Abstract: Apart from the lightweight and excellent mechanical properties, sandwich panels can be endowed with tailorable in-plane coefficient of thermal expansion (CTE) through an elaborate design of periodic face-sheets. However, albeit that the microstructural topology of their periodic face-sheets promises unique thermal expansion behaviors, it may also bring significant influences to the structural stiffness of sandwich panels. In this study, we apply the topology optimization method to design face-sheet microstructures to enable the sandwich panels to possess desired in-plane CTEs, lightweight and benign mechanical properties, simultaneously. By introducing the patch-based cell as initial configuration, the existing thermally bending adjustment mechanism for thermal deformation control is integrated to the process of topology optimization. The entire topology optimization process including the equivalent mechanical properties prediction and the sensitivity computation is performed within an in-house program coupled with commercial finite element analysis software. To this end, a matching numerical sensitivity analysis method to extract sensitivities straightforwardly from software’s output is also developed on the basis of asymptotic homogenization method. Three types of specific optimization problems in terms of different objective functions and constraint conditions are proposed, solved, and studied, namely, in-plane zero thermal expansion combining with maximum stiffness, the other for in-plane zero thermal expansion optimal specific stiffness, and minimizing in-plane isotropic thermal expansion. Some specific resulting topologies, microstructural features, and design details are subsequently obtained. In particular, the current strategy of integrating effective mechanism and topological technology can be extended to design more microstructures for simultaneously tailorable CTE and high mechanical performance by replacing present thermal deformation control mechanism with others. PubDate: 2021-05-11

Abstract: The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape, and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a non-linear transient PDE and space-time state dependent pointwise constraints. An elegant bi-level reformulation of the optimization problem is introduced which makes it possible to manage the infinite number of design parameters and state constraints efficiently. The computational cost of this algorithm is independent of the number of constraints. The validity and efficiency of the presented method are supported by several examples, from simple benchmarks to complex industrial castings. According to numerical results, the presented approach makes a complete solution to the problem of automatic optimal riser design in the shape casting process. PubDate: 2021-05-10

Abstract: In the ever-expanding fields of thickness and topology optimization, there is a research gap for simultaneous and direct optimization of thickness and material for complex shell structures using fully analytical sensitivities, with prevention of coincident material layers. This paper introduces a novel method to fill this gap: concurrent thickness and material optimization (CTMO) based on a gradient-based approach. This proposed formulation determines optimal thickness and material choice for shell elements within a finite element (FE) model design space. The method of moving asymptotes (MMA) is used for optimization, and material interpolation is handled with solid isotropic material with penalization (SIMP). The behavior of this solver is demonstrated with several academic examples, through a series of extensive parameter sweeps of mass fraction, and minimum and maximum designable thickness, for the compliance minimization objective function. The proposed methodology is geared towards practical design of complex structures, allowing for feasible interpretation into actual engineering solutions. As such, optimization of a small aerobatic aircraft wing is conducted with study of several key design factors. The effects of design restriction and filter size are studied to determine best practices for design procedures. To demonstrate the practical utility of this algorithm, a selected wing optimization result is interpreted into a set of complete, industry style designs, verified through finite element analysis (FEA) to determine deviation from the ideal optimum. It is demonstrated that designs can be interpreted faithfully from optimization results with mass and compliance errors of less than 2%, alongside a discussion of pertinent factors. Finally, several areas with potential for future work are explored. PubDate: 2021-05-08

Abstract: Time-variant reliability analysis plays a vital role in improving the validity and practicability of product reliability evaluation over a specific time interval. Sampling-based extreme value method is the most direct way to implement accurate reliability assessment. Its adoption for time-variant reliability analysis, however, is limited due to the computational burden caused by repeatedly evaluating performance function. This paper proposes a semi-analytical extreme value method to improve the computational efficiency of extreme value method. The time-variant performance function is transformed into dependent instantaneous performance functions in which the stochastic processes are discretized by the expansion optimal linear estimation method to simulate the dependence among different time instants. Each instantaneous function is separately approximated by Taylor series expansion at the most probable point through instantaneous reliability analysis. Based on the approximated performance functions, the computational cost of sampling-based extreme value method is significantly reduced. Results of three numerical examples demonstrate the efficacy of the proposed method. PubDate: 2021-05-05

