Session: Research Posters

Paper Number: 112622

112622 - Higher Order Sensitivity Analysis for Elastic Problems Using the Multidual Finite Element Method 

This research work evaluated the accuracy and efficiency of the multidual complex-valued finite element method (ZFEM) in computing higher-order derivatives of output variables with respect to input variables of elastic problems, up to the third order. As Multidual ZFEM is capable of calculating hundreds of multi-order derivatives in a single analysis, the accuracy of the methodology is evaluated in elastic problems by comparing multi-order derivatives of the displacement and stress fields with respect to material, geometric, and loading parameters in a thick-walled cylinder problem under internal pressure. A mesh convergence analysis with standard mesh refinement techniques was performed to determine the convergence rate of the results produced by Multidual ZFEM. The -norm and -norm error between the evaluated analytical solution and the solution produced by Multidual ZFEM revealed that the higher order derivative terms of the output variable of interest converge at a slower rate than the traditional output of the analysis for elastic behavior. Derivatives resulting from geometric perturbations were converging at a slower rate in comparison to derivatives from material or load perturbations. In addition, the results indicated that higher-order derivatives with respect to material parameters are generally more accurate than those relating to geometry, as the geometric derivatives are heavily affected by the perturbation techniques and region. This trend was also observed for mixed derivatives between a variety of different types of input parameters, i.e., mixed derivatives between shape and material parameters. The error present within mixed derivatives is retained from the error of a non-mixed derivatives, and thus derivatives relating to geometry will result in greater error to their non-mixed higher order counterpart. Overall, Multidual ZFEM is capable of calculating accurate derivatives in elastic problems regardless of the type of input parameter in a single analysis in comparison to conventional numerical techniques, such as Finite Difference, which require multiple analyses to determine the appropriate step size of the perturbation of the input variable and Automatic Differentiation, which requires memory reduction techniques and high level, abstract understanding of the subject of interest. The implication of these findings is that there may be an existing limit to where the error of the higher order term may not be acceptable for a desired problem, even with mesh refinement techniques. The higher-order derivatives provided by Multidual ZFEM can be useful in many branches of engineering, including uncertainty quantification, mechanics of solids, reduced order model generation, sensitivity analysis optimization, and structural analysis.

Presenting Author: David Avila University of Texas-San Antonio

Presenting Author Biography: David Avila was born in Brownsville, Texas, on May 30, 1995. They attended Skinner Elementary School, Incarnate Word Academy, and The Science Academy of South Texas. During
high school in 2012, they founded RDA Technologies, an electronics recycling company while
becoming enamored with engineering and space technology under the NASA HAS program. They
graduated Texas A&M University-Kingsville with a cooperative NASA senior project on the installation of electrical bulkheads on the ISS. They received a Bachelor of Science in Mechanical
Engineering with Minors in Nuclear Engineering and Mathematics. They returned to work at RDA
Technologies to expand the company even further and succeeded in completing contracts for local,
state, and federal government agencies. He then pursued his Master’s degree at the University of
Texas-San Antonio in 2019 with the assistance of an NRC Fellowship. They received a Master
of Science Degree in Mechanical Engineering with a concentration in Mechanics and Materials in
August 2022.

Authors:

David Avila University of Texas-San Antonio
Arturo Montoya University of Texas-San Antonio
Harry Millwater University of Texas-San Antonio