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Abstract: Abstract This paper compares four methods for formulating stability constraints in topology optimization with geometric nonlinearity. The methods are: a direct approach to compute the critical load factor, an approximation using an eigenvalue analysis at a load factor of 1, a new method based on an eigenvalue analysis at the constraint limit load factor, and an implicit method based on stiffness reduction, which has not previously been investigated for stability constraint formulation. These four methods are described in detail and then compared qualitatively and quantitatively (including optimization examples) in terms of accuracy, robustness, and computational efficiency. The results show that formulating the constraint using an eigenvalue analysis at a load factor of 1 is the most robust approach, as it is least likely to experience mode switching or mode skipping during optimization, which leads to poor convergence for the other three methods. It is also the most efficient, as it only requires a single eigenvalue solve, whereas other methods require additional linear solves to compute the constraint value. However, an eigenvalue analysis at a load factor of 1 only approximates the critical load factor, which may be over, or under-estimated. Therefore, none of the methods fully satisfy the criteria of accuracy, robustness, and efficiency, highlighting the need for further research, e.g., by improving the accuracy of the method based on an eigenvalue analysis at a load factor of 1, or by improving the robustness and efficiency of the direct approach. PubDate: 2023-12-05
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Abstract: Abstract This paper proposes a new fully automatic computational framework from continuum structural topology optimization to beam structure design. Firstly, the continuum structural topology optimization is performed to find the optimal material distribution. The centers of the elements (i.e., vertices) in the final topology are considered as the original model of the skeleton extraction. Secondly, the Floyd-Warshall algorithm is used to calculate the geodesic distances between vertices. By combining the geodesic distance-based mapping function and a coarse-to-fine partition scheme, the original model is partitioned into regular components. The skeleton can be extracted by using edges to link the barycenter of the components and decomposed into branches by identified joint vertices. Each branch is normalized into a straight line. After mesh generation, a beam finite element model is established. Compared to other methods in the literature, the beam structures reconstructed by the proposed method have a desirable centeredness and keep the homotopy properties of the original models. Finally, the cross-sectional areas of members in the beam structure are considered as the design variables, and the sizing optimization is performed. Four numerical examples, both 2D and 3D, are employed to demonstrate the validity of the automatic computational framework. The proposed method extracts a parameterized beam finite element model from the topology optimization result that bridges the gap between the topology optimization of continuum structures and the subsequent optimization or design that enables a fully automatic design of beam-like structures. PubDate: 2023-11-29
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Abstract: Abstract This paper presents an efficient MATLAB code for the discrete adjoint-based level set method, which is compact and provided for 2D stress-constrained problems. The discrete adjoint-based level set method inherits the implicit representation of standard level set methods, but advances the design boundaries using discrete adjoint sensitivities instead of shape derivatives. This proposed method allows for the application of general mathematical programming algorithms, which can be conveniently extended to handle multiple constraints. The Method of moving asymptotes (MMA) is chosen as the mathematical programming solver. Three typical stress-constrained volume minimization problems are presented to verify the effectiveness of the proposed level set code. The MATLAB code presented in this paper can be extended to resolve different 2D topology optimization problems. Overall, the presented MATLAB code provides a useful tool for researchers and engineers working on stress-constrained 2D topology optimization problems with level set method. The MATLAB code used in this work can be downloaded from: https://github.com/denghaopitts/Level-set-topology-optimization and is intended for educational purposes only. PubDate: 2023-11-29
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Abstract: Abstract In this paper, a co-optimization design method for thermal-stress coupling 3-dimensional integrated system with through silicon via is proposed based on the finite element method, support vector machine model and modified particle swarm optimization algorithm. In the cause of analyzing the effects of geometrical parameters (radius of through silicon via, oxide thickness and the height of oxide insolation layer) on the thermal-stress distribution, the finite element method based COMSOL software is conducted to simulate the thermal-stress coupling 3-dimensional integrated system. Based on the simulation data obtained by COMSOL, the support vector machine models are adopted to establish the database for describing the relationships between the geometrical parameters