Abstract: Topology optimization of fluid flow problems is still a challenging open problem, especially when considering turbulence, compressibility, or the addition of different physics. In the current implementation of topology optimization for fluids considering density methods, there are essentially three problems. First, the grayscale in the result makes it difficult to identify the precise contour of the fluid region, which may be a problem in some applications and during the optimization process as well. Second, even for low Reynolds flow design problems, a continuation scheme of the material model penalization parameters is necessary to avoid a grayscale and to obtain a clear boundary. Third, in complex fluid flow optimization problems, it is difficult to specify the maximum value of the inverse permeability to avoid the fluid to flow inside the solid. This work proposes a novel methodology that tackles the first two problems, i.e., it avoids the grayscale and obtains clear boundaries. The goal of this work is to implement the Topology Optimization of Binary Structures (TOBS) (Sivapuram and Picelli, Finite Elem Anal Des 139:49–61, 2018) for fluid flow design, which is a novel topology optimization method that has been used in solid mechanics to generate optimized structural solutions considering only binary {0,1} design variables. The main advantage of {0,1} methods is the clear definition of the interface and the absence of grayscale. It is a method easy to implement which preserves the material distribution features. Some classic fluid problems are considered to illustrate the problem, such as the double channel and the bend pipe, and also a more complex example that usually presents grayscale issues, which is the fluid diode design. The optimization results show the feasibility of the TOBS when applied to fluid flow problems. The physical problem is solved by using the finite element method and the optimization problem with CPLEXⒸ, a proprietary optimization package from IBM. The present work successfully eliminates the grayscale problem, bringing clear boundaries in the interface fluid-solid. PubDate: 2021-05-03

Abstract: This work aims to perform the topology optimizationof frequency separation interval of continuous elastic bi-dimensional structures in the high-frequency domain. The studied structures are composed of two materials. The proposed algorithm is an adaptation of the Bidirectional Evolutionary Structural Optimization (BESO). As the modal density is high in this frequency domain, the objective function, based on the weighted natural frequency, is formulated to consider an important number of modes. To implement the algorithm, a mode tracking method is necessary to avoid problems stemming from mode-shifting and local modes. As the obtained results by using structural dynamics analysis present quasi-periodic topology, further calculations are done to compare the results with and without imposed periodicity. A dispersion analysis based on wave propagation theory is performed by using the unit cell previously obtained from the structural optimization to investigate the band gap phenomenon. The resulting band gaps from the dispersion analysis are compared with respect to the dynamic behavior of the structure. The topology optimization methodology and the wave propagation analysis are assessed for different boundary conditions and geometries. Comparison between both analyses shows that the influence of the boundary conditions on the frequency separation interval is small. However, the influence from the geometry is more pronounced. The optimization procedure does not present significant numerical instability. The obtained topologies are well-defined and easily manufacturable, and the obtained natural frequency separation intervals are satisfactory. PubDate: 2021-05-01

Abstract: Aleatory and epistemic uncertainties usually coexist within a mechanistic model, which motivates the hybrid structural reliability analysis considering random and interval variables in this paper. An introduction of the interval variable requires one to recursively evaluate embedded optimizations for the extremum of a performance function. The corresponding structural reliability analysis, hence, becomes a rather computationally intensive task. In this paper, physical characteristics for potential optima of the interval variable are first derived based on the Karush-Kuhn-Tucker condition, which is further programmed as a simulation procedure to pair qualified candidate samples. Then, an outer truncation boundary provided by the first-order reliability method is used to link the size of a truncation domain with the targeted failure probability, whereas the U function is acted as a refinement criterion to remove inner samples for an increased learning efficiency. Given new samples detected by the revised reliability-based expected improvement function, an adaptive Kriging surrogate model is determined to tackle the hybrid structural reliability analysis. Several numerical examples in the literature are presented to demonstrate applications of this proposed algorithm. Compared to benchmark results provided by the brute-force Monte Carlo simulation, the high accuracy and efficiency of this proposed approach have justified its potentials for the hybrid structural reliability analysis. PubDate: 2021-05-01

