Abstract: Abstract Without proper flow channelization, congestion and overcrowding in pedestrian traffic may lead to significant inefficiency and safety hazards. Thus, the design of guideway networks that provide a fine balance between traffic congestion and infrastructure construction investment is vital. This paper presents a mathematical formulation and topology optimization framework for paved pedestrian guideway design under physics-based traffic equilibrium in a continuous space. Pedestrians are homogeneous, and their destination and path choices under the Nash equilibrium condition are described by a set of nonlinear partial differential equations. The design framework optimizes the deployment of pavement, which alters the road capacity and directly affects pedestrians’ free flow travel speed. A maximum crowd density constraint is included in the design model to address public safety concerns (e.g., over stampede risks). A series of numerical experiments are conducted to illustrate the effectiveness of the proposed model as well as solution techniques. The proposed framework, which builds on the traffic equilibrium theory, produces optimized guideway designs with controllable maximum pedestrian density, accounts for budget constraints (through an adjustable multiplier that balances pavement construction and travel costs), and allows for control of the spatial configuration of road branches. Comparison with lamellar structures and more conventional guideway designs demonstrates better performance of the outcomes from the proposed modeling and optimization framework. PubDate: 2021-01-16
Abstract: Abstract In the presence of both random and interval hybrid uncertainty (RI-HU), investigating global reliability sensitivity (GRS) can identify the effect of random input on the structural safety globally. To this end, this work establishes the GRS index model and its corresponding efficient solution, and the innovation includes three aspects. Firstly, the GRS of the random input is defined by the average absolute difference between the failure probability upper bound (FP-UB) and the conditional FP-UB on the fixed random input under the RI-HU, and it can reflect the effect of the fixed random input on the structural safety. Secondly, the conditional FP-UB on fixing the random input at the realization is approximated by the conditional FP-UB on fixing the random input in a differential interval. Then the conditional probability theorem can be employed to convert estimating the GRS into the state recognition of the samples, which is the by-product of estimating the FP-UB by the numerical simulation. Finally, by the strategy of surrogating the performance function twice, the meta-importance sampling method is developed to efficiently estimate the GRS in presence of the RI-HU. The rationality of the proposed GRS index model and the efficiency of the developed estimation method are fully verified by the numerical and engineering examples. PubDate: 2021-01-16
Abstract: Abstract This paper presents an isogeometric configuration design optimization of curved beam structures for maximizing fundamental eigenfrequency. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity of repeated eigenvalues is used. A special attention is paid to the computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. The developed design optimization method is demonstrated through several illustrative examples. PubDate: 2021-01-16
Abstract: Abstract Structural topology optimization considering both performance and manufacturability is very attractive in engineering applications. This work proposes a formulation for structural topology optimization to achieve such a design, in which material strength, structural stiffness, and connectivity are simultaneously considered by integrating stress and simply-connected constraints into the compliance minimization problem. An effective solution algorithm consisting of different optimization techniques is introduced to handle various numerical difficulties resulted from this relatively complex multi-constraint and multi-field problem. Except for the stress penalization and aggregation techniques, the regional measure strategy is used together with the stability transformation method-based correction scheme to address stress constraints, which is also applied to the Poisson equation-based scalar field constraint in the simply-connected constraint. Numerical examples are presented to assess the features of the achieved design along with the performance of the employed algorithm. Comparisons with pure compliance, pure stress, and pure connectivity designs are provided to illustrate differences arising in the proposed design with respect to traditional approaches, also the necessity. Innovative manufacturing-oriented designs with consideration of the strength, stiffness, and connectivity are now available. PubDate: 2021-01-13
Abstract: 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: 2021-01-12
Abstract: Abstract This paper presents a new method for optimizing the layout of post-tensioned cables in concrete slabs. The cables are modeled using three-dimensional B-splines so that the prestressing forces are derived according to the exact geometry and subsequently projected onto the finite element mesh of the concrete slab. The control points of the splines serve as shape design variables, allowing non-trivial 3D cable layouts to emerge and thus extend the design capabilities beyond traditional concepts. Results of several realistic design examples show that significant reduction in cable weight is possible while maintaining the required structural performance. Savings in the order of 20% in cable weight are demonstrated for simple and regular floor plans. For irregular plans, the savings can exceed 50%, when compared to contemporary practical design approaches. PubDate: 2021-01-12
