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Topology optimization methods for structures subjected to random excitations are difficult to widely apply in aeronautic and aerospace engineering, primarily due to the high computational cost of frequency response analysis for large-scale systems. Conventional methods are either unsuitable or inefficient for large-scale engineering structures, especially for structures consisting of multi-materials with non-proportional damping systems. To address this challenge, an accurate and highly efficient reduced-order method (ROM) based on the second-order Krylov subspace and the multigrid method is proposed in this paper, which is applicable to non-proportional damping systems. Moreover, a novel multigrid reduced-order topology optimization scheme for structures subjected to stationary random excitations is proposed based on the pseudo-excitation method (PEM). Two 3D numerical examples demonstrate the accuracy and efficiency of the proposed scheme for multi-material topology optimization. For a cantilever beam with about 6.7 × 10 5 degrees of freedom (DOFs), compared against the original reduced-order method, the efficiency of pseudo-harmonic analysis of the multigrid reduced-order method is improved by about 91% with sufficient accuracy, and the efficiency of the whole optimization process of the multigrid reduced-order method is improved by more than 71%. For a pedestal structure with about 3.5 × 10 5 DOFs, compared against the original reduced-order method, the efficiency of pseudo-harmonic analysis of the multigrid reduced-order method is improved by about 61%. [ABSTRACT FROM AUTHOR]

In surrogate-based optimization (SBO), the recognized issues associated with the high-dimensional surrogate models focus on the prohibitive computational costs and the low model accuracy. However, there is a lack of effective solutions in the face of the ‘curse of dimensionality’. In this paper, we propose a novel Kriging metamodel to remedy this deficiency. The Kriging model based on projection correlation (KPC) introduces the projection correlation into the Kriging modeling process as prior information, taking into account the nature of hyperparameters. The effectiveness and accuracy of the KPC are illustrated through 10–70-dimensional numerical examples. Furthermore, a parallel computing strategy that combines the multi-peak characteristics of expected improvement and minimizing prediction (MEI&MP) is proposed to further improve high-dimensional optimization efficiency and potential. The global performance and optimization efficiency of our method are validated via typical test functions and structural optimization problems. [ABSTRACT FROM AUTHOR]

Grid-stiffened structures are widely used in industrial equipment, where the layout of stiffener unit cells is critical in the structural performance. However, owing to the lack of design techniques, existing stiffener unit cell designs are often achieved only by comparative selection among several common cell configurations. In this study, a deep learning-based intelligent optimization framework for the stiffener unit cell of grid-stiffened panels was proposed. First, a database containing nearly 10,000 stiffener unit cells was generated by traversal while considering the manufacturability. Feature extraction was then performed on the generated database using a variational autoencoder and mapped to a 16-dimensional continuous latent design space according to geometric features. Subsequently, in this latent space, a Gaussian process model was established, and the maximum expected improvement criterion was utilized to drive the model update and optimization search, thus realizing data-driven optimization for the stiffener unit cell of grid-stiffened panels. In three typical numerical examples, compared with the best of the traditional stiffener unit cells, the obtained optimal designs were improved by 25.61%, 25.88%, and 10.66%, respectively, demonstrating the effectiveness of this method as an alternative stiffener unit cell design method. Furthermore, this study also indicates the significant potential of geometric feature extraction and further structural layout optimization via deep learning. [ABSTRACT FROM AUTHOR]

The huge computational cost is a main barrier of structural reliability assessment for complex engineering. Surrogate models can release the CPU burden of reliability assessment, however, it is very challenging to guarantee the prediction accuracy of failure probability. In this study, we propose an Adversarial Learning-Based Kriging model (ALBK), where two models learn from and compete with each other to achieve an improved model accuracy. First, the initial models are established, and fitting accuracy is evaluated by each other with the proposed criterion. Then, the modeling parameters are optimized according to the evaluation results. The data-driven criteria and adversarial relationship promote the evolution of modeling parameters. Moreover, a triple-indicator method is provided to choose the final model and avoid oscillation. The ALBK adjusts modeling parameters with alternative evolution, while the predicted values are more accurate than those of Kriging. Finally, an adaptive ALBK method is provided with new samples added to improve the accuracy of reliability assessment. Through several numerical examples, it can be seen that the ALBK always provides the best results with the fewest assessment calls, and the robustness is also good. [ABSTRACT FROM AUTHOR]

