Structural and Multidisciplinary Optimization最新文献

Over the past decade, advances in MDO have enabled the aerodynamic and structural design of aircraft wings to be simultaneously optimized using high-fidelity models. Using RANS CFD and detailed structural finite element models in these optimizations enables an accurate trade-off between cruise drag and structural mass. Modeling the coupling of aerodynamics and structures allows the optimizer to aeroelastically tailor the wing, taking advantage of flexibility for improved performance. These capabilities make MDO a key enabling technology for the next generation of flexible and efficient high-aspect-ratio transport aircraft. However, as their aspect ratios increase, these wings increasingly exhibit geometrically nonlinear behavior that linear structural analysis methods cannot model. This work demonstrates the first simultaneous optimization of a wing's aerodynamic shape and structural sizing using high-fidelity geometrically nonlinear models. To enable this we implement a novel geometrically nonlinear shell element, an efficient nonlinear solver, and a constitutive model for stiffened shells. We then couple these nonlinear structural analysis tools to CFD through a geometrically nonlinear transfer scheme. Using these capabilities, we optimize a single-aisle commercial transport aircraft wing with 547 design variables and 1277 constraints. Although the optimized designs exhibit extreme flexibility-an aspect ratio above 19 and deflections exceeding 30% semispan-geometric nonlinearity has minimal impact on aerodynamic performance, planform design, and overall aircraft mass. However, the Brazier effect causes internal loads that linear analysis misses, requiring geometrically nonlinear analysis to produce a feasible design. The developed framework enables the pursuit of next-generation high-aspect-ratio wing designs by providing the computational foundation needed to exploit extreme wing flexibility as a design opportunity rather than a constraint.

Automated fiber placement (AFP) has made it possible to vary the steering angle along curvilinear fiber paths, thus improving mechanical performance compared to traditional composite materials. Variable-angle tow (VAT) or variable-stiffness composites (VSC) have been developed to enhance structural performance through material optimization and effective load-bearing configurations. These advanced materials contribute to achieving optimal performance while reducing the weight of aircraft and aerospace structures. However, defects such as gaps and overlaps may arise during the manufacturing process. Whereas the latter increases local thickness, the former causes resin-rich areas within each lamina. The mass and structural optimization of this kind of structure is challenging as it combines discrete and continuous design variables, namely the number of layers and the fiber path parameters, where the latter influence the presence of defects within the laminate. To tackle this optimization problem, this work proposes a mixed-integer strategy specifically designed to select the least-weight design of a VAT laminate while also fulfilling requirements on the first natural frequency and buckling load while accounting for the manufacturing signature of the AFP process. This study combines the Carrera unified formulation (CUF) and the defect layer method (DLM) to model the VAT laminates and incorporating the fabrication defects. The research has two main aims: (i) to determine the minimum number of layers required to satisfy the fundamental frequency and buckling constraints, considering the manufacturing signature, and (ii) to investigate the influence of the selected structural theory on the optimal design solutions.

Bayesian Optimization (BO) is a foundational strategy in engineering design optimization for efficiently handling black-box functions with many constraints and expensive evaluations. This paper introduces a novel constraint-handling framework for Bayesian Optimization (BO) using Prior-data Fitted Networks (PFNs), a foundation transformer model. Unlike traditional approaches requiring separate Gaussian Process (GP) models for each constraint, our framework leverages PFN's transformer architecture to evaluate objectives and constraints simultaneously in a single forward pass using in-context learning. Through comprehensive benchmarking across 15 test problems spanning synthetic, structural, and engineering design challenges, we demonstrate an order of magnitude speedup while maintaining or improving solution quality compared to conventional GP-based methods with constrained expected improvement (CEI). Our approach particularly excels at engineering problems by rapidly finding feasible, optimal solutions. This benchmark framework for evaluating new BO algorithms in engineering design will be published at https://github.com/rosenyu304/BOEngineeringBenchmark.