Abstract: Abstract Over the past decade, several acquisition functions have been proposed for kriging-based reliability analysis. Each of these acquisition functions can be used to identify an optimal sequence of samples to be included in the kriging model. However, no single acquisition function provides better performance over the others in all cases. Further, the best-performing acquisition function can change at different iterations over the sequential sampling process. To address this problem, this paper proposes a new acquisition function, namely expected uncertainty reduction (EUR), that serves as a meta-criterion to select the best sample from a set of optimal samples, each identified from a large number of candidate samples according to the criterion of an acquisition function. EUR does not rely on the local utility measure derived based on the kriging posterior of a performance function as most existing acquisition functions do. Instead, EUR directly quantifies the expected reduction of the uncertainty in the prediction of limit-state function by adding an optimal sample. The uncertainty reduction is quantified by sampling over the kriging posterior. In the proposed EUR-based sequential sampling process, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Each of these samples is optimal with respect to the selection criterion of the corresponding acquisition function. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical and one practical case studies show that (1) EUR-based sequential sampling can perform as well as or outperform the single use of any acquisition function in the portfolio, and (2) the best-performing acquisition function may change from one problem to another or even from one iteration to the next within a problem. PubDate: 2021-01-12
Abstract: Abstract This add-on discussion addresses a shortcoming of the paper in the title – the authors missed an important reference by Clausen et al. (2015). Differences between the current work and the said reference are clarified in this comment. In addition, some mistakes in the commented paper were corrected. PubDate: 2021-01-09
Abstract: Abstract An approach for the topology optimization of structures composed of nonlinear beam elements under time-varying excitation is presented. Central to this approach is a hysteretic beam finite element model that accounts for distributed plasticity and axial-moment interaction through appropriate hysteretic interpolation functions and yield/capacity function, respectively. Nonlinearity is represented via the hysteretic variables for curvature and axial deformations that evolve according to first order nonlinear ordinary differential equations (ODEs), referred to as evolution equations, and the yield function. Hence, the governing dynamic equilibrium equations and hysteretic evolution equations can thus be concisely presented as a system of first-order nonlinear ODEs that can be solved using general ODE solvers without the need for linearization. The approach is applied for the design of frame structures with an objective to minimize the total volume in the domain, such that the maximum displacement at specified node(s) satisfies a specified constraint (i.e., drift limit) for the given excitation. The maximum displacement is approximated using the p-norm and thus permits the completion of the analytical sensitivities required for gradient-based updating. Several numerical examples are presented to demonstrate the approach for the design of structural frames subjected to pulse, harmonic, and seismic base excitation. Topologies obtained using the suggested, nonlinear approach are compared to solutions obtained from topology optimization problems assuming linear-elastic material behavior. These comparisons show that although similarities between the designs exist, in general the nonlinear designs differ in composition and, importantly, outperform the linear designs when assessed by nonlinear dynamic analysis. PubDate: 2021-01-09
Abstract: Abstract A robust three-dimensional multiscale structural optimization framework with concurrent coupling between scales is presented. Concurrent coupling ensures that only the microscale data required to evaluate the macroscale model during each iteration of optimization is collected and results in considerable computational savings. This represents the principal novelty of this framework and permits a previously intractable number of design variables to be used in the parametrization of the microscale geometry, which in turn enables accessibility to a greater range of extremal point properties during optimization. Additionally, the microscale data collected during optimization is stored in a reusable database, further reducing the computational expense of optimization. Application of this methodology enables structures with precise functionally graded mechanical properties over two scales to be derived, which satisfy one or multiple functional objectives. Two classical compliance minimization problems are solved within this paper and benchmarked against a Solid Isotropic Material with Penalization (SIMP)–based topology optimization. Only a small fraction of the microstructure database is required to derive the optimized multiscale solutions, which demonstrates a significant reduction in the computational expense of optimization in comparison to contemporary sequential frameworks. In addition, both cases demonstrate a significant reduction in the compliance functional in comparison to the equivalent SIMP-based optimizations. PubDate: 2021-01-08