and key indexes (peak temperature, peak stress and temperature difference) to improve the design efficiency. Based on the desired key indexes of thermal-stress coupling 3-dimensional integrated system, the multi-objective evaluation function is formulated. Then, the geometrical parameters are optimized by the modified particle swarm optimization algorithm. The finite element simulation is conducted to verify the effectiveness of the proposed strategy. In three cases, the errors between the simulated and desired temperature differences are all less than 0.28 K, and the relative errors between the simulated and desired peak temperature/peak stress are all less than 4.78%, which indicates that the geometrical parameters can be optimized to control the key indexes of thermal-stress coupling 3-dimensional integrated system. Therefore, the developed method can be used in the design and manufacture of 3-dimensional integrated system. PubDate: 2023-11-29
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Abstract: Abstract The structural characteristics of a Body Weight Support System (BWSS) significantly influence the rehabilitation effect and control system of a lower-limb robot. This study considers vibration characteristics to design and optimize a BWSS. First, the design principles of the BWSS are formulated, and the force of the system during the rehabilitation training process is analyzed. Second, the BWSS optimization model is established by considering the vibration characteristics, including the design object, selected materials, design variables, optimization objective functions and constraints in static and dynamic analyses. Third, a hybrid multi-objective optimization method combining the finite element method, Kriging metamodel and Multi-Objective Genetic Algorithm (MOGA) is proposed. After performing optimization, the Kriging metamodel is discussed, and the final design parameters of a single-arm support structure are obtained by the MOGA. Finally, different MOGA parameters and the screening algorithm are compared and analyzed. Simultaneously, the experimental vibration acceleration data and the shock data of the actual original rehabilitation robot are compared with the numerical results of the optimized design. The numerical results indicate that the proposed hybrid multi-objective optimization method is reliable in terms of designing the BWSS, and the vibration characteristics of the designed BWSS are improved over those of the actual original BWSS. PubDate: 2023-11-28
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Abstract: Abstract A finite element model of a thin-walled square tube is developed for evaluating its crushing performance. The axial crushing behavior of the square tube is experimentally evaluated, and the obtained force–displacement responses are applied to estimate the accuracy of the model. The validated model is subsequently used to study the crushing performances of the polygonal single and double tubes under different angle loadings. It is shown that the double tube has higher specific energy absorption and energy absorption capacity under axial and small-angle oblique loadings. However, the energy absorption characteristics of the double tube are more sensitive to the loading angle, and it is more prone to occur global bending deformation under loadings at large angles. The energy absorption characteristics of the polygonal double tubes with different cross-sectional forms are calculated and ranked. The results show that the B9 double tube has the best comprehensive performance. The B9 double tube is constructed with a gradient thickness instead of a uniform thickness to improve its crushing performance under large-angle loadings and raise its critical angle of occurring global bending deformation. A multiobjective optimization procedure is proposed to find the optimal design of the FGT double tube for enhanced crashworthiness performance. PubDate: 2023-11-27
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Abstract: Abstract This paper presents an end-to-end framework for robust structure/control optimization of an industrial benchmark. When dealing with space structures, a reduction of the spacecraft mass is paramount to minimize the mission cost and maximize the propellant availability. However, a lighter design comes with a bigger structural flexibility and the resulting impact on control performance. Two optimization architectures (distributed and monolithic) are proposed in order to face this issue. In particular the Linear Fractional Transformation (LFT) framework is exploited to formally set the two optimization problems by including parametric uncertainties. Large sets of uncertainties have to be indeed taken into account in spacecraft control design due to the impossibility to completely validate structural models in micro-gravity conditions with on-ground experiments and to the evolution of spacecraft dynamics during the mission (structure degradation and fuel consumption). In particular the Two-Input Two-Output Port (TITOP) multi-body approach is used to build the flexible dynamics in a minimal LFT form. The two proposed optimization algorithms are detailed and their performance are compared on an ESA future exploration mission, the ENVISION benchmark. With both approaches, an important reduction of the mass is obtained by coping with the mission’s control performance/stability requirements and a large set of uncertainties. PubDate: 2023-11-27