Stiffened plates are widely used in aerospace structures as load-bearing components. In order to obtain a novel design of stiffened structures with excellent performance, a generative design method of stiffened plates (GDMSP) based on the homogenization method is proposed in this paper, which optimizes the stiffener layout based on an equivalent model. Then, the detailed model can then be obtained by extracting the stiffener path from the discrete distribution of stiffener angles. Moreover, the optimized design can be obtained by size optimization based on the detailed model. Two examples are used to illustrate the proposed framework, including the stiffness maximization of a rectangle stiffener plate and the buckling load maximization of a square stiffener plate. The optimized stiffener configurations are characterized by streamlines and uniform lines, respectively. For the first example, the stiffness of the stiffener design has an improvement of 17%. For the second example, the optimized design improves the buckling load by 35%. Results indicate that the proposed method can effectively provide a novel generative design for stiffened plates. Moreover, the obtained results have a clear stiffener path and have a noticeable improvement in performance, which can be directly used to establish a detailed model. [ABSTRACT FROM AUTHOR]

In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling, or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle. [ABSTRACT FROM AUTHOR]

Multi-fidelity surrogate (MFS) method is very promising for the optimization of complex problems. The optimization capability of MFS can be improved by infilling samples in the optimization process. Furthermore, once the gradient information is provided, the gradient-enhanced kriging (GEK) can be utilized to construct a more accurate MFS model. However, for the existing infill sampling criterions, it is difficult to improve the optimization speed without sacrificing the optimization gains. In this paper, a novel infill sampling criterion named Adaptive Multi-fidelity Expected Improvement (AMEI) is proposed, in which the prediction accuracy and the optimization potential of the surrogate model are both considered. With a set of extra samples calculated, the AMEI determines which fidelity model for the new sample is to be added. Through two numerical examples and two engineering examples, it can be found that the AMEI always provides the best optimization result with the fewest analysis calls, and the robustness is also good. The optimization capability and efficiency of the AMEI have been demonstrated compared with traditional criterions. [ABSTRACT FROM AUTHOR]

To resist external pressure, stiffened spherical domes have been widely used in underwater vehicles. In traditional design of these thin-walled structures, uniform stiffeners are usually utilized and overly conservative safety factor method is employed to envelop the multi-source uncertainties mainly caused by manufacturing. In this study, a concept of non-uniformly stiffened spherical dome (NUSPD) is developed to improve the structural buckling capacity. Furthermore, an efficient reliability-based design optimization (RBDO) framework is established for NUSPD, which includes a deterministic optimization loop to fix the stiffener layout, and subsequently followed by a RBDO loop to determine the detailed stiffener dimensions and decrease the structural weight under geometric and material property uncertainties. Since the RBDO of stiffened spherical domes is very complex, an improved enhanced chaos control method together with surrogate model is proposed to improve the convergence rate. Finally, the efficiency of the proposed RBDO framework is demonstrated by the NUSPD example. [ABSTRACT FROM AUTHOR]

Variable-stiffness panel is very promising for the cutout reinforcement of composite structures. However, due to the increase of design variables, the optimization of variable-stiffness panels becomes very challenging, even if surrogate model is utilized, because the fidelity of surrogate model is difficult to guarantee for high-dimensional problems. In this study, isogeometric analysis method (IGA) is employed to predict the buckling load of variable-stiffness panels, which can produce accurate prediction with less computational cost compared to traditional FEA, moreover, it can provide analytical sensitivity for optimization. On this basis, an adaptive gradient-enhanced kriging (GEK) model assisted by a novel multiple points infilling criterion is constructed for the global optimization of variable-stiffness composite panels. The proposed method is compared with traditional surrogate model, and results show that the proposed method can find a better optimum design in a more efficient manner. It can be concluded that the proposed method is able to fully explore the advantages of IGA including exact modelling, analysis and analytical sensitivity, which is particularly suitable for the design of variable-stiffness panels and other complex structures. [ABSTRACT FROM AUTHOR]