Abstract: Abstract A vital necessity when employing state-of-the-art deep neural networks (DNNs) for topology optimization is to predict near-optimal structures while satisfying pre-defined optimization constraints and objective function. Existing studies, on the other hand, suffer from the structural disconnections which result in unexpected errors in the objective and constraints. In this study, a two-stage network model is proposed using convolutional encoder-decoder networks that incorporate a new way of loss functions to reduce the number of structural disconnection cases as well as to reduce pixel-wise error to enhance the predictive performance of DNNs for topology optimization without any iteration. In the first stage, a single DNN model architecture is proposed and used in two parallel networks using two different loss functions for each called the mean square error (MSE) and mean absolute error (MAE). Once the priori information is generated from the first stage, it is instantly fed into the second stage, which acts as a rectifier network over the priori predictions. Finally, the second stage is trained using the binary cross-entropy (BCE) loss to provide the final predictions. The proposed two-stage network with the proposed loss functions is implemented for both two-dimensional (2D) and three-dimensional (3D) topology optimization datasets to observe its generalization ability. The validation results showed that the proposed two-stage framework could improve network prediction ability compared to a single network while significantly reducing compliance and volume fraction errors. PubDate: 2021-01-07
Abstract: Abstract Time-dependent failure possibility (TDFP) can reasonably measure the safety degree of time-dependent structure under fuzzy uncertainty, but there lacks design optimization under the constraint of TDFP for the trade-off of the performance and the safety. Thus, a time-dependent failure possibility-based design optimization (T-PBDO) under fuzzy uncertainty is established, and a time-dependent performance measure approach (T-PMA) for solving T-PBDO is proposed in this paper. In the proposed T-PMA, the TDFP constraint is equivalently transformed into the performance function constraint corresponding to the required target TDFP. The minimum performance target point (MPTP) and its corresponding time instant in the performance function constraint with respect to the target TDFP are determined by the single-loop optimization method of inverse TDFP analysis. This strategy completed by the inverse TDFP analysis with respect to the target TDFP can avoid analysis of the performance function under the unnecessary membership level, and then lead to improve the numerical stability and computational efficiency of solving the T-PBDO model. A numerical and three engineering case studies are introduced to verify the effectiveness of the proposed method. The results show that the proposed T-PMA is accurate, and its efficiency is higher than that of the direct optimization method. PubDate: 2021-01-07
Abstract: Abstract Due to the limited joint position space and the consideration of reducing the moment of inertia and vibration for industrial robot, the design optimization for rotate vector (RV) reducer is becoming a new and urgent problem in industry. Currently, the existing researches focus on deterministic design optimization, which may cause unreliable designs without considering uncertainties. Therefore, the study focuses on the implementation of reliability-based design optimization (RBDO) to the RV reducer. The aim is to make the RV reducer smaller in size while ensuring a higher reliability. Firstly, a modified advanced mean value (MAMV) method is proposed to improve efficiency and robustness of the advanced mean value method, which encounters inefficiency and numerical instability for the concave or highly nonlinear performance measure functions. Secondly, a mathematical model of RBDO for the RV reducer is established. Thirdly, the proposed MAMV method is integrated into double-loop method to optimize the established mathematical model of RBDO with different target reliability. The results show that the proposed MAMV method is efficient compared with other methods. In addition, the volume of the RV reducer is correspondingly reduced by 9.44%, 7.89%, and 5.66% compared with that before optimization when the target reliabilities are 99.38%, 99.87%, and 99.98%. PubDate: 2021-01-07
Abstract: Abstract This article presents an extended algorithm for topology optimization of compliant mechanisms and structures with design-dependent pressure loadings using the moving iso-surface threshold (MIST) method. In this algorithm, the fluid-structure interface is modeled using the finite element method via considering equivalent virtual strain energy and work and is tracked by an element-based searching scheme. Design-dependent pressure loads are directly applied on interface boundary and are calculated as virtual work equivalent nodal forces in the interface elements based on the finite element formulation. Several numerical examples are presented for topology optimization of mean compliance and compliant mechanisms. The present algorithm is validated through benchmarking with the results in literature and/or full finite element analysis (FEA) results of the optimum compliant mechanism and structure designs. PubDate: 2021-01-07
Abstract: 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: 2021-01-07
Abstract: 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: 2021-01-07