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Abstract: Abstract Topology optimization is a technique to solve the material distribution problem. However, to consider manufacturing constraints within this technique can be challenging. A type of manufacturing constraint that has not been thoroughly addressed is the ability to optimally select among a set of design subdomains. Examples of situations that may require such constraint in their design process are: the design and optimal location of a bridge pier, and the design and location of an outrigger system for a high-rise building, to name a few. This paper presents a novel formulation to address the simultaneous optimal subdomain selection and topology design problem which is based on the well-known SIMP formulation. The proposed method optimally selects the design subdomains in (2D and 3D) structures, and topology optimizes these with the remainder of the design domain which does not belong to any subdomain. PubDate: 2023-11-21
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Abstract: Abstract The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). Herein, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods. PubDate: 2023-11-21
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Abstract: Abstract Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems. PubDate: 2023-11-21
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Abstract: Abstract Topology optimization of eigenfrequencies has significant applications in science, engineering, and industry. Eigenvalue problems as constraints of optimization with partial differential equations are solved repeatedly during optimization and design process. The nonlinearity of the eigenvalue problem leads to expensive numerical solvers and thus requires huge computational costs for the whole optimization process. In this paper, we propose a simple yet efficient linearization approach and use a phase field method for topology optimization of eigenvalue problems with applications in two models: vibrating structures and photonic crystals. More specifically, the eigenvalue problem is replaced by a linear source problem every few optimization steps for saving computational costs. Numerical evidence suggests first-order accuracy of approximate eigenvalues and eigenfunctions with respect to the time step and mesh size. Numerical examples are presented to illustrate the effectiveness and efficiency of the algorithms. PubDate: 2023-11-16
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Abstract: Abstract In this work, we propose a method to optimize the material thickness distribution of partition panels for maximized sound insulation while constraining material usage. A framework is developed to couple structural optimization with diffuse field sound transmission loss (STL) predictions based on deterministic-statistical energy analysis (Det-SEA). The methodology can handle the design of both single panels, including a single mechanical plate, and double panels, in which two mechanical plates are separated by an air cavity. Three formulations of the optimization problem are developed and compared in terms of final obtained performance and computational cost. In the first formulation, the resonance dips in the STL are suppressed by pushing the panel eigenfrequencies as far away as possible from the target frequency. In the second and the third formulations, the diffuse STL of the panel is directly maximized respectively at the target frequency and in a frequency band around the target frequency. The practical advantages of the method are investigated for different target frequencies in the audible range and for relevant design cases, such as the suppression of the STL dip located around the critical frequency of single panels and around the mass–spring–mass resonance frequency of double panels. For single panels, all three different formulations lead to significant insulation improvements, with no big differences in the final obtained performance. For double panels instead, we show that simply suppressing the resonance dips with the first formulation does not lead to adequate insulation improvements, but a direct maximization of STL is needed. PubDate: 2023-11-16
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Abstract: Abstract This paper presents a method for optimizing the cavitation performance of aviation fuel centrifugal pump inducer based on surrogate model with highly accurate simulations. To mitigate the interface blurring effect caused by the dissipation of convective terms, this study first introduces an artificial convective term into the phase control equation to enhance the numerical discretization accuracy and stability. The numerical simulation considering cavitation phase transition effects is implemented based on the OpenFOAM platform; next, a GPR surrogate model for the inducer cavitation performance is constructed using a full-factorial experimental design method. The global sensitivity of the inducer's structural parameters and the mechanism of their interaction effects are revealed, and the numerical errors of the surrogate model are quantified; finally, particle swarm optimization is employed to optimize the design of the inducer component, and the global convergence of results is verified based on the expected improvement function used in Bayesian optimization. Results show that the cavitation number obtained through simulation is 0.052, with an error of only 3.6% compared to experimental results, and the GPR model for fitting the cavitation performance simulator exhibits very small prediction uncertainty. After optimization, the blade inlet angle and edge position are adjusted, and as a result, the cavitation number is reduced from 0.0456 to 0.0407, indicating an obvious improvement of cavitation performance. PubDate: 2023-11-10