A novel geometry parameterisation method constructed from a volume-of-solid driven cellular automata is presented. The method is capable of describing complex geometry of arbitrary topology using a set of volume-of-solid parameters applied to a geometry control mesh. This is done by approximating the smooth geometry of minimum surface area subject to a set of localised constraints on contained volume defined by both the control mesh and volume-of-solid parameters. Localised control mesh refinement is possible through splitting of control mesh cells to provide additional degrees of freedom where necessary. The parameterisation is shown to reconstruct over 98% of a library of aerofoil geometries to within a standard wind tunnel-equivalent geometric tolerance, and to recover known analytical optima in supersonic flow. Using gradient-free optimisation methods, the parameterisation is then shown to construct aerodynamic geometries consisting of multiple objects to package a set of existing geometries. Finally, the parameterisation is used to construct an optimal supersonic multi-body geometry with less than half the drag of the equivalent volume optimal single body.

Truss layout optimization and continuum topology optimization are both well-established methods, with each having a wide range of applications. Whereas truss layout optimization is best suited for low volume fraction problems (i.e. where the optimal structure occupies a low proportion of the original design domain), continuum topology optimization is best suited for medium and high volume fraction problems. However, real-world design problems often include both high and low volume fraction regions. To address this, a two-step hybrid optimization approach is proposed. First, low and high volume fraction regions are identified within a problem. These are then populated with truss and continuum elements respectively, which are connected via suitable interfaces. The combined optimization formulation is conic, and can be efficiently solved using interior point solvers. Numerical examples are presented to demonstrate the efficacy of the proposed approach. The results show that the approach is capable of identifying structures which contain a mixture of length scales, incorporating both bulk continuum regions and fine truss elements.

The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and to accurately compute response quantities such as the von Mises stress. Therefore, the computational cost of solving a fine-mesh topology optimization problem quickly adds up. To address this challenge, we consider a multi-level adaptive refinement and coarsening strategy based on configurational forces. Configurational forces based on the Eshelby stress predict configurational changes such as crack propagation or dislocation motion. Due to a relaxation in the calculation of (Eshelby) stresses with respect to the design variables, discrete configurational forces increase not only in highly stressed regions, but also in gray transition regions (design boundaries). For this reason, they constitute an ideal criterion for mesh adaptivity in topology optimization, especially when avoiding stress failure is a priority. By using configurational forces for refinement, we obtain a high-resolution structure where the refined mesh is present along the design boundaries as well as in stress-critical regions. At the same time, multi-level coarsening using the same criterion drastically minimizes the computational effort.

A novel feature mapping topology optimization method is presented, allowing for the creation of features with highly flexible shapes. The method easily integrates with conventional density-based formulations. Feature shapes are implicitly described by NURBS control points. The feature shape dictates the locations of two sets of projection points to represent the solid void boundaries. At these projection points, density values are projected onto a finite element mesh. The method optimizes feature shapes in a gradient-based manner, while allowing more specific control of the feature shapes than classical level set methods. Several feature fields can be combined to create a final output design. It is found that the eminent flexibility of the NURBS-based feature definition is a benefit but also requires additional regularization to guarantee stability of the optimization.

This paper investigates a novel approach to efficiently construct and improve surrogate models in problems with high-dimensional input and output. In this approach, the principal components and corresponding features of the high-dimensional output are first identified. For each feature, the active subspace technique is used to identify a corresponding low-dimensional subspace of the input domain; then a surrogate model is built for each feature in its corresponding active subspace. A low-dimensional adaptive learning strategy is proposed to identify training samples to improve the surrogate model. In contrast to existing adaptive learning methods that focus on a scalar output or a small number of outputs, this paper addresses adaptive learning with high-dimensional input and output, with a novel learning function that balances exploration and exploitation, i.e., considering unexplored regions and high-error regions, respectively. The adaptive learning is in terms of the active variables in the low-dimensional space, and the newly added training samples can be easily mapped back to the original space for running the expensive physics model. The proposed method is demonstrated for the numerical simulation of an additive manufacturing part, with a high-dimensional field output quantity of interest (residual stress) in the component that has spatial variability due to the stochastic nature of multiple input variables (including process variables and material properties). Various factors in the adaptive learning process are investigated, including the number of training samples, range and distribution of the adaptive training samples, contributions of various errors, and the importance of exploration versus exploitation in the learning function.