Abstract: Abstract Reliability-based design optimization (RBDO) offers a powerful tool to deal with the structural design with heterogeneous interval parameters concurrently. However, it is time-consuming in the practical engineering design. Therefore, a novel sequential moving asymptote method (SMAM) is proposed to improve the computational efficiency for convex model in this study, in which the nested double-loop optimization problem is decoupled to a sequence of deterministic suboptimization problems based on the method of moving asymptotes. In addition, the sensitivity of reliability index is derived, so the finite difference for the nested optimization loop can be avoided to tremendously improve the computational efficiency. Then, the accuracy of the SMAM is proved based on the error analysis. Furthermore, the Kreisselmeier-Steinhauser (KS) function is used to assemble the multiple constraints to deal with the parallel and series RBDO problems. One benchmark mathematical example, three numerical examples, and one complex civil engineering example, i.e., tower crane, are tested to demonstrate the efficiency of the proposed method by comparison with other existing methods, and the results indicate that SMAM offers a general and effective tool for non-probabilistic reliability analysis and optimization. PubDate: 2021-01-07
Abstract: Abstract Reliability-based design optimization (RBDO) has been widely used to search for the optimal design under the presence of parameter uncertainty in the engineering application. Unlike traditional deterministic optimization, RBDO problem takes the uncertainty of design variables and probabilistic reliability constraints into consideration. In the context of RBDO, a large number of model evaluations are required in the reliability analysis to estimate the failure probability. However, the intensive computation of reliability analysis makes it infeasible to address complex and expensive problems. In order to relieve the computational burden, an efficient polynomial chaos-enhanced radial basis function (PCE-RBF) approach is proposed. In this approach, RBF combined with sparse PC method is constructed to enhance predictive accuracy of metamodel. To refine the metamodel, local variation with minimum distance sampling criterion is proposed to select the sample points sequentially. Then, the refined PCE-RBF metamodel with acceptable accuracy is used to perform gradient-based optimization for solving RBDO problem. The performance of the proposed method is validated by four benchmark examples and truss structure issue. PubDate: 2021-01-07
Abstract: Abstract Recently, multi-cell structures have received increased attention for crashworthiness applications due to their superior energy absorption capability. However, such structures were featured with high peak collapsing force (PCL) forming a serious safety concern, and this limited their application for vehicle structures. Accordingly, this paper proposes windowed shaped cuttings as a mechanism to reduce the high PCL of the multi-cell hexagonal tubes and systemically investigates the axial crushing of different windowed multi-cell tubes and also seeks for their optimal crashworthiness design. Three different multi-cell configurations were constructed using wall-to-wall (WTW) and corner-to-corner (CTC) connection webs. Validated finite element models were generated using explicit finite element code, LS-DYNA, and were used to run crush simulations on the studied structures. The crashworthiness responses of the multi-cell standard tubes (STs), i.e., without windows, and multi-cell windowed tubes (WTs) were determined and compared. The WTW connection type was found to be more effective for STs and less favorable for WTs. Design of experiments (DoE), response surface methodology (RSM), and multiple objective particle swarm optimization (MOPSO) tools were employed to find the optimal designs of the different STs and WTs. Furthermore, parametric analysis was conducted to uncover the effects of key geometrical parameters on the main crashworthiness responses of all studied structures. The windowed cuttings were found to be able to slightly reduce the PCL of the multi-cell tubes, but this reduction was associated with a major negative implication on their energy absorption capability. This work provides useful insights on designing effective multi-cell structures suitable for vehicle crashworthiness applications. PubDate: 2021-01-07
Abstract: Abstract Thin-walled beams are extensively applied in the engineering structures, in which the conceptual design of cross-sectional shape and topology is the most important issue. Traditional topology optimization methods cannot easily obtain the thin-walled features. Therefore, a thin-walled cross-sectional design method using the moving morphable components (MMC) approach is proposed in this paper. To acquire a thin-walled structure with a high stiffness-to-mass ratio, the cross-sectional area is defined as the objective function, and the cross-sectional bending and torsional moments of inertia are selected as constraints. The bending and torsional moments of inertia in arbitrary domain are both solved by using the finite element method. In addition, the sensitivities of cross-sectional area, bending moments of inertia, and torsional moment of inertia with respect to geometrical parameters of components are derived in the MMC framework, respectively. To demonstrate the effectiveness and accuracy of this method, numerical examples are given to consider the torsional, the bending, and the combined conditions, respectively. By post-process, the obtained thin-walled features can be further transformed into stamping sheets. PubDate: 2021-01-07
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