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Abstract: Abstract This paper presents an efficient computational method for optimal structural design in the presence of uncertain Young’s modulus modeled using discretized random fields. To quantify and propagate the uncertainty, random matrix theory is employed to quantify uncertainty in the context of robust topology optimization (RTO) for the minimization of compliance. Random matrix theory employs statistical inference methods to model the matrix-variate probability distribution of the finite element stiffness matrix. This provides analytical expressions for the mean and the standard deviation of the compliance, a combination of which is minimized in RTO. The novel random matrix theory-based RTO is computationally efficient due to the intrusive nature of the method, and is flexible as its computational performance and robustness remain consistent regardless of the correlation lengths or the variance of the random field, as demonstrated through numerical cases. The random matrix RTO method is applied to several two-dimensional numerical problems where the random fields of the modulus are assigned with ranges of correlation lengths and variances to illustrate the versatility of the method. The performance of random matrix RTO is compared with Monte Carlo RTO and stochastic collocation RTO to explore the efficiency and accuracy of the method. PubDate: 2023-11-10
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Abstract: Abstract The design of buildings has become a complex and multidisciplinary problem involving multiple conflicting objectives as architects and designers address competing technical, economic, environmental, and societal concerns. This has been driving research in Architecture, Engineering, and Construction (AEC) toward rigorous multidisciplinary decision-making frameworks that generate and evaluate numerous design alternatives using multi-objective optimization in concert with simulation and analysis models of varying fidelity and computational expense. While such frameworks are well known and widely employed in the aerospace and systems engineering domains, efforts by design professionals and researchers in the AEC field are scattered at best. In this paper, we provide a detailed review of recent developments in optimization frameworks in the AEC field and subsequently highlight how such developments are largely compartmentalized into separate domains such as structural, energy, daylighting, and other performance factors. We further discuss the technical challenges involved in concurrent coupled multidisciplinary design optimization (MDO) in the AEC field such as interoperability issues between Building Information Modeling (BIM) environments, analysis/simulation tools, and optimization frameworks. We conclude by outlining research needed for more unified modeling and simulation-based optimization frameworks to aid in complex and multidisciplinary building design processes. We also highlight the need for the identification and development of multi-fidelity simulation tools for use across multiple design phases. As such, this paper contributes a novel roadmap to leverage aerospace and systems engineering research in MDO into the field of AEC, along with a call for researchers in the MDO community to seek collaborations in AEC field. PubDate: 2023-11-08
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Abstract: Abstract This work proposes a multifidelity modeling approach to mitigate adverse characteristics of airfoil dynamic stall through aerodynamic shape optimization (ASO). Cokriging regression (CKR) is used to efficiently determine an optimum airfoil shape by combining data from high-fidelity (HF) and low-fidelity (LF) computational fluid dynamics simulations. The HF dynamic stall response is modeled using the unsteady Reynolds-averaged Navier–Stokes equations and Menter’s SST turbulence model, whereas the LF model is developed by simplifying the HF model with a coarser discretization and relaxed convergence criteria. The CKR model, constructed using various infill criteria to model the objective and constraint functions with six PARSEC parameters, is utilized to find the optimal design. The results show that the optimal shape from CKR delays the dynamic stall angle over 3° while reducing the peak values of the aerodynamic coefficients compared to the baseline airfoil (NACA 0012). Comparing the optimized shapes from the CKR and a HF Kriging regression (HF-KR) shows a similar delay in dynamic stall angle; however, the CKR optimum provides a better design for the current problem formulation while requiring 39% less computational time than the HF-KR approach. This work presents a new multifidelity modeling approach to saving the computational burden of dynamic stall mitigation through ASO. The approach used in this work is general and can be applied for other unsteady aerodynamic applications and optimization. PubDate: 2023-11-06