Reliability-based design optimization (RBDO) has been widely implemented for engineering design optimization when considering the uncertainty. The single loop approaches (SLA) are highly efficient but is prone to converge with inappropriate results for highly nonlinear probabilistic constraints. In this paper, a novel RBDO algorithm is proposed based on single loop approach and the enhanced chaos control method, named as enhanced single-loop method (ESM). The performance of SLA is enhanced using an adaptive inverse reliability method with limited number of iterations. The adaptive step size is computed based on a merit function which is computed using the results of the new and previous iterations. The iterations of the probabilistic constraints of RBDO models are manually controlled in the range from 1 to 10 in ESM. The efficiency and accuracy of the ESM are compared through four nonlinear RBDO problems with complex constraints, including a nonlinear mathematical problem, two engineering problems and a practical complex stiffened panel example with complex buckling constraint for aircraft design. Results illustrate that the proposed ESM is more efficient and robust than the performance measure approach and reliability index approach for RBDO problems. [ABSTRACT FROM AUTHOR]

For tailoring the non-uniform axial compression, each sub-panel of stiffened shells should be designed separately to achieve a high load-carrying efficiency. Motivated by the challenge caused by numerous variables and high computational cost, a fast procedure for the minimum weight design of non-uniform stiffened shells under buckling constraint is proposed, which decomposes a hyper multi-dimensional problem into a hierarchical optimization with two levels. To facilitate the post-buckling optimization, an efficient equivalent analysis model of stiffened shells is developed based on the Numerical Implementation of Asymptotic Homogenization Method. In particular, the effects of non-uniform load, internal pressure and geometric imperfections are taken into account during the optimization. Finally, a typical fuel tank of launch vehicle is utilized to demonstrate the effectiveness of the proposed procedure, and detailed comparison with other optimization methodologies is made. [ABSTRACT FROM AUTHOR]

In the reliability-based design optimization (RBDO), the Advanced mean value (AMV) method sometimes yields unstable results such as chaotic and periodic solutions for highly nonlinear probabilistic constraints. The chaos control (CC), modified chaos control (MCC) and adaptive chaos control (ACC) methods are more robust than the AMV but inefficient for some moderately nonlinear performance functions. In this paper, a self-adaptive modified chaos control (SMCC) method is developed based on a dynamical control factor to improve the efficiency of MCC for reliability analysis and RBDO. The self-adaptive control factor is dynamically computed based on the new and previous results. The efficiency and robustness of the proposed SMCC are compared with the AMV, CC, MCC and ACC methods using several nonlinear structural/mathematical performance functions and RBDO problems. The results illustrate that the SMCC is more efficient than CC, MCC, and ACC methods, and also more robust than AMV method for highly nonlinear problems. [ABSTRACT FROM AUTHOR]

This note presents an inverse design methodology of metal nanostructures for localized surface plasmon resonances, based on the topology optimization approach. Using the proposed method, determination of the metal distribution in nanostructures is implemented for surface enhanced Raman spectroscopy to maximize the enhancement factor. The obtained results demonstrate that the outlined approach can be used to design metal nanostructure with resonant peak and significant enhancement factor at specified incident wavelength, and to control the shift of the resonant peak by topologically optimizing the nanostructure. [ABSTRACT FROM AUTHOR]

In this study, a two-stage optimization framework is proposed for cylindrical or flat stiffened panels under uniform or non-uniform axial compression, which are extensively used in the aerospace industry. In the first stage, traditional sizing optimization is performed. Based on the buckling or collapse-like deformed shape evaluated for the optimized design, the panel can be divided in sub-regions each of which shows characteristic deformations along axial and circumferential directions. Layout optimization is then performed using a stiffener spacing distribution function to represent the location of each stiffener. A layout coefficient is assigned to each sub-region and the overall layout of the panel is optimized. Three test problems are solved in order to demonstrate the validity of the proposed optimization framework: remarkably, the load-carrying capacity improves by 17.4 %, 66.2 % and 102.2 % with respect to the initial design. [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shells subjected to axial compression are sensitive to initial geometrical imperfections. Firstly, the influence of a single dimple imperfection on the load-carrying capacity of cylindrical shells is investigated by varying the amplitudes, directions and positions of the dimple imperfection. Then a single delta function is introduced to describe the profile of the dimple imperfection in a more general form, which enables to analyze conveniently the effect of the imperfect zone area on the load-carrying capacity of cylindrical shells. Thereafter, a surrogate-based optimization framework of determining the worst realistic imperfection is proposed to study the reduction of the buckling load of cylindrical shells based on a finite number of dimple imperfections. The possible dimple imperfections may be introduced during the service of cylindrical shells. Finally the effectiveness of the present method is demonstrated by an illustrative example. [ABSTRACT FROM AUTHOR]