Abstract: The present contribution describes an optimization-based design technique of elastic isotropic periodic microarchitectures with crystal symmetries aiming at the realization of composites with extreme properties. To achieve this goal, three consecutive procedures are followed: (i) a series of inverse homogenization problems with symmetry constraints, (ii) a correlation analysis between symmetries and effective elastic properties of the attained microarchitectures, and (iii) the pattern resemblance recognition of these topologies and their redesign, by adopting microstructures with two length-scales, through optimized parametric geometries. This paper is devoted to assessing the third procedure because the first two procedures have been evaluated in previous works of the authors, and here they are only summarized. By applying the methodology, two plane group symmetries are assessed to define two families of 2D periodic parameterized microarchitecture. Once the parameters have been optimized, the resulting composites achieve elastic isotropic properties close to the whole range of the theoretically estimated bounds. Particularly, an unprecedented microstructure attaining the theoretical maximum stiffness is reported. Starting from these parameterized topologies, simple, one-length scale, and easily manufacturable geometries are defined. One of the so-designed microarchitectures has been manufactured and tested, displaying an effective Poisson’s ratio of − 0.90 simultaneously with a high shear modulus. PubDate: 2021-05-01

Abstract: Topology optimization, as a powerful conceptual design method, has been widely adopted in both academic research and industrial applications. To further promote the development of topology optimization, many computer programs have been published for educational purposes over the past decades. However, most of the computer programs are constructed based on a linear assumption. On the basis of bi-directional evolutionary structural optimization (BESO) method, the paper presents a MATLAB implementation of the geometrically nonlinear topology optimization code for compliance minimization of statically loaded structures. Excluding 19 lines which are used for explanation, only 118 lines are needed for the initialization of the design parameters, nonlinear finite element analysis, sensitivity calculation, sensitivity filtration, and topological design variables update. Different design problems can be solved by modifying several lines in the proposed program. The complete 137-line code is included as an Appendix and is intended for educational purposes only. PubDate: 2021-05-01

Abstract: Metamaterial systems have opened new, unexpected, and exciting paths for the design of acoustic devices that only few years ago were considered completely out of reach. However, the development of an efficient design methodology still remains challenging due to highly intensive search in the design space required by the conventional optimization-based approaches. To address this issue, this study develops two machine learning (ML)-based approaches for the design of one-dimensional periodic and non-periodic metamaterial systems. For periodic metamaterials, a reinforcement learning (RL)-based approach is proposed to design a metamaterial that can achieve user-defined frequency band gaps. This RL-based approach surpasses conventional optimization-based methods in the reduction of computation cost when a near-optimal solution is acceptable. Leveraging the capability of exploration in RL, the proposed approach does not require any training datasets generation and therefore can be deployed for online metamaterial design. For non-periodic metamaterials, a neural network (NN)-based approach capable of learning the behavior of individual material units is presented. By assembling the NN representation of individual material units, a surrogate model of the whole metamaterial is employed to determine the properties of the resulting assembly. Interestingly, the proposed approach is capable of modeling different metamaterial assemblies satisfying user-defined properties while requiring only a one-time network training procedure. Also, the NN-based approach does not need a pre-defined number of material unit cells, and it works when the physical model of the unit cell is not well understood, or the situation where only the sensor measurements of the unit cell are available. The robustness of the proposed two approaches is validated through numerical simulations and design examples. PubDate: 2021-05-01

Abstract: Computational cost of high-fidelity simulations limits the number of evaluations which may be performed in design exploration and optimization. Surrogates based on samples of multiple fidelities are used to decrease computational cost and lower error from single-fidelity surrogates. This paper develops a novel multi-fidelity surrogate model based on principal components which are shared between multiple fidelities of finite element model samples. This method does not require a common grid between the fidelities, further reducing computational cost. The new method was tested on various design spaces of the Transonic Purdue Research Compressor and compared to other common and novel multi-fidelity methods. The new method was more accurate and required less computational cost than the other tested methods. Little to no increase in computational cost was needed to reduce surrogate error to 50% of the single-fidelity error. For fixed error, the computational cost was reduced by more than 75%. These results were also validated by testing the method on a more complex turbomachinery blade, Parametric Blade Study Rotor 4. The decreased error and computational cost improve effectiveness of design exploration and optimization. Such improvements help meet the demand for cleaner and safer engines by allowing high-fidelity design exploration within reasonable time frames. PubDate: 2021-05-01

