Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150026

150026 - 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, actively aid surgical operations, transition between one stable mechanical configuration to another, and exhibit  tunable mechanical properties. In order to compute the behavior of a structure after its critical point, numerical continuation methods, also known as path-following methods, are used. These computational techniques allow us to study how the response of a structure changes while it transitions from the stable regime to the unstable regime, also known as the 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 Y. Risk-Mora is a Ph.D. student and Graduate Research Assistant in Mechanical Engineering at the University of Texas at San Antonio; he specializes in the study of elastic instability and its applications in designing advanced mechanical systems. His research focuses on leveraging computational techniques such as the finite element method, numerical continuation methods, and HYPercomplex Automatic Differentiation (HYPAD) to analyze and optimize the postbuckling behavior of structures. David also focuses on the field of mechanical metamaterials, applying his expertise in sensitivity analysis and uncertainty quantification to develop innovative solutions for engineering challenges. His work aims to advance the understanding and practical implementation of tunable mechanical properties and stability in engineering designs.

Authors:

David Y. Risk-Mora The University of Texas at San Antonio
Juan D. Navarro The University of Texas at San Antonio
Mauricio Aristizabal The University of Texas at San Antonio
Harry R. Millwater The University of Texas at San Antonio
David Restrepo The University of Texas at San Antonio