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Abstract: Abstract Feature-mapping (FM) optimisation frameworks have received much attention for structural topology optimisation with explicit geometric parameters. This paper presents a methodology for constructing parametric feature-based CAD models from designs generated using Moving Morphable Components (MMC). Emphasis is placed on constructing feature-based CAD models that conform to conventional modelling practices, where individual parameterised features are modelled using feature templates and united through Boolean union operations. This involves the use of algorithms to facilitate feature clean-up and identify connexions between features. The progression through several examples demonstrates how the developed algorithms can realise a feature-based CAD model from the results of an FM optimisation. Integration with a commercial CAD system provides a wide range of modelling capabilities to the designer for downstream design tasks. PubDate: 2023-11-06
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Abstract: Abstract The application of lattice structures provides significant benefits for lightweight structural design. To further strengthen structural stiffness, multi-morphology lattice structures are integrated into topology optimization. Considering the high costs associated with microstructural mechanical calculations and modeling, a novel three-dimensional Convolutional Neural Network (3D-CNN) with Transfer Learning (TL) is proposed to rapidly predict the performance of lattice structures with any morphology. The optimization framework is reconstructed to accommodate multi-morphology lattice structure design, combining density updates with cell topology iteration using a modified sensitivity formula. Furthermore, a cutting-edge post-processing method based on 3D-CNN is employed to achieve a substantial improvement in structural resolution levels within acceptable costs. Through comprehensive simulations comparing with both single-morphology and existing multi-morphology optimizations of lattice structures, we demonstrate the superiority of our proposed approach. Lastly, the effectiveness of the result through post-processing is validated by the Finite Element Method (FEM). PubDate: 2023-11-04
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Abstract: Abstract Optimal automobile seat design can play a significant role in passenger safety during high-speed accidents. To tackle the challenge of optimizing automotive seats, this paper presents a detailed optimization design method. In detail, the finite element models firstly established and validated through eight typical working conditions of automotive seats based on experimental data. Then, the optimized variables are screened and determined through contribution analysis, in which, the various perspectives are taken into account, such as the total cost and mass of seat materials, safety performance, and comfort index. Subsequently, an optimization strategy is constructed, which combines optimal Latin hypercube sampling, response surface method surrogate models, non-dominated sorting genetic algorithm-II, fuzzy analytic hierarchy process, entropy weighting method, gray relational analysis, and Visekriterijumsko KOmpromisno Rangiranje method for the optimal design of the automotive seat frame. Finally, a comprehensive comparative analysis of the optimal trade-off solution is carried out in terms of both decision methods and optimization strategies. The results show that ensuring the safety performance, the total cost, and total mass of the seat frame material decreased by 17.22% and 11.52%, respectively, as a result of the optimization strategy proposed in this paper, and the comfort performance is also improved to some extent. Therefore, the multi-objective optimization strategy proposed in this paper performs well in terms of both accuracy and effectiveness and provides a reliable reference for related multi-objective optimization. PubDate: 2023-11-04
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Abstract: Abstract The vibration characteristics of composite structures are influenced not only by the macro-layout and micro-configuration of the viscoelastic material but are also intricately linked with the inherent properties of the material. In this study, we present a concurrent topology design methodology for multi-scale viscoelastic materials that simultaneously considers both frequency and temperature dependencies. The equivalent properties of the biphasic viscoelastic material, comprising stiffness-phase and damping-phase constituents, are determined utilizing the homogenization technique. The optimization objective is defined as the intrinsic/weighted modal loss factors obtained through the non-linear eigensolver. A density-driven optimization framework is formulated, and sensitivity analysis is conducted. The resemblance is defined to quantitatively distinguish the different design configurations at two scales. The proposed approaches are verified using numerical simulations. The results reveal that the natural frequencies of viscoelastic structures vary slightly at different ambient temperatures and excitation frequencies, while the modal loss factors manifest considerable discrepancies. Moreover, concerning configuration similarity, the design results at both macro- and microscales remain notably consistent across different frequencies, and the obvious diversities at the two scales can be observed for all cases of different temperatures. Furthermore, it is observed that the macroscopic optimization performance exhibits an optimal value concerning changes in the microscopic component ratio, with this optimal value being influenced by temperature variations. PubDate: 2023-11-03
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