Abstract: The majority of topology optimization methods for porous infill designs is based on the assumption of deterministic loads. However, in practice, quantities such as positions, weights, and directions of applied loads may change accidentally. Deterministic load-based designs might deliver poor structural performance under loading uncertainties. Such uncertain factors need to be taken into account in topological optimization to seek robust results. This paper presents a novel robust concurrent topology optimization method for the design of uniform/non-uniform porous infills under the accidental change of loads. A combination of moving morphable bars (MMBs) and loading uncertainties is proposed to directly model multiscale structures and seek robust designs. The macro- and microscopic structures can be simultaneously optimized through the minimization of the weighted sum of the expected compliance and standard deviation. The geometries of adaptive geometric components (AGCs) are straightforwardly optimized. The AGCs consist of two classes of geometric components: macroscopic bars describing the overall structure and microscopic bars describing the material microstructures. Automatic mesh-refinement is utilized to enhance computing efficiency. Numerical examples demonstrate that robust porous design can be obtained with only one global volume constraint while the material continuity of neighboring unit cells and the structural porosity can be maintained without additional constraints. The robust designs yield a more robust structural performance along with a smaller standard deviation compared with deterministic porous designs under loading uncertainties. PubDate: 2021-05-01

Abstract: A significant challenge with reliability-based design optimization (RBDO) is the high computational cost associated with the double-loop structure that entails a large number of function calls for both the optimization process and reliability analysis. Several decoupling methods have been developed to improve the efficiency of RBDO. In addition, surrogate models have been used to replace the original time-consuming models and improve the computational efficiency. This paper proposes a novel quantile-based sequential RBDO method using Kriging surrogate models for problems with independent constraint functions. An error-controlled adaptive Kriging scheme is integrated to derive accuracy information of surrogate models and develop a strategy that facilitates independent training of the models for the performance function. The proposed independent training avoids unnecessary performance function evaluations while ensuring the accuracy of reliability estimates. Moreover, a new sampling approach is proposed that allows refinement of surrogate models for both deterministic and probabilistic constraints. Five numerical examples are carried out to demonstrate the performance of the proposed method. It is observed that the proposed method is able to converge to the optimum design with significantly fewer function evaluations than the state-of-the-art methods based on surrogate models given the constraint functions are independent. PubDate: 2021-05-01

Abstract: Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty, but the heavy computational cost is still a challenge in estimating the failure credibility. To alleviate this issue, an iterative method combining adaptive Kriging and fuzzy simulation (AK-FS) has been developed by Ling et al. However, for the problem with complex performance function, a large candidate sampling pool is needed in the AK-FS, which makes the training process of the Kriging model fairly time consuming. In order to improve the estimation efficiency of failure credibility through reducing the size of candidate sampling pool in AK-FS, an efficient sample reduction strategy based on adaptive Kriging (SR-AK) is proposed in this paper. In the SR-AK, the estimation of failure credibility is transformed into searching two active points in candidate sampling pool. After updating the Kriging model in each circle, current active points can be easily identified. Then, according to the properties of the active points and the prediction characteristics of Kriging model, the samples in current candidate sampling pool can be divided into two sets, i.e., the samples affect the estimation of active points and the samples have no effect on it. Obviously, the samples in the latter set can be deleted from current candidate sampling pool to reduce its size. By using this sample reduction strategy, the process for training Kriging model is accelerated circle by circle, which is very helpful to save the analysis time and improve the computational efficiency in estimating failure credibility. Four examples are employed to demonstrate the performance of the proposed SR-AK in fuzzy safety degree analysis. PubDate: 2021-05-01

Abstract: This paper presents a density-based topology optimization approach to design self-supporting and lightweight infill structures with efficient mechanical properties for enclosed structural shells. A new overhang constraint is developed based on the additive manufacturing (AM) filter to ensure that the infills are not only self-supporting in a specified manufacturing direction but can also provide necessary supports to the external shell for successful manufacturing. Two-field–based parametrization and topology optimization formulations are used to impose minimum length scales and to avoid the impractical design solutions that exhibit one-node connection structural members. Besides, a localized volume constraint is utilized to achieve a porous infill pattern. By solving the optimization problem, a shell-infill design can be obtained with very few overhang elements that can be easily post-processed without affecting the mechanical properties of the overall structure. As a result, the optimized design contains no overhang elements and exhibits a better mechanical property than that with predefined periodic infill patterns of the same weight. Numerical examples are given to demonstrate the effectiveness and applicability of the proposed approach. PubDate: 2021-05-01

