. This is done by studying and tailoring the response while transitioning from the stable regime to the unstable regime, also known as postbuckling behavior. In the previously mentioned work, it is common to see design methods relying on intuition or trial and error of the model properties until the desired postbuckling behavior is found; which can be time-consuming and inefficient. Additionally, elastic instability is a naturally nonlinear and chaotic phenomenon which results the postbuckling behavior having high sensitivity to defects or variations in certain model parameters. Therefore, the key to tailoring postbuckling behaviors for various applications, quantifying the local effect of defects, and performing global sensitivity analysis can all reduce to finding accurate, high-order, partial derivatives of these nonlinear postbuckling models.

We will introduce a new computational approach for quantifying both local and global sensitivity analyses in geometrically nonlinear mechanical systems that is accurate, efficient, and of arbitrary order. This methodology allows for the solution of a sequence of linear systems of equations to sequentially determine new orders of sensitivities as post-processing of the actual Finite Element Method (FEM) analysis. Our approach is based on the Hypercomplex Automatic Differentiation (HYPAD) method, which enables the computation of highly accurate estimates of arbitrary-order sensitivities related to shape, material properties, or loading conditions for any model parameter, eliminating dependency on step size.

The availability of highly accurate local sensitivities enables a new, fast moment-based approach to Uncertainty Quantification (UQ) for assessing the global sensitivities of mechanical systems. This innovative UQ method approximates the statistical moments of the simulation outputs, offering a measure of statistical importance through Sobol indices, which indicate the proportion of output variance explained by the variance of each input variable. These probabilistic sensitivities provide a comprehensive understanding of the critical parameters influencing the post-buckling behavior of mechanical systems. Existing methods for obtaining global sensitivities face significant drawbacks, such as reliance on polynomial chaos or design of experiment techniques that limit the number of parameters evaluated, or dependence on Monte Carlo sampling of simplified or surrogate models, which compromises accuracy. In contrast, our method integrates HYPAD-FEM with a rapid moment-based UQ technique, leveraging the high fidelity of a finite element model to yield previously unattainable information in a single simulation

Presenting Author: David Y. Risk-Mora The University of Texas at San Antonio

Presenting Author Biography: David Risk is currently conducting his Ph.D. in Mechanical Engineering at the Klesse College of Engineering & Integrated Design (KCEID) at the University of Texas at San Antonio. Before this he obtained his bachelor's degree in Mechanical Engineering from the Universidad Autónoma de Manizales in 2021. David's is part of the Advanced Materials and Mechanical Systems Laboratory (AMMS Lab) in the Department of Mechanical Engineering at The University of Texas at San Antonio. His research focuses on the development of a computational framework for conducting local and global sensitivity analysis of the post-buckling of mechanical systems. Moreover, this requires the integration of computational simulations, theoretical analysis, and experimental design to verify and validate these frameworks.

Authors:

David Y. Risk-Mora The University of Texas at San Antonio
Melvin Hernandez The University of Texas at San Antonio
Mauricio Aristizabal The University of Texas at San Antonio
Harry Millwater The University of Texas at San Antonio
David Restrepo The University of Texas At San Antonio