You're invited to attend the
(Advisor: Prof. Dimitri Mavris)
"Structural Analysis and Optimization of Aircraft Wings Through Dimensional Reduction"
Tuesday, December 15
9:00 a.m. (EST)
Federal Aviation Regulations (FARs) are critical drivers of aircraft design. Early-stage aircraft design involves a tight coupling between structural dynamics, aerodynamics, and flight mechanics, with time-dependent loads arising from the considerations of the FARs. The current state-of-the-art decouples the time-domain simulation from the structural failure computation due to high computational costs associated with time-domain structural failure computation. The need to account for the dynamic loads specified by the FARs while simultaneously achieving low structural weight for fuel efficiency in early-stage aircraft design motivates the following question: How to enable computationally efficient structural analysis and optimization of early-stage aircraft wing design, considering dynamics?
Existing methods simplify the dynamic loads to equivalent static ones and design the structure using shell-based analysis. Other literature approaches use computationally efficient beam models for structural sizing but make assumptions on the geometry and/or material distribution. Higher-order beam theories for structural analysis have been successfully applied to the design of slender structures subjected to time-dependent loads, like rotorcraft blades. While aircraft wings can be considered slender structures, aperiodicity, and inhomogeneity along the span render beam theory ineffective.
The present work aims to bridge this gap by proposing a method for analyzing 3-D structures through dimensional reduction. The use of the Variational Asymptotic Method (VAM) is explored for the systematic reduction of 3-D structures to 1-D models and further, recover 3-D stresses and strains after solving the 1-D problem.
A stiffness matching approach is proposed to dimensionally reduce 3-D features such as stiffeners by locally smearing them on the base plate. The proposed method allows for stiffeners of varying dimensions, topology, and spacing to be smeared. The stiffness matching further allows the beam cross-sectional properties computed from VAM to be equal to a box-beam cross-section. The equivalence enables the use of Euler-Bernoulli type analytical stiffness computation while retaining the accuracy of VAM. Analytical expressions allow for rapid evaluation of the beam properties and stress recovery and further permit the use of Automatic Differentiation (AD) to obtain partial derivatives. The proposed structural analysis method is applied to the wing structural analysis of a novel distributed electric propulsion aircraft- NASA's PEGASUS concept, and the open-source CRM.
A general adjoint method for dynamic simulations is presented and applied to a nonlinear Timoshenko beam theory. It combines general beam residual equations with an adjoint method to extract gradient information from the load time-history. Aggregated constraints implemented for sizing are stress-based, combining axial stresses at the beam corners with shear stresses from torsion and external loads at both corners and mid-sections. CasASDi, an open-source tool for nonlinear optimization and algorithmic differentiation, is used to generate expressions and calculate derivatives for the relevant equations used for analysis and optimization. Numerical tests are conducted to test the accuracy of the adjoint computations and scalability as the number of design variables increase. A structural optimization framework is developed for the beam-based dynamic analysis method presented, allowing for the structure's sizing under strength-based failure considerations. The PEGASUS concept is used as a testbed to demonstrate the sizing capabilities. The structure is sized for FARs specified maneuver loads– static 2.5g and -1.0g, and dynamic gusts.
Findings show that: 1) the use of VAM allows for the systematic extraction of beam properties for aircraft wings, 2) the displacement and stress response of the aircraft using beam models match reasonably well against those produced by shell-based models, 3) for dynamic simulations, the derived adjoint method computes accurate gradients efficiently to be used in structural optimization, 4) sizing of aircraft wings for FARs specified maneuvers using the proposed approach produces a 6% error compared to the shell-based method, but with a 7.8x speed-up.
The proposed approach provides improvements on the existing literature methods- it is computationally efficient, provides reasonable accuracy for early-stage structural sizing and weight prediction, and includes dynamic effects. The computational efficiency makes it well-suited for many-query applications like optimization, uncertainty quantification, and generating data for surrogate modeling.
- Prof. Dimitri N. Mavris – School of Aerospace Engineering (advisor)
- Prof. Dewey H. Hodges – School of Aerospace Engineering
- Prof. Graeme J. Kennedy – School of Aerospace Engineering
- Dr. Jason A. Corman – School of Aerospace Engineering
- Mr. Robert Wm. Martin – Federal Aviation Administration