Abstract: Decreasing fuel consumption and tailpipe emissions have been an important issue nowadays for automotive industry after new regulations. Fuel consumption is also an important parameter that highly affects the customers’ choice. Reduction of total vehicle weight with optimization is one of the common methods to improve fuel consumption and emissions. There are a lot of studies on body, interior, and engine components of the vehicle to improve fuel efficiency and emissions including design modifications, using alternative material and architectural optimizations. In this article, the optimization of an aluminum support bracket that carry alternator and hydraulic steering pump is studied. First, design space is determined with layout analysis defining constraints and fixing points. Then, topology optimization method is applied in order to explore the load carrying path of the component. Final design is frozen through computational analysis verifications and industrialization phase modifications. A comparison of the new design with the actual production showed that the mass of the current design could be reduced by 37%, while all product expectations were met. PubDate: 2021-05-01

Abstract: This paper presents a model for generating strut-based lattice structures using topology optimization and their efficient direct slicing. These structures exhibit better physical properties and can represent the partial densities at the macro-scale level, which often appear in designs based on topology optimization. The fabrication of such large member structures with intricate geometries is possible by the additive manufacturing technologies which offer design freedom to produce the optimized parts for engineering applications. However, these structures generate millions of planer manifolds describing the strut members and result in large data files, thus making conventional procedures in additive manufacturing highly ineffective. Therefore, the design process for such structures requires efficient data manipulation and storage of the lattice topology. In the current work, a mathematical model for the strut primitive which connects two nodes in a cell is developed. Based on the proposed strut model, a structural optimization formulation is presented for lattice structures design under volume fraction constraint. A matrix-oriented compact data structure to express the lattice topology and the direct slicing algorithm which makes queries on the proposed compact data structure is presented as part of this work. The slicing kernel has been tailored for parallel implementation to handle engineering-scale applications which often consist of structures over a million struts. The article is organized into the “Introduction” section explaining the requirement and the novelty of this work. Following which, the automated design framework based on topology optimization procedure for lattice structures is given. The mathematical derivations and data structure of the strut-based lattice will be explained and the operations on model data for the direct slicing procedure are elaborated. Numerical experiments verifying the proposed method will be presented toward the end. PubDate: 2021-05-01

Abstract: This paper describes the development of a new topology optimization framework that controls, captures, isolates, switches, or separates particles depending on their material properties and initial locations. Controlling the trajectories of particles in laminar fluid has several potential applications. The fluid drag force, which depends on the fluid and particle velocities and the material properties of particles, acts on the surfaces of the particles, thereby affecting the trajectories of the particles whose deformability can be neglected. By changing the drag or inertia force, particles can be controlled and sorted depending on their properties and initial locations. In several engineering applications, the transient motion of particles can be controlled and optimized by changing the velocity of the fluid. This paper presents topology optimization schemes to determine optimal pseudo rigid domains in fluid to control the motion of particles depending on their properties, locations, and geometric constraints. The transient sensitivity analysis of the positions of particles can be derived with respect to the spatial distributed design variables in topology optimization. The current optimization formulations are evaluated for effectiveness based on different conditions. The experimental results indicate that the formulations can determine optimal fluid layouts to control the trajectories of multiple particles. PubDate: 2021-05-01

Abstract: New computational methods are proposed for robust design optimization (RDO) of complex engineering systems subject to input random variables with arbitrary, dependent probability distributions. The methods are built on a generalized polynomial chaos expansion (GPCE) for determining the second-moment statistics of a general output function of dependent input random variables, an innovative coupling between GPCE and score functions for calculating the second-moment sensitivities with respect to the design variables, and a standard gradient-based optimization algorithm, establishing direct GPCE, single-step GPCE, and multi-point single-step GPCE design processes. New analytical formulae are unveiled for design sensitivity analysis that is synchronously performed with statistical moment analysis. Numerical results confirm that the proposed methods yield not only accurate but also computationally efficient optimal solutions of several mathematical and simple RDO problems. Finally, the success of conducting stochastic shape optimization of a steering knuckle demonstrates the power of the multi-point single-step GPCE method in solving industrial-scale engineering problems. PubDate: 2021-03-01 DOI: 10.1007/s00158-020-02820-z

Abstract: Multi-fidelity approaches combine different models built on a scarce but accurate dataset (high-fidelity dataset), and a large but approximate one (low-fidelity dataset) in order to improve the prediction accuracy. Gaussian processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the multi-fidelity deep Gaussian process (MF-DGP) model. This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, deep Gaussian processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multi-fidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems. PubDate: 2021-02-23 DOI: 10.1007/s00158